Abstract

X-ray grating interferometry, which has been spotlighted in the last decade as a multi-modal X-ray imaging technique, can provide three independent images, i.e., absorption, differential-phase, and visibility-contrast images. We report on a cause of the visibility contrast, an effect of insufficient temporal coherence, that can be observed when continuous-spectrum X-rays are used. This effect occurs even for a sample without unresolvable random structures, which are known as the main causes of visibility contrast. We performed an experiment using an acrylic cylinder and quantitatively explained the visibility contrast due to this effect.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

For the last decade, X-ray grating interferometry [162], which is an X-ray phase-contrast imaging technique [6365], has attracted increasing attention because it works even with continuous-spectrum X-rays from a low-brilliance laboratory source. One of the advantages of this sort of interferometry is its multi-modality: it can provide three independent images i.e., transmittance, differential-phase, and visibility-contrast [7, 12, 1417, 1921, 2634, 3644, 4660] images. The third modality was first reported by Pfeiffer et al. [7] as a dark-field contrast, and the visibility contrast due to unresolvable random structures (typically of the order of µm), arising from ultra-small-angle X-ray scattering, was quantitatively explained [19].

So far, several other causes of visibility contrast have been reported for monochromatic [36, 55, 57, 58] and continuous-spectrum [56, 59] X-rays. For monochromatic X-rays, it was found that the effects of more than first-order differential phase [36, 58] and unresolvable sharp edges [55] can cause visibility contrast. For continuous-spectrum X-rays, even a uniform sample can cause the visibility contrast due to the so-called beam-hardening effect [56, 59].

In this paper, we report another cause of the visibility contrast, i.e., the effect of insufficient temporal coherence. This effect occurs when continuous-spectrum X-rays are largely refracted. In the next section, the effect of insufficient temporal coherence on the visibility contrast is theoretically described. In Section 3, we show the results of an experiment using a low-temporal-coherence X-ray beam that demonstrates the effect occurs. In Section 4, we will discuss the potential applications of the effect.

2. Effect of temporal coherence

A typical experimental setup of X-ray grating interferometry is shown in Fig. 1. X-ray grating interferometry uses a self-imaging phenomenon called the Talbot effect [66, 67]. In the figure, a grating (G1) is illuminated by partially spatially coherent X-rays, so that self-images of G1 are generated downstream of it. When a sample is located in front of or behind the grating, it refracts the X-rays, so that the self-image becomes deformed. From this deformation, an image called a differential-phase image can be obtained, and the deformation is often detected as a deformation of moiré fringes arising from overlaying the second grating (G2; an absorption grating). Besides the differential phase image, two other images, called transmittance and visibility-contrast images, can be formed from the average intensity and the visibility of the moiré fringes.

 figure: Fig. 1

Fig. 1 Typical experimental setup of millisecond-order X-ray tomography (side view).

Download Full Size | PPT Slide | PDF

To discuss the effect of insufficient temporal coherence on the visibility of the self-image, which determines the visibility of the moiré fringes, we briefly review how the self-image is described mathematically. We consider a case where an X-ray grating interferometer with two gratings G1 and G2 (an X-ray Talbot interferometer) is constructed around the optical axis (the z-axis), as shown in Fig. 1. Here, G1 is a one-dimensional grating with a pitch of d1, the lines of which are aligned parallel and perpendicular to the y and z axes, respectively. First, we assume that G1 is illuminated by perfectly spatially coherent X-rays from an infinitely small source at a distance of R1 upstream from G1. The electric field EG1 for monochromatic X-rays immediately behind G1 is expressed as

EG1(x1,y1)=E1nTn(x1)
=E1nanexp(2πinx1d1),
where the x1y1 plane is defined on G1 perpendicular to the z-axis, E1 is the electric field just in front of G1, Tn is the amplitude (complex) transmission function of G1 for the nth diffraction order, given by
Tn(x1)anexp(2πinx1d1)
and an is the nth Fourier coefficient of the complex transmission function of G1. The electric field Eself of the self-image generated at a distance of z12 downstream of G1 for monochromatic X-rays with a wavelength λ can be expressed in the paraxial approximation as
Eself(x2,y2)E2nanexp(2πinx2d2),
where
E2E1exp[2πiz12λ]R1R2,
ananexp(n2πiλz12d1d2),
R2R1 + z12, and d2 = d1(R2/R1), corresponding to the pitch of the self-image of G1 with a compression ratio of 1. Here, the x2y2 plane is defined on the self-image parallel to the x1y1 plane such that it satisfies (x2,y2)=R2R1(x1,y1), and we have assumed that d1λ for the Talbot effect to occur. The intensity Iself,0 of the self-image for the infinitely small X-ray source is thus expressed as
Iself,0(x2,y2)I2nbnexp(2πinx2d2),
where
I2|E1|2R22R12,
and
bn=nan+nan*exp[πi((n+n)2n2)z12d1d2].

For considering the effect of partial coherence of X-rays, we interpret Eq. (4) in geometrical wave optics as follows. We rewrite Eq. (4) into

Eself(x2,y2)=E2nanexp(n2πiλz12d1d2)exp(2πinx1d1)exp(n22πiλz12d1d2),
=E2nanexp(n2πiλz12d1d2)exp(2πin(x1nλz12d2)d1),
=E2nanexp(nπiΔθnz12d1)exp(2πin(x1Δθnz12)d1),
=E2nanexp(2πinΔxn2d1)exp(2πin(x1Δxn)d1)
Here, we used x2/d2 = x1/d1, and defined Δθn and Δxn by
Δθnnλd2,
Δxnz12Δθn.
Equation (13) can be more simply rewritten by
Eself(x2,y2)=E2nTn(x1Δxn)exp(2πiΔl2λ),
where
ΔlnnΔxnλ2d1.
Noted that Δθn corresponds to an angle geometrically given by z12 and Δxn, as shown in Fig. 2(a).

 figure: Fig. 2

Fig. 2 Schematic illustration of geometrical-optics interpretation of the Talbot effect for monochromatic X-rays (a) without and (b) with a sample. Without a sample, the electric field at a distance z12 downstream of G1 is formed from the interference of the waves passing through the points Pn on G1 (n = 0, ±1, ±2, ⋯), where Pn is separated at a distance of Δxn from P0. Here, Δln is the optical path difference between the nth and 0th order, and Δθn is geometrically defined by Δxn and z12. With a sample, an additional optical path s,n is introduced into the nth order by the refraction of the sample.

Download Full Size | PPT Slide | PDF

Equation (16) allows for the Talbot effect to be incorporated in the interpretation of geometrical wave optics: the nth-order diffracted wave propagates along the path passing through the point Pn shown in Fig. 2(a) and Eself is formed from the interference of all the diffraction orders. In fact, Tn (x1 − Δxn) corresponds to the complex transmission function of the nth order at Pn, and the optical path difference between the nth and the 0th orders, passing through the points Pn and P0, respectively, is approximately given by

(R12+Δxn2+z122+Δxn2)(R1+z12)Δxn22(1R1+1z12),
=Δxn22R1+z12R11z12,
=Δxn2d1d2Δxnz12,
=Δxn2d1(nλ),
which corresponds to Δln in Eq. (16). We used R1, z12 ≫ Δxn in Eqs. (18) and R2/R1 = d2/d1 from Eq. (19) to Eq. (20).

Note that, using the Talbot order p defined such that it satisfies

z12=pd1d2λ,
Δxn is simply given by
Δxn=npd1.
For convenience in the following description, we define an as
ananexp(2πinΔxnd1),
by which Eself can be expressed as
Eself(x2,y2)=E2nanexp(2πiΔlnλ)exp(2πinxnd1).

Next, we consider a case where G1 is illuminated by X-rays with a continuous spectrum from a chaotic X-ray source with a finite size. By defining the X0Y0 coordinate on a plane including the X-ray source such that it satisfies (X0, Y0) = (x2, y2), we can express the intensity Iself of the self-image as

Iself(x2,y2)Iself,0(x2,y2;X0,Y0;ν)dX0dY0dν,
where νc/λ (c : the velocity of light) and Iself,0 (x2, y2; X0,Y0; ν) is the intensity of the self-image at (x2, y2) generated by a point source at (X0, Y0). From Eq. (7), the intensity can be written in the following form:
Iself(x2,y2)nexp(2πinx2d2)μn(ν)bn(ν)dν,
where
μn(ν)I2(x2,y2;X0,Y0;ν)exp(2πiX0ΔxnR1λ)dX0dY0,
Here, I2(x2, y2; X0, Y0; ν) is the contribution from a point source at (X0, Y0) to the intensity at (x2, y2) without G1. For simplicity, we assume that the spectrum of X-rays is independent of (X0, Y0) (the condition of the so-called cross-spectral purity [68] is satisfied). In this case, I2(x2, y2; X0, Y0; ν) can be expressed by
I2(x2,y2;X0,Y0,ν)=S(ν)I^2(x2,y2;X0,Y0),
where S(ν) is the spectrum of the X-ray source and I^2(x2,y2;X0,Y0) is the normalized intensity that satisfies I^2(x2,y2;X0,Y0)dX0dY0=1. Substituting Eq. (29) into Eq. (28)Iself(x2, y2) can be expressed as
Iself(x2,y2)nμ^nexp(2πinx2d2)S(ν)bn(ν)dν,
where
μ^nI^2(x2,y2;X0,Y0)exp(2πiX0ΔxnR1λ)dX0dY0,
corresponding to a complex coherence factor [68, 69] at two point separated by Δxn on G1. Equation (31) is equivalent to the van-Cittert-Zernike theorem for the X-ray source with a finite size. Note that, because Δxn is proportional to λ, μ^n is independent of ν. In addition, in the paraxial approximation, μ^n is independent of (x2, y2) when the size of the X-ray source is sufficiently smaller than R1.

Equation (30) can be related to the Wiener-Khintchine’s theorem as follows. From Eqs. (7) and (25), bn (ν) can be rewritten as

bn(ν)=nan+n(ν)a*n(ν)exp[2πiν(τn+nτn)],
where
τnΔln/c.
Substituting Eq. (32) into Eq. (30), we obtain
Iself(x2,y2)nμ^nexp(2πinx2d2)
×nS(ν)an+n(ν)an*(ν)exp[2πiν(τn+nτn)]dν,
and, we finally obtain
Iself(x2,y2)nμ^nexp(2πinx2d2)[nγ^n+n,n(Δτn+n,n)Sn+n,n],
where
Δτn+n,nτn+nτn,
γ^n+n,n(τ)Tν[S(ν)an+n(ν)an*(ν)]S(ν)an+n(ν)an*(ν)dν,
 
and
Sn+n,nS(ν)an+n(ν)an*(ν)dν.
Here, Tν express the Fourier transform with respect to ν.

The factor γ^n+n,n(Δτn+n,n) in Eq. (36) corresponds to the Wiener-Khintchine’s theorem, i.e., it represents the effect of temporal coherence for the n′ + n and n′ orders, and μ^nγ^n+n,n(Δτn+n,n) corresponds to the complex coherence factor for the n′ + n and n′ orders. It should be noted that, for monochromatic (more precisely, quasi-monochromatic [69]) X-rays with a frequency of ν0 illuminating G1 with a perfect temporal coherence, S(ν) = S(ν0)δ(νν0) and

γ^n+n,n(Δτn+n,n)=exp[2πiν0(Δτn+n,n)].
As a result, we only have to take the effect of the spatial coherence of the X-rays on G1 into account:
Iself(x2,y2)S(ν0)nμ^nbn(ν0)exp(2πinx2d2).
When the width of the spectrum of S(ν)an+n(ν)an*(ν) increases, |γ^n+n,n| decreases, and the visibility of the self-image therefore decreases. However, this reduction in visibility is not large even for a broad spectrum because, for the Talbot effect to occur, d1λ, and τn+nτn for a small n is very small. This means that an X-ray beam with a wide energy bandwidth is available for the Talbot effect to be observed.

The visibility V of the self-image, which is normally obtained with a fringe scanning method [7072] or a Fourier transform method [73], is given by the 0th- and 1st-order Fourier components of Iself(x2, y2):

V=μ^1[nγ^n+1,n(Δτn+1,n)Sn+1,n]μ^0[nγ^n,n(0)Sn,n],
=μ^1[nγ^n+1,n(Δτn+1,n)Sn+1,n]nSn,n.
Here, we used μ^0=1 and γ^n,n(0)=1. Especially when a π/2 phase grating with a duty cycle of 0.5 is used, Eq. (44) can be further simplified into
V=μ^1[γ^1,0(Δτ1,0)S1,0]nSn,n,
where ℜ[z] represents the real part of a complex number z.

Finally, we consider the effect of a sample. We define Rs to be the distance of the sample from the X-ray source and (xs, ys) to be a coordinate on the sample such that (xs,ys)=RsR1(x1,y1), as shown in Fig. 1. For X-rays passing through the sample, Tn (x1 − Δxn) in Eq. (16) is replaced with

Tn(x1Δxn)exp(2πiΦ^n(x1,y1,ν),
where
Φ^n(x1,y1,ν)Φ^(xsnpsd1,ys,ν),
={Φ^(RsR1(x1Δxn),RsR1y1,ν)(0<RsR1)Φ^(RsR1x1R2RsR2R1Δxn,RsR1y1,ν)(R1RsR2)
Here, ps is the effective Talbot order for the sample, defined by
ps{pRsR1(0<RsR1)pR2RsR2R1(R1RsR2),
exp[2πiΦ^(xs,ys,ν)] represents the transmittance of the sample, and the real and imaginary parts of Φ^(xs,ys,ν) represent the effects of the phase shift and absorption caused by the sample, respectively. From Eq. (46)an in Eq. (24) is replaced by
anexp(2πiΦ^n(x1,y1,ν)).
For simplicity, we neglect the imaginary part of Φ^(xs,ys,ν) for a while. Expressing Φ^(xs,ys,ν) by
Φ^n(xs,ys,ν)=Φ^n(xs,ys,ν0)(νν0+Cn(xs,ys,ν)),
where ν0 is a frequency around the center of the spectrum of nμ^nexp(2πinx2d2)S(ν)bn(ν) in Eq. (30), Eq. (35) can be rewritten in the following form:
Iself(x2,y2)nμ^nexp(2πinx2d2)
×nS(ν)an+n(ν)an*
×exp[2πi(Φ^n+n(ν0)Cn+n(ν)Φ^n(ν0)Cn(ν))]
×exp[2πiν(Δτn+n,n+Δτs,n+n,n)]dν,
where
τs,n=Φ^n(ν0)ν0,
Δτs,n+n,nτs,n+nτs,n.
Here, we omitted the dependence of Φ^n(ν) and Cn(ν) on the coordinate (xs, ys). Hence, we obtain the intensity of the self-image with the sample:
Iself(x2,y2)nμ^nexp(2πinx2d2)[nγ^n+n,n(Δτn+n,n+Δτs,n+n,n)Sn+n,n],
where
γ^n+n,n(τ)Tν[S(ν)an+n(ν)an*(ν)exp[2πi(Φ^n+n(ν0)Cn+n(ν)Φ^n(ν0)Cn(ν))]]S(ν)an+n(ν)an*(ν)exp[2πi(Φ^n+n(ν0)Cn+n(ν)Φ^n(ν0)Cn(ν))]dν,
and
Sn+n,nS(ν)an+n(ν)an*(ν)exp[2πi(Φ^n+n(ν0)Cn+n(ν)Φ^n(ν0)Cn(ν))]dν.
The visibility Vs with the sample is thus expressed as
Vs=μ^1[nγ^n+1,n(Δτn+1,n+Δτs,n+1,n)Sn+1,n]nSn,n.
The normalized visibility Vs/V, which is the visibility with the sample divided by that without the sample, is given by
VsV=nSn,nnSn,nnγ^n+1,n(Δτn+1,n+Δτs,n+1,n)Sn+1,nnγ^n+1,n(Δτn+1,n)Sn+1,n
For a π/2 phase grating, we have
Vs=μ^1[S1,0γ^1,0(Δτ1,0+Δτs,1,0)+S0,1γ^0,1(Δτ0,1+Δτs,0,1)]nSn,n,
VsV=nSn,nnSn,nS1,0γ^1,0(Δτ0,1+Δτs,0,1)+S0,1γ^0,1(Δτ1,1+Δτs,1,1)S1,0γ^1,0(Δτ0,1)+S0,1γ^0,1(Δτ1,1).

Comparing Eqs. (61) and (63) with Eqs. (44) and (45), we find that Sn+n,n and γ^n+n,n in Eqs. (44) and (45) are replaced by Sn+n,n and γ^n+n,n in Eqs. (61) and (63) and that an additional term Δτs,n+1,n is added to Δτn+1,n in the argument of γ^n+n,n. The replacements of Sn+n,n and γ^n+n,n into Sn+n,n and γ^n+n,n are due to the change in spectral phase when the sample is inserted, while the additional term Δτs,n+n,n comes from the additional path difference s,n introduced when X-rays are refracted, as shown in Fig. 2(b). The change in the spectrum only slightly affects the temporal coherence, or rather makes the temporal coherence length longer for a large Φ^n+n(ν0)Cn+n(ν)Φ^n(ν0)Cn in Eq. (59), so that it may not reduce the visibility of the self-image. On the other hand, the term Δτs,n,1 can reduce the visibility because it makes the temporal coherence length that is necessary for the Talbot effect to occur longer. Thus, a large refraction by a sample can cause a reduction in the visibility of the self-image due to insufficient temporal coherence.

Note that, when G2 overlays the self-image to generate moiré fringes, the spectrum behind G2 changes. As a result, S(ν) in Eqs. (62) and (64) should be replaced with

S(ν)c1(ν),
where cn(ν) is the nth-order Fourier component of the intensity transmission function of G2. Furthermore, when we further take into consideration the absorptions by the air, the sample, the substrates of G1 and G2, and other optical components such as filters, together with the detection efficiency of the detector, Φ^n(ν) is replaced with [Φ^n(ν)] and S(ν) is replaced with
S(ν)c1α(ν)ϵ(ν)exp[4πJ[Φ^n(ν)]],
where α(ν) represents the absorptions, ϵ(ν) is the detection efficiency, and J[z] represents the imaginary part of a complex number z.

3. Experiment

The experimental setup by which we observed the effect of insufficient temporal coherence on the visibility contrast is shown in Fig. 3. We constructed an X-ray grating interferometer with two gratings G1 and G2 (an X-ray Talbot interferometer) at BL28B2, SPring-8, Japan, where a white synchrotron X-ray beam from a bending magnet source is available. The size (standard deviation) of the X-ray source is 100 µm (horizontal) × 12.2 µm (vertical) [74]. A gold π/2-phase grating with a pitch of 5.3 µm for an X-ray energy of 25 keV was used as G1, and it was located 48.5 m downstream from the X-ray source. The lines of G1 were aligned in the horizontal direction in order to use the spatial coherence in the vertical direction, which is higher than that in the horizontal direction. A gold absorption grating with a pitch of 5.3 µm and a thickness of 70 µm was located at a distance of 283 mm downstream of G1, which corresponds to a Talbot order p of 0.5 for the energy of 25 keV. Both gratings were fabricated on 200-µm-thick Si substrates. An X-ray image detector consisting of a 40-µm-thick Ce:Gd3Al2Ga3O12 (GAGG) single crystal scintillator screen, lenses, and a CMOS camera (Photoron FASTCAM MiniAX100) with an effective pixel size of 5.2 µm was located just behind G2. The full width at half maximum (FWHM) of the line spread function of the detector, which mainly determined the spatial resolution of the interferometer, was estimated to be 20 µm from the experimentally obtained modulation transfer function.

 figure: Fig. 3

Fig. 3 Experimental setup for observing the effect of insufficient temporal coherence (side view).

Download Full Size | PPT Slide | PDF

An acrylonitrile butadiene styrene (ABS) cylinder with a diameter of 40 mm, height of 20 mm, and density of 1.18 g/cm3 was used as the sample, and the X-ray beam was incident on its top flat surface at a small absolute value of glancing angle θin, as shown in Fig. 3, so as to introduce a sufficiently large Δτs,1,0 and Δτs,0,−1 in Eq. (63) (a large differential phase 2πΦ^/xs) and heavily reduce the visibility of the self-image. The sample was located just in front of or/146 mm downstream of G1, corresponding to effective Talbot orders ps (defined in Eq. (49)) of 0.5 and 0.24 for the sample, and the glancing angle of the X-ray beam to the top flat surface of the cylinder was changed while the axis of the cylinder was kept in the vertical plane including the optical axis.

4. Results

The three images in Fig. 4 are examples of 4(b) the transmittance, 4(c) moiré-phase, and 4(d) normalized visibility images in an area consisting of 600 × 400 pixels (in the square in 4(a)) obtained for the moiré image with the sample located in front of G1 (ps = 0.5). Here, θin was fixed at −0.95°. A Fourier transform method was used to obtain the three images from moiré images with and without the sample. Each of the moiré images was captured with an exposure time of 25 µs. The middle area in the three images corresponds to the top flat surface with a small |θin| (a large constant value of |2πΦ^/xs|). It can be seen in Fig. 4(d) that the normalized visibility is reduced by a large |2πΦ^/xs|.

 figure: Fig. 4

Fig. 4 Examples of (b) transmittance, (c) moiré-phase (proportional to psd1Φ^/xs), and (d) normalized visibility images at a glancing angle θin of −0.95° in an area of 600 × 400 pixels (the square in Fig. 4(a)). Gray scales: (b)0-1.2, (c)-5.78-0.5, (c)0-1.2.

Download Full Size | PPT Slide | PDF

The filled circles in Fig. 5 show the experimentally obtained θin-dependences of 5(a) the unwrapped moiré-phase and 5(b) normalized visibility averaged along the horizontal middle lines passing through the center of the top surface (see the dashed lines in Figs. 4(c) and 4(d)) for ps = 0.5. In Fig. 5(b), the normalized visibility drastically changes depending on θin. This behavior of the normalized visibility can be qualitatively explained by the insufficient temporal coherence: a smaller |θin| (a larger |2πΦ^/xs|) causes a longer s,1 in Fig. 2 (b), which makes the temporal coherence length for the Talbot effect to occur longer, and hence, for a given temporal coherence, the visibility of the self-image decreases. It should be noted that, because the thickness of the sample (20 mm/cos(θin )) was almost constant in this range of θin, the reduction in visibility can not be explained by the beam hardening effect reported in a previous paper [56] or unresolvable random structures. In addition, the reduced visibility is not due to the total external reflection by the top flat surface, because the visibility decreases even for a negative θin. Furthermore, the observed reduced visibility is not due to the effect of unresolvable sharp edges, which occurs even for monochromatic X-rays as reported in a previous paper [55], since |2πΦ^/xs| is constant (resolvable) within the spatial resolution of the detector.

 figure: Fig. 5

Fig. 5 θin-dependences of (a) the unwrapped moiré-phase and (b) normalized visibility averaged along the horizontal middle lines passing through the center of the top surface (the dashed lines in Fig. 4(c) and 4(d)) for ps = 0.5.

Download Full Size | PPT Slide | PDF

The solid lines in Figs. 5(a) and 5(b) are results of the simulation based on the theoretical formulation described in Section 2. In the simulation, we used the on-axis spectrum of the incident X-ray beam calculated by SPECTRA [75]. In addition, we took into account the absorptions by the sample, the two gratings and their substrates, and the air, and assumed that the number of scintillation photons detected by the CMOS camera is proportional to the energy of X-rays absorbed by the scintillator screen, but that the K-fluorescent X-rays from Gd in the screen escape. We also assumed a constant background level for the captured moiré images for parasitic X-ray scattering. The simulation results are in good agreement with the experimentally obtained ones, which that our formulation for the normalized visibility is correct even for a large indicates |2πΦ^/xs|.

Figure 6 shows the θin-dependences of 6(a) the unwrapped moiré-phase and 6(b) normalized visibility averaged along the middle lines for ps = 0.24. Similar to the result for ps = 0.5, the normalized visibility drastically changes depending on θin, but the width of the region where the reduced visibility is observed is about half of that for ps = 0.5. This narrower width can be simply explained from Fig. 2(b) or Eqs. (47), (49), (56), (57), and (61): because the additional path difference s,n due to the refraction by the sample is proportional to ps, |2πΦ^/xs| at |θin| for ps = 0.5 induces almost the same effect on the visibility as about twice of |2πΦ^/xs| (i.e., the differential phase at half of |θin|) for ps = 0.24. The simulation results for ps = 0./24 ((solid curves in Figs. 6(a) and 6(b))) also matched the experimental ones. Thus, insufficient temporal coherence well explained the experimentally observed reduction in the visibility.

 figure: Fig. 6

Fig. 6 θin-dependences of (a) the unwrapped moiré-phase and (b) normalized visibility averaged along the horizontal middle lines passing through the center of the top surface for ps = 0.24.

Download Full Size | PPT Slide | PDF

5. Discussion

As described in Section 4, we experimentally showed that insufficient temporal coherence reduces the normalized visibility of the moiré fringes obtained in X-ray grating interferometry. We explained the reduced visibility in terms of an additional temporal coherence length s,n (see Fig. 2(b)) that is necessary for the Talbot effect to occur. In fact, it can also be explained qualitatively in terms of spectral dispersion. The angle of deflection caused by refraction by a sample is inversely proportional to the frequency ν of X-rays. A large angle of deflection drastically shifts a large moiré phase, which is also inversely proportional to ν, and even phase wrapping in the ν space occurs. As a result, the visibility of the moiré fringes integrated in the ν space decreases. The experimental result for an effective Talbot order ps of 0.24 (see Fig. 6(b)) can also be qualitatively explained by the ν-dependence of the moiré-phase shift: because a smaller ps induces a smaller moiré-phase shift, a larger refraction is necessary to observe the reduced visibility. We formulated in this paper the relation between the reduced visibility and temporal coherence and showed that the reduced visibility can be even quantitatively explained. This formulation may lead to a method to quantitatively determine the temporal coherence length of X-rays.

It may also be possible to perform X-ray imaging using the reduced visibility for a large refraction. In X-ray grating interferometry, it is normally assumed that the moiré-phase shift ΔP by a sample is linearly proportional to the differential phase 2πΦ^/xs, but, in a previous paper [62], we showed a criterion that defines the range within which this linearity fails:

|ΔP|>π2ν0Δν,
where Δν is the band width of the spectrum detected by the detector. This means that quantitative phase imaging, which is essential for quantitative tomographic reconstruction, is not possible for a sample giving a large |ΔP|. By using the |2πΦ^/xs|-dependence of not only the moiré-phase shift but also the reduced visibility, as shown in Figs. 5 and 6, it may be possible to quantitatively determine a large differential phase even when a continuous-spectrum X-ray source with a wide bandwidth is used.

6. Conclusion

We reported on a cause of reduced visibility in X-ray grating interferometry, the effect of insufficient temporal coherence, which can be observed when continuous-spectrum X-rays are used. We theoretically showed that insufficient temporal coherence reduces the visibility of the self-image in X-ray grating interferometry (Section 2). The results of an experiment using a white X-ray beam and an ABS cylinder with a diameter of 40 mm and a height of 20 mm as a sample were consistent with our theoretical description and showed that the reduced visibility evident in Figs. 46 is caused by insufficient temporal coherence when X-rays are largely refracted, and not due to the other known causes such as unresolvable random structures, the beam-hardening effect, or total external reflection (Section 3). Thus, we concluded that insufficient temporal coherence is a cause of the reduced visibility in X-ray grating interferometry.

In the experiment, we used a white synchrotron X-ray beam, but this phenomenon can also occur in the X-ray grating interferometry using a laboratory source with a continuous spectrum for clinical investigations and non-destructive inspections and in the neutron grating interferometry [7691] with a continuous spectrum integrated to increase the neutron flux used for obtaining images. We have to carefully interpret the moiré-phase shift and visibility contrast especially for quantitative phase imaging in tomographic reconstruction.

Acknowledgments

The experiment was performed at SPring-8 (proposal numbers: 2017A). This research was partly supported by a grant from the Japan Society for the Promotion of Science (JSPS KAKENHI Grant Number JP15H03590).

References and links

1. C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002). [CrossRef]  

2. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003). [CrossRef]  

3. T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005). [CrossRef]  

4. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005). [CrossRef]   [PubMed]  

5. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006). [CrossRef]  

6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006). [CrossRef]  

7. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008). [CrossRef]  

8. W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008). [CrossRef]  

9. A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008). [CrossRef]  

10. A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009). [CrossRef]  

11. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009). [CrossRef]   [PubMed]  

12. Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009). [CrossRef]  

13. W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009). [CrossRef]   [PubMed]  

14. M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010). [CrossRef]   [PubMed]  

15. A. F. Stein, J. Ilavsky, R. Kopace, E. E. Bennett, and H. Wen, “Selective imaging of nano-particle contrast agents by a single-shot x-ray diffraction technique,” Opt. Express 18, 13271–13278 (2010). [CrossRef]   [PubMed]  

16. G.-H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010). [CrossRef]   [PubMed]  

17. T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010). [CrossRef]   [PubMed]  

18. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010). [CrossRef]  

19. W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010). [CrossRef]   [PubMed]  

20. M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010). [CrossRef]   [PubMed]  

21. T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010). [CrossRef]  

22. A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).

23. A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011). [CrossRef]   [PubMed]  

24. H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011). [CrossRef]  

25. A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011). [CrossRef]  

26. S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W.-K. Lee, N. Y. Morgan, and H. H. Wen, “Interpretation of dark-field contrast and particle-size selectivity in grating interferometers,” Appl. Opt. 50, 4310–4319 (2011). [CrossRef]   [PubMed]  

27. V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011). [CrossRef]  

28. W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011). [CrossRef]  

29. M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011). [CrossRef]  

30. W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011). [CrossRef]  

31. P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012). [CrossRef]   [PubMed]  

32. W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012). [CrossRef]  

33. G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012). [CrossRef]   [PubMed]  

34. A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012). [CrossRef]  

35. S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012). [CrossRef]   [PubMed]  

36. Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012). [CrossRef]   [PubMed]  

37. V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012). [CrossRef]  

38. T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013). [CrossRef]   [PubMed]  

39. A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013). [CrossRef]   [PubMed]  

40. T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013). [CrossRef]   [PubMed]  

41. F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013). [CrossRef]  

42. F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013). [CrossRef]  

43. V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013). [CrossRef]  

44. F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013). [CrossRef]   [PubMed]  

45. M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013). [CrossRef]  

46. Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013). [CrossRef]   [PubMed]  

47. M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014). [CrossRef]  

48. F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014). [CrossRef]   [PubMed]  

49. A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014). [CrossRef]  

50. W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).

51. T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014). [CrossRef]  

52. P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014). [CrossRef]   [PubMed]  

53. P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014). [CrossRef]  

54. F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014). [CrossRef]   [PubMed]  

55. W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015). [CrossRef]   [PubMed]  

56. W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015). [CrossRef]   [PubMed]  

57. J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015). [CrossRef]  

58. T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016). [CrossRef]   [PubMed]  

59. G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016). [CrossRef]   [PubMed]  

60. Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017). [CrossRef]  

61. W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017). [CrossRef]  

62. W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017). [CrossRef]  

63. R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23–26 (2000). [CrossRef]  

64. A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005). [CrossRef]  

65. K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010). [CrossRef]  

66. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

67. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII (Elsevier, 1989). [CrossRef]  

68. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995). [CrossRef]  

69. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999). [CrossRef]  

70. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974). [CrossRef]   [PubMed]  

71. H. Schreiber and J. H. Bruning, Optical Shop Testing, D. Malacara, ed. (Wiley Interscience, 2007), Chap. 14

72. E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011). [CrossRef]   [PubMed]  

73. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-based Topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]  

74. http://www.spring8.or.jp/en/about_us/whats_sp8/facilities/accelerators/storage_ring/

75. T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001). [CrossRef]  

76. C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008). [CrossRef]   [PubMed]  

77. C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008). [CrossRef]  

78. M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008). [CrossRef]   [PubMed]  

79. S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009). [CrossRef]  

80. M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009). [CrossRef]  

81. I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010). [CrossRef]   [PubMed]  

82. S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011). [CrossRef]  

83. C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013). [CrossRef]  

84. S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013). [CrossRef]  

85. J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014). [CrossRef]  

86. F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014). [CrossRef]  

87. M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 7243 (2014). [CrossRef]   [PubMed]  

88. B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015). [CrossRef]  

89. F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015). [CrossRef]  

90. T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016). [CrossRef]  

91. Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017). [CrossRef]  

References

  • View by:

  1. C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
    [Crossref]
  2. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
    [Crossref]
  3. T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
    [Crossref]
  4. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
    [Crossref] [PubMed]
  5. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
    [Crossref]
  6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
    [Crossref]
  7. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
    [Crossref]
  8. W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
    [Crossref]
  9. A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
    [Crossref]
  10. A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
    [Crossref]
  11. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
    [Crossref] [PubMed]
  12. Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
    [Crossref]
  13. W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
    [Crossref] [PubMed]
  14. M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
    [Crossref] [PubMed]
  15. A. F. Stein, J. Ilavsky, R. Kopace, E. E. Bennett, and H. Wen, “Selective imaging of nano-particle contrast agents by a single-shot x-ray diffraction technique,” Opt. Express 18, 13271–13278 (2010).
    [Crossref] [PubMed]
  16. G.-H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
    [Crossref] [PubMed]
  17. T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
    [Crossref] [PubMed]
  18. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
    [Crossref]
  19. W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
    [Crossref] [PubMed]
  20. M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
    [Crossref] [PubMed]
  21. T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
    [Crossref]
  22. A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).
  23. A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
    [Crossref] [PubMed]
  24. H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
    [Crossref]
  25. A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
    [Crossref]
  26. S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W.-K. Lee, N. Y. Morgan, and H. H. Wen, “Interpretation of dark-field contrast and particle-size selectivity in grating interferometers,” Appl. Opt. 50, 4310–4319 (2011).
    [Crossref] [PubMed]
  27. V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
    [Crossref]
  28. W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
    [Crossref]
  29. M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
    [Crossref]
  30. W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
    [Crossref]
  31. P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
    [Crossref] [PubMed]
  32. W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012).
    [Crossref]
  33. G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
    [Crossref] [PubMed]
  34. A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
    [Crossref]
  35. S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012).
    [Crossref] [PubMed]
  36. Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012).
    [Crossref] [PubMed]
  37. V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
    [Crossref]
  38. T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
    [Crossref] [PubMed]
  39. A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
    [Crossref] [PubMed]
  40. T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
    [Crossref] [PubMed]
  41. F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
    [Crossref]
  42. F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
    [Crossref]
  43. V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
    [Crossref]
  44. F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
    [Crossref] [PubMed]
  45. M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
    [Crossref]
  46. Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013).
    [Crossref] [PubMed]
  47. M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
    [Crossref]
  48. F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
    [Crossref] [PubMed]
  49. A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
    [Crossref]
  50. W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).
  51. T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
    [Crossref]
  52. P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
    [Crossref] [PubMed]
  53. P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
    [Crossref]
  54. F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
    [Crossref] [PubMed]
  55. W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015).
    [Crossref] [PubMed]
  56. W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
    [Crossref] [PubMed]
  57. J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
    [Crossref]
  58. T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
    [Crossref] [PubMed]
  59. G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
    [Crossref] [PubMed]
  60. Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
    [Crossref]
  61. W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
    [Crossref]
  62. W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
    [Crossref]
  63. R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23–26 (2000).
    [Crossref]
  64. A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
    [Crossref]
  65. K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
    [Crossref]
  66. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
  67. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII (Elsevier, 1989).
    [Crossref]
  68. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).
    [Crossref]
  69. M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
    [Crossref]
  70. J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital Wavefront Measuring Interferometer for Testing Optical Surfaces and Lenses,” Appl. Opt. 13, 2693 (1974).
    [Crossref] [PubMed]
  71. H. Schreiber and J. H. Bruning, Optical Shop Testing, D. Malacara, ed. (Wiley Interscience, 2007), Chap. 14
  72. E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011).
    [Crossref] [PubMed]
  73. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-Transform Method of Fringe-Pattern Analysis for Computer-based Topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [Crossref]
  74. http://www.spring8.or.jp/en/about_us/whats_sp8/facilities/accelerators/storage_ring/
  75. T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001).
    [Crossref]
  76. C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
    [Crossref] [PubMed]
  77. C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
    [Crossref]
  78. M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
    [Crossref] [PubMed]
  79. S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
    [Crossref]
  80. M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
    [Crossref]
  81. I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
    [Crossref] [PubMed]
  82. S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
    [Crossref]
  83. C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
    [Crossref]
  84. S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
    [Crossref]
  85. J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
    [Crossref]
  86. F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
    [Crossref]
  87. M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 7243 (2014).
    [Crossref] [PubMed]
  88. B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
    [Crossref]
  89. F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
    [Crossref]
  90. T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
    [Crossref]
  91. Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
    [Crossref]

2017 (4)

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
[Crossref]

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

2016 (3)

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

2015 (5)

W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015).
[Crossref] [PubMed]

W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
[Crossref] [PubMed]

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

2014 (11)

J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
[Crossref]

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 7243 (2014).
[Crossref] [PubMed]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).

T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
[Crossref]

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

2013 (11)

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013).
[Crossref] [PubMed]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

2012 (7)

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012).
[Crossref]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
[Crossref]

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012).
[Crossref] [PubMed]

Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012).
[Crossref] [PubMed]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

2011 (10)

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W.-K. Lee, N. Y. Morgan, and H. H. Wen, “Interpretation of dark-field contrast and particle-size selectivity in grating interferometers,” Appl. Opt. 50, 4310–4319 (2011).
[Crossref] [PubMed]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011).
[Crossref] [PubMed]

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
[Crossref]

2010 (10)

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[Crossref]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

A. F. Stein, J. Ilavsky, R. Kopace, E. E. Bennett, and H. Wen, “Selective imaging of nano-particle contrast agents by a single-shot x-ray diffraction technique,” Opt. Express 18, 13271–13278 (2010).
[Crossref] [PubMed]

G.-H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

2009 (6)

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[Crossref] [PubMed]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

2008 (6)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

2006 (2)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

2005 (3)

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

2002 (1)

C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

2001 (1)

T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001).
[Crossref]

2000 (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

1982 (1)

1974 (1)

1836 (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Abis, M.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

Achterhold, K.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Ahn, C. W.

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Albrecht, F.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Anton, G.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Arif, M.

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

Auweter, S.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Auxier, J.

Bamberg, F.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Banhart, J.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Bao, Y.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Bauer, J. S.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

Baum, T.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

Bayer, F.

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Bayer, F. L.

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

Bech, M.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012).
[Crossref]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

Beckmann, M. W.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Behr, G.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Bellotti, R.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

Bennett, E. E.

Betz, B.

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Bevins, N.

Biernath, T.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Bohla, A.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Böni, Peter

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Brangaccio, D. J.

Bravin, A.

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

Brendel, C.

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

Bruning, J. H.

Bunk, O.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

Burke, J.

E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011).
[Crossref] [PubMed]

Chabior, M.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

Chen, G.-H.

Chen, Z.-Q.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Cheng, X.

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

Cho, G.

J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
[Crossref]

Cloetens, P.

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Cong, W.

David, C.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Dawson, M.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

De Caro, L.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

Deyhle, H.

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Di Bella, C.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Diaz, A.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Diemoz, P. C.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Dierolf, M.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Dommann, A.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

Donath, T.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

Duc, G. Le

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

Durst, J.

Dürst, J.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Ebrahimi, O.

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

Eggl, E.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

Eichholz, J. A.

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

Eickelberg, O.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Endrizzi, M.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Farago, T.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Fasching, P. A.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Feidenhans’l, R.

T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
[Crossref]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Fiederle, M.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Fitzgerald, R.

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

Fratzl, P.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Frei, G.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Fukui, R.

Gallagher, J. E.

Gao, K.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Garcia, E. G.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

Gasser, U.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Gibmeier, J.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

Gifford, M.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Griffa, M.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Grünzweig, C.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Guzenko, V. A.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

Haas, W.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Hack, E.

E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011).
[Crossref] [PubMed]

Hahn, D.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Han, W.

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

Harasse, S.

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

Harti, R. P.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

Hartmann, A.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

Hentschel, M.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Herriott, D. R.

Herzen, J.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Hilger, A.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

Horisberger, M.

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

Horn, F.

Hovind, J.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

Hu, R.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Hu, S.

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

Huang, Z.-F.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Hussey, D. S.

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

Ilavsky, J.

Ina, H.

Ishikawa, T.

Jacobson, D. L.

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

Jefimovs, K.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Jensen, T. H.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

Jerjen, I.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

Jiang, M.

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Jones, J. L.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Jun, Y. K.

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
[Crossref]

Kaestner, A.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Kagias, M.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

Kajiwara, K.

W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
[Crossref]

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

Kang, K.-J.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Kardjilov, N.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

Kastner, J.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

Kato, H.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Kato, K.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Kaufmann, R.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Kawabara, K.

Kawabata, K.

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Keil, S.

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

Kemble, C. K.

Kenntner, J.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Kerschnitzki, M.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Kim, J.

J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
[Crossref]

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Kitamura, H.

T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001).
[Crossref]

Kiyanagi, Y.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Klaushofer, K.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Kobayashi, S.

Koenig, T.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Kohlbrecher, J.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Kohmura, Y.

Kopace, R.

Kopecek, J.

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Kottler, C.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Kreuer, S.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Kudo, H.

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

Kuhne, G.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Kühne, G.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Kunka, D.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Kupsch, A.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Kuwabara, H.

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

Kwon, O. Y.

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
[Crossref]

Lange, A.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Lasser, K. T.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

Lauridsen, E. M.

T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
[Crossref]

Lauridsen, T.

T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
[Crossref]

Lee, S. W.

J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
[Crossref]

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
[Crossref]

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

Lee, W.-K.

Lehmann, E.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Lejcek, P.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Loewen, R.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Louis, A. K.

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Lura, P.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Lüthi, T.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

Lynch, S. K.

Maier, A.

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

Maikusa, H.

Maisenbacher, J.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

Malecki, A.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
[Crossref]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).
[Crossref]

Manke, I.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

Matsuyama, S.

Meinel, F. G.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Meiser, J.

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

Meyer, P.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Michel, T.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

Millard, T. P.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Mizutani, H.

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

Modregger, P.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

Mohr, J.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Momose, A.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015).
[Crossref] [PubMed]

W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
[Crossref] [PubMed]

W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012).
[Crossref] [PubMed]

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).

Morgan, N. Y.

Mühlbauer, S.

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

Neels, A.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

Nikolaou, K.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Noda, D.

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
[Crossref]

Noël, P. B.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

Nöhammer, B.

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Nugent, K. A.

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[Crossref]

Olbinado, M. P.

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

Olivo, A.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Otake, Y.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Pai, V.

Parker, J. D.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Patorski, K.

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII (Elsevier, 1989).
[Crossref]

Pelzer, G.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Peter, S.

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

Pfeiffer, F.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
[Crossref]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012).
[Crossref]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Pinzer, B. R.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

Plank, B.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

Pofahl, S.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Potdevin, G.

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
[Crossref]

Prade, F.

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Qi, Z.

Radicke, M.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Rauh, C.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Reimann, T.

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

Reiser, M. F.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Revol, V.

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Reznikova, E.

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Rieger, J.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

Riess, C. P.

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

Ritter, A.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Robinson, I. K.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Ronnow, H. M. R.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Roschger, P.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Rosenfeld, D. P.

Ruth, R.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Rutishauser, S.

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Sadeghilaridjani, M.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Sarapata, A.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Scattarella, F.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

Schafer, R.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

Schäfer, R.

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Schaff, F.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

Schleede, S.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Schreiber, H.

H. Schreiber and J. H. Bruning, Optical Shop Testing, D. Malacara, ed. (Wiley Interscience, 2007), Chap. 14

Schroer, C.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

Schulz, M.

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

Schulz-Wendtland, R.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Schuster, M.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

Schüttler, M.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

Schütz, P.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

Schwab, F.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Seki, Y.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Sennhauser, U.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

Shao, Q.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Shinohara, T.

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

Sievers, P.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Sim, C. M.

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

Solak, H. H.

C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

Speller, R. D.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

Sperl, J. I.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

Stampanoni, M.

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013).
[Crossref] [PubMed]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Stein, A. F.

Straumann, U.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Strobl, M.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 7243 (2014).
[Crossref] [PubMed]

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

Suzuki, Y.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

Takeda, M.

Takeda, Y.

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[Crossref] [PubMed]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
[Crossref]

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).

Takeuchi, A.

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Tamasaku, K.

Tanaka, T.

T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001).
[Crossref]

Tang, X.

Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012).
[Crossref] [PubMed]

Tangaro, S.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

Terui, Y.

Tian, Y.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Trimborn, B.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Uder, M.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Ueda, R.

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

Urban, C.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Vagovic, P.

W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
[Crossref] [PubMed]

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

Van Swygenhoven, H.

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

Volk, T.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Wachter, D. L.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Wagermaier, W.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

Wandner, J.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

Wang, G.

W. Cong, F. Pfeiffer, M. Bech, and G. Wang, “X-ray dark-field imaging modeling,” J. Opt. Soc. Am. A 29, 908–912 (2012).
[Crossref]

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

Wang, S.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Wang, Y.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Wang, Z.

Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013).
[Crossref] [PubMed]

Wang, Z.-T.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

Wanner, A.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

Weber, T.

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

Weitkamp, T.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Wen, H.

Wen, H. H.

Wenkel, E.

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

White, A. D.

Willer, K.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).
[Crossref]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

Wolf, J.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

Xiao, X.

Yabashi, M.

Yamauchi, K.

Yamazaki, T.

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

Yang, F.

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Yang, Y.

Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012).
[Crossref] [PubMed]

Yaroshenko, A.

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

Yashiro, W.

W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
[Crossref]

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
[Crossref] [PubMed]

W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015).
[Crossref] [PubMed]

W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012).
[Crossref] [PubMed]

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
[Crossref] [PubMed]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
[Crossref]

W. Yashiro, Y. Takeda, and A. Momose, “Efficiency of Capturing a Phase Image using Cone-beam X-ray Talbot Interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).

Yildirim, A. Ö.

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Yokoyama, H.

Zabler, S.

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

Zambelli, J.

Zanette, I.

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

Zang, A.

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Zhou, T.

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Zhou, Y.

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

Zhu, P.

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Ziegler, E.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

Zuber, M.

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

Adv. Phys. (1)

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59, 1–99 (2010).
[Crossref]

Appl. Opt. (2)

Appl. Phys. A (1)

T. Lauridsen, E. M. Lauridsen, and R. Feidenhans’l, “Mapping misoriented fibers using X-ray dark field tomography,” Appl. Phys. A 115, 741–745 (2014).
[Crossref]

Appl. Phys. Express (4)

M. P. Olbinado, P. Vagovič, W. Yashiro, and A. Momose, “Demonstration of Stroboscopic X-ray Talbot Interferometry Using Polychromatic Synchrotron and Laboratory X-ray Sources,” Appl. Phys. Express 6, 096601 (2013).
[Crossref]

W. Yashiro, D. Noda, and K. Kajiwara, “Sub-10-ms X-ray tomography using a grating interferometer,” Appl. Phys. Express 10, 052501 (2017).
[Crossref]

H. Kuwabara, W. Yashiro, S. Harasse, H. Mizutani, and A. Momose, “Hard-X-ray Phase-Difference Microscopy with a Low-Brilliance Laboratory X-ray Source,” Appl. Phys. Express 4, 062502 (2011).
[Crossref]

A. Momose, H. Kuwabara, and W. Yashiro, “X-ray Phase Imaging Using Lau Effect,” Appl. Phys. Express 4, 066603 (2011).
[Crossref]

Appl. Phys. Lett. (7)

C. David, B. Nöhammer, and H. H. Solak, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[Crossref]

T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005).
[Crossref]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[Crossref]

P. Modregger, S. Rutishauser, J. Meiser, C. David, and M. Stampanoni, “Two-dimensional ultra-small angle X-ray scattering with grating interferometry,” Appl. Phys. Lett. 105, 024102 (2014).
[Crossref]

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett. 104, 024106 (2014).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kuhne, R. Schafer, S. Pofahl, H. M. R. Ronnow, and F. Pfeiffer, “Bulk magnetic domain structures visualized by neutron dark-field imaging,” Appl. Phys. Lett. 93, 112504 (2008).
[Crossref]

F. Yang, F. Prade, M. Griffa, I. Jerjen, C. Di Bella, J. Herzen, A. Sarapata, F. Pfeiffer, and P. Lura, “Dark-field X-ray imaging of unsaturated water transport in porous materials,” Appl. Phys. Lett. 105, 154105 (2014).
[Crossref]

Biol. Opt. Express (1)

J. Wolf, J. I. Sperl, F. Schaff, M. Schüttler, A. Yaroshenko, I. Zanette, J. Herzen, and F. Pfeiffer, “Lens-term- and edge-effect in X-ray grating interferometry,” Biol. Opt. Express 6, 4812–4824 (2015).
[Crossref]

EPL (3)

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, K. T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” EPL 105, 38002 (2014).
[Crossref]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” EPL 99, 48001 (2012).
[Crossref]

F. Prade, A. Yaroshenko, J. Herzen, and F. Pfeiffer, “Short-range order in mesoscale systems probed by X-ray grating interferometry,” EPL 112, 68002 (2015).
[Crossref]

J. Appl. Crystr. (1)

T. Reimann, S. Mühlbauer, M. Horisberger, B. Betz, Peter Böni, and M. Schulz, “The new neutron grating interferometer at the ANTARES beamline: design, principles and applications,” J. Appl. Crystr. 49, 1488–1500 (2016).
[Crossref]

J. Appl. Phys. (3)

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys. 110, 044912 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys. 112, 114903 (2012).
[Crossref]

J. Kor. Phys. Soc. (1)

S. W. Lee, Y. Zhou, T. Zhou, M. Jiang, J. Kim, C. W. Ahn, and A. K. Louis, “Visibility studies of grating-based neutron phase contrast and dark-field imaging by using partial coherence theory,” J. Kor. Phys. Soc. 63, 2093–2097 (2013).
[Crossref]

J. Korean Phys. Soc. (1)

S. W. Lee, Y. K. Jun, and O. Y. Kwon, “A Neutron Dark-field Imaging Experiment with a Neutron Grating Interferometer at a Thermal Neutron Beam Line at HANARO,” J. Korean Phys. Soc. 58, 730–734 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Phys. Soc. Jpn. (1)

Y. Seki, T. Shinohara, J. D. Parker, W. Yashiro, A. Momose, K. Kato, H. Kato, M. Sadeghilaridjani, Y. Otake, and Y. Kiyanagi, “Development of Multi-colored Neutron Talbot-Lau Interferometer with Absorption Grating Fabricated by Imprinting Method of Metallic Glass,” J. Phys. Soc. Jpn. 86, 044001 (2017).
[Crossref]

J. Synchrotron Rad. (1)

T. Tanaka and H. Kitamura, “SPECTRA: a synchrotron radiation calculation code,” J. Synchrotron Rad. 8, 1221–1228 (2001).
[Crossref]

Jpn. J. Appl. Phys. (7)

A. Momose, W. Yashiro, and Y. Takeda, “Sensitivity of X-ray Phase Imaging Based on Talbot Interferometry,” Jpn. J. Appl. Phys. 47, 8077–8080 (2008).
[Crossref]

A. Momose, W. Yashiro, H. Kuwabara, and K. Kawabata, “Grating-Based X-ray Phase Imaging Using Multiline X-ray Source,” Jpn. J. Appl. Phys. 48, 076512 (2009).
[Crossref]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-Ray Talbot interferometry,” Jpn. J. Appl. Phys. 42, L866–L868 (2003).
[Crossref]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45, 5254–5262 (2006).
[Crossref]

W. Yashiro and A. Momose, “Grazing-incidence ultra-small-angle X-ray scattering imaging with X-ray transmission gratings: A feasibility studey,” Jpn. J. Appl. Phys. 53, 05FH04 (2014).

W. Yashiro, R. Ueda, K. Kajiwara, D. Noda, and H. Kudo, “Sub-10-ms X-ray tomography using a grating interferometer,” Jpn. J. Appl. Phys. 56, 112503 (2017).
[Crossref]

A. Momose, “Recent advances in x-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

Med. Phys. (2)

G. Pelzer, G. Anton, F. Horn, J. Rieger, A. Ritter, J. Wandner, T. Weber, and T. Michel, “A beam hardening and dispersion correction for x-ray dark-field radiography,” Med. Phys. 43, 2774–2779 (2016).
[Crossref] [PubMed]

Y. Yang and X. Tang, “The second-order differential phase contrast and its retrieval for imaging with x-ray Talbot interferometry,” Med. Phys. 39, 7237–7253 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

I. Manke, N. Kardjilov, R. Schäfer, A. Hilger, M. Strobl, M. Dawson, C. Grünzweig, G. Behr, M. Hentschel, C. David, A. Kupsch, A. Lange, and J. Banhart, “Three-dimensional imaging of magnetic domains,” Nat. Commun. 1, 125 (2010).
[Crossref] [PubMed]

Nat. Mat. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mat. 7, 134–137 (2008).
[Crossref]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

NDT&E International (1)

V. Revol, B. Plank, R. Kaufmann, J. Kastner, C. Kottler, and A. Neels, “Laminate fibre structure characterisation of carbon fibre-reinforced polymers by X-ray scatter dark field imaging with a grating interferometer,” NDT&E International 58, 64–71 (2013).
[Crossref]

Nuc. Inst. Meth. A (2)

S. W. Lee, D. S. Hussey, D. L. Jacobson, C. M. Sim, and M. Arif, “Development of the grating phase neutron interferometer at a monochromatic beam line,” Nuc. Inst. Meth. A 605, 16–20 (2009).
[Crossref]

M. Strobl, A. Hilger, N. Kardjilov, O. Ebrahimi, S. Keil, and I. Manke, “Differential phase contrast and dark field neutron imaging,” Nuc. Inst. Meth. A 605, 9–12 (2009).
[Crossref]

Nucl. Instrum. Meth. A (1)

J. Kim, S. W. Lee, and G. Cho, “Visibility evaluation of a neutron grating interferometer operated with a polychromatic thermal neutron beam,” Nucl. Instrum. Meth. A 746, 26–32 (2014).
[Crossref]

Opt. Express (11)

T. Weber, G. Pelzer, F. Bayer, F. Horn, J. Rieger, A. Ritter, A. Zang, J. Durst, G. Anton, and T. Michel, “Increasing the darkfield contrast-to-noise ratio using a deconvolution-based information retrieval algorithm in X-ray grating-based phase-contrast imaging,” Opt. Express 21, 18011–18020 (2013).
[Crossref] [PubMed]

W. Yashiro and A. Momose, “Effects of unresolvable edges in grating-based X-ray differential phase imaging,” Opt. Express 23, 9233–9251 (2015).
[Crossref] [PubMed]

W. Yashiro, P. Vagovič, and A. Momose, “Effect of beam hardening on a visibility-contrast image obtained by X-ray grating interferometry,” Opt. Express 23, 23462–23471 (2015).
[Crossref] [PubMed]

F. Bayer, S. Zabler, C. Brendel, G. Pelzer, J. Rieger, A. Ritter, T. Weber, T. Michel, and G. Anton, “Projection angle dependence in grating-based X-ray dark-field imaging of ordered structures,” Opt. Express 21, 19923–19933 (2013).
[Crossref]

A. F. Stein, J. Ilavsky, R. Kopace, E. E. Bennett, and H. Wen, “Selective imaging of nano-particle contrast agents by a single-shot x-ray diffraction technique,” Opt. Express 18, 13271–13278 (2010).
[Crossref] [PubMed]

G.-H. Chen, N. Bevins, J. Zambelli, and Z. Qi, “Small-angle scattering computed tomography (SAS-CT) using a Talbot-Lau interferometer and a rotating anode x-ray tube: theory and experiments,” Opt. Express 18, 12960–12970 (2010).
[Crossref] [PubMed]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[Crossref] [PubMed]

A. Momose, W. Yashiro, S. Harasse, and H. Kuwabara, “Four-dimensional X-ray phase tomography with Talbot interferometry and white synchrotron radiation: dynamic observation of a living worm,” Opt. Express 19, 8423–8432 (2011).
[Crossref] [PubMed]

W. Yashiro, Y. Terui, K. Kawabara, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 16890–16901 (2010).
[Crossref] [PubMed]

S. Matsuyama, H. Yokoyama, R. Fukui, Y. Kohmura, K. Tamasaku, M. Yabashi, W. Yashiro, A. Momose, T. Ishikawa, and K. Yamauchi, “Wavefront measurement for a hard-X-ray nanobeam using single-grating interferometry,” Opt. Express 20, 24977 (2012).
[Crossref] [PubMed]

Philos. Mag. (1)

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Phys. Med. (1)

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. 29, 478–486 (2013).
[Crossref] [PubMed]

Phys. Med. Biol. (6)

T. Michel, J. Rieger, G. Anton, F. Bayer, M. W. Beckmann, J. Dürst, P. A. Fasching, W. Haas, A. Hartmann, G. Pelzer, M. Radicke, C. Rauh, A. Ritter, P. Sievers, R. Schulz-Wendtland, M. Uder, D. L. Wachter, T. Weber, E. Wenkel, and A. Zang, “On a dark-field signal generated by micrometer-sized calcifications in phase-contrast mammography,” Phys. Med. Biol. 58, 2713–2732 (2013).
[Crossref] [PubMed]

Z. Wang and M. Stampanoni, “Quantitative x-ray radiography using grating interferometry: a feasibility study,” Phys. Med. Biol. 58, 6815–6826 (2013).
[Crossref] [PubMed]

T. Koenig, M. Zuber, B. Trimborn, T. Farago, P. Meyer, D. Kunka, F. Albrecht, S. Kreuer, T. Volk, and M. Fiederle, “On the origin and nature of the grating interferometric dark-field contrast obtained with low-brilliance x-ray sources,” Phys. Med. Biol. 61, 3427 (2016).
[Crossref] [PubMed]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol. 57, 3451–3461 (2012).
[Crossref] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol. 55, 5529–5539 (2010).
[Crossref] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol. 55, 3317–3323 (2010).
[Crossref] [PubMed]

Phys. Rev. B (3)

T. H. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B 82, 214103 (2010).
[Crossref]

W. Yashiro, S. Harasse, K. Kawabata, H. Kuwabara, T. Yamazaki, and A. Momose, “Distribution of unresolvable anisotropic microstructures revealed in visibility-contrast images using x-ray Talbot interferometry,” Phys. Rev. B 84, 094106 (2011).
[Crossref]

C. Grünzweig, J. Kopecek, B. Betz, A. Kaestner, K. Jefimovs, J. Kohlbrecher, U. Gasser, O. Bunk, C. David, E. Lehmann, T. Donath, and F. Pfeiffer, “Quantification of the neutron dark-field imaging signal in grating interferometry,” Phys. Rev. B 88, 125104 (2013).
[Crossref]

Phys. Rev. Lett. (5)

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. M. R. Ronnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

M. Strobl, C. Grünzweig, A. Hilger, I. Manke, N. Kardjilov, C. David, and F. Pfeiffer, “Neutron Dark-Field Tomography,” Phys. Rev. Lett. 101, 123902 (2008).
[Crossref] [PubMed]

W. Yashiro, Y. Takeda, A. Takeuchi, Y. Suzuki, and A. Momose, “Hard-X-Ray Phase-Difference Microscopy Using a Fresnel Zone Plate and a Transmission Grating,” Phys. Rev. Lett. 103, 180801 (2009).
[Crossref] [PubMed]

P. Modregger, M. Kagias, S. Peter, M. Abis, V. A. Guzenko, C. David, and M. Stampanoni, “Multiple Scattering Tomography,” Phys. Rev. Lett. 113, 020801 (2014).
[Crossref] [PubMed]

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the Ultrasmall-Angle X-Ray Scattering Distribution with Grating Interferometry,” Phys. Rev. Lett. 108, 048101 (2012).
[Crossref] [PubMed]

Phys. Today (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

PLOS ONE (1)

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, E. G. Garcia, T. Baum, P. B. Noël, J. S. Bauer, and F. Pfeiffer, “Coherent Superposition in Grating-Based Directional Dark-Field Imaging,” PLOS ONE 8, e61268 (2013).
[Crossref] [PubMed]

PNAS (1)

F. L. Bayer, S. Hu, A. Maier, T. Weber, G. Anton, T. Michel, and C. P. Riess, “Reconstruction of scalar and vectorial components in X-ray dark-field tomography,” PNAS 111, 12699–12704 (2014).
[Crossref] [PubMed]

Radiat. Phys. Chem. (1)

Y. Bao, Q. Shao, R. Hu, S. Wang, K. Gao, Y. Wang, Y. Tian, and P. Zhu, “Effect of particle-size selectivity on quantitative X-ray dark-field computed tomography using a grating interferometer,” Radiat. Phys. Chem. 137260–263 (2017).
[Crossref]

Rev. Sci. Instr. (1)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instr. 81, 073709 (2010).
[Crossref]

Rev. Sci. Instrum. (2)

E. Hack and J. Burke, “Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms,” Rev. Sci. Instrum. 82, 061101 (2011).
[Crossref] [PubMed]

B. Betz, R. P. Harti, M. Strobl, J. Hovind, A. Kaestner, E. Lehmann, H. Van Swygenhoven, and C. Grünzweig, “Quantification of the sensitivity range in neutron dark-field imaging,” Rev. Sci. Instrum. 86, 123704 (2015).
[Crossref]

Sci. Rep. (2)

M. Strobl, “General solution for quantitative dark-field contrast imaging with grating interferometers,” Sci. Rep. 4, 7243 (2014).
[Crossref] [PubMed]

F. Schaff, A. Malecki, G. Potdevin, E. Eggl, P. B. Noël, T. Baum, E. G. Garcia, J. S. Bauer, and F. Pfeiffer, “Correlation of X-Ray Vector Radiography to Bone Micro-Architecture,” Sci. Rep. 4, 3695 (2014).
[Crossref] [PubMed]

Siam. J. Appl. Math. (1)

W. Han, J. A. Eichholz, X. Cheng, and G. Wang, “A Theoretical Framework of X-ray Dark-Field Tomograpy,” Siam. J. Appl. Math. 71, 1557–1577 (2011).
[Crossref]

Z. Med. Phys. (2)

M. Bech, T. H. Jensen, O. Bunk, T. Donath, C. David, T. Weitkamp, G. Le Duc, A. Bravin, and P. Cloetens, “Advanced contrast modalities for X-ray radiology: Phase-contrast and dark-field imaging using a grating interferometer,” Z. Med. Phys. 20, 7–16 (2010).
[Crossref] [PubMed]

F. Schwab, S. Schleede, D. Hahn, M. Bech, J. Herzen, S. Auweter, F. Bamberg, K. Achterhold, A. Ö. Yildirim, A. Bohla, O. Eickelberg, R. Loewen, M. Gifford, R. Ruth, M. F. Reiser, K. Nikolaou, F. Pfeiffer, and F. G. Meinel, “Comparison of contrast-to-noise ratios of transmission and dark-field signal in grating-based X-ray imaging for healthy murine lung tissue,” Z. Med. Phys. 23, 236–242 (2013).
[Crossref]

Other (6)

K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics XXVII (Elsevier, 1989).
[Crossref]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, (Cambridge University, 1995).
[Crossref]

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).
[Crossref]

A. Momose, W. Yashiro, and Y. Takeda, Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems, Y. Censor, M. Jiang, and G. Wang, eds. (Medical Physics Publishing, 2010).

http://www.spring8.or.jp/en/about_us/whats_sp8/facilities/accelerators/storage_ring/

H. Schreiber and J. H. Bruning, Optical Shop Testing, D. Malacara, ed. (Wiley Interscience, 2007), Chap. 14

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Typical experimental setup of millisecond-order X-ray tomography (side view).
Fig. 2
Fig. 2 Schematic illustration of geometrical-optics interpretation of the Talbot effect for monochromatic X-rays (a) without and (b) with a sample. Without a sample, the electric field at a distance z12 downstream of G1 is formed from the interference of the waves passing through the points P n on G1 (n = 0, ±1, ±2, ⋯), where P n is separated at a distance of Δxn from P0. Here, Δln is the optical path difference between the nth and 0th order, and Δθn is geometrically defined by Δxn and z12. With a sample, an additional optical path s, n is introduced into the nth order by the refraction of the sample.
Fig. 3
Fig. 3 Experimental setup for observing the effect of insufficient temporal coherence (side view).
Fig. 4
Fig. 4 Examples of (b) transmittance, (c) moiré-phase (proportional to p s d 1 Φ ^ / x s ), and (d) normalized visibility images at a glancing angle θin of −0.95° in an area of 600 × 400 pixels (the square in Fig. 4(a)). Gray scales: (b)0-1.2, (c)-5.78-0.5, (c)0-1.2.
Fig. 5
Fig. 5 θin-dependences of (a) the unwrapped moiré-phase and (b) normalized visibility averaged along the horizontal middle lines passing through the center of the top surface (the dashed lines in Fig. 4(c) and 4(d)) for ps = 0.5.
Fig. 6
Fig. 6 θin-dependences of (a) the unwrapped moiré-phase and (b) normalized visibility averaged along the horizontal middle lines passing through the center of the top surface for ps = 0.24.

Equations (67)

Equations on this page are rendered with MathJax. Learn more.

E G 1 ( x 1 , y 1 ) = E 1 n T n ( x 1 )
= E 1 n a n exp ( 2 π i n x 1 d 1 ) ,
T n ( x 1 ) a n exp ( 2 π i n x 1 d 1 )
E self ( x 2 , y 2 ) E 2 n a n exp ( 2 π i n x 2 d 2 ) ,
E 2 E 1 exp [ 2 π i z 12 λ ] R 1 R 2 ,
a n a n exp ( n 2 π i λ z 12 d 1 d 2 ) ,
I self , 0 ( x 2 , y 2 ) I 2 n b n exp ( 2 π i n x 2 d 2 ) ,
I 2 | E 1 | 2 R 2 2 R 1 2 ,
b n = n a n + n a n * exp [ π i ( ( n + n ) 2 n 2 ) z 12 d 1 d 2 ] .
E self ( x 2 , y 2 ) = E 2 n a n exp ( n 2 π i λ z 12 d 1 d 2 ) exp ( 2 π i n x 1 d 1 ) exp ( n 2 2 π i λ z 12 d 1 d 2 ) ,
= E 2 n a n exp ( n 2 π i λ z 12 d 1 d 2 ) exp ( 2 π i n ( x 1 n λ z 12 d 2 ) d 1 ) ,
= E 2 n a n exp ( n π i Δ θ n z 12 d 1 ) exp ( 2 π i n ( x 1 Δ θ n z 12 ) d 1 ) ,
= E 2 n a n exp ( 2 π i n Δ x n 2 d 1 ) exp ( 2 π i n ( x 1 Δ x n ) d 1 )
Δ θ n n λ d 2 ,
Δ x n z 12 Δ θ n .
E self ( x 2 , y 2 ) = E 2 n T n ( x 1 Δ x n ) exp ( 2 π i Δ l 2 λ ) ,
Δ l n n Δ x n λ 2 d 1 .
( R 1 2 + Δ x n 2 + z 12 2 + Δ x n 2 ) ( R 1 + z 12 ) Δ x n 2 2 ( 1 R 1 + 1 z 12 ) ,
= Δ x n 2 2 R 1 + z 12 R 1 1 z 12 ,
= Δ x n 2 d 1 d 2 Δ x n z 12 ,
= Δ x n 2 d 1 ( n λ ) ,
z 12 = p d 1 d 2 λ ,
Δ x n = n p d 1 .
a n a n exp ( 2 π i n Δ x n d 1 ) ,
E self ( x 2 , y 2 ) = E 2 n a n exp ( 2 π i Δ l n λ ) exp ( 2 π i n x n d 1 ) .
I self ( x 2 , y 2 ) I self , 0 ( x 2 , y 2 ; X 0 , Y 0 ; ν ) d X 0 d Y 0 d ν ,
I self ( x 2 , y 2 ) n exp ( 2 π i n x 2 d 2 ) μ n ( ν ) b n ( ν ) d ν ,
μ n ( ν ) I 2 ( x 2 , y 2 ; X 0 , Y 0 ; ν ) exp ( 2 π i X 0 Δ x n R 1 λ ) d X 0 d Y 0 ,
I 2 ( x 2 , y 2 ; X 0 , Y 0 , ν ) = S ( ν ) I ^ 2 ( x 2 , y 2 ; X 0 , Y 0 ) ,
I self ( x 2 , y 2 ) n μ ^ n exp ( 2 π i n x 2 d 2 ) S ( ν ) b n ( ν ) d ν ,
μ ^ n I ^ 2 ( x 2 , y 2 ; X 0 , Y 0 ) exp ( 2 π i X 0 Δ x n R 1 λ ) d X 0 d Y 0 ,
b n ( ν ) = n a n + n ( ν ) a * n ( ν ) exp [ 2 π i ν ( τ n + n τ n ) ] ,
τ n Δ l n / c .
I self ( x 2 , y 2 ) n μ ^ n exp ( 2 π i n x 2 d 2 )
× n S ( ν ) a n + n ( ν ) a n * ( ν ) exp [ 2 π i ν ( τ n + n τ n ) ] d ν ,
I self ( x 2 , y 2 ) n μ ^ n exp ( 2 π i n x 2 d 2 ) [ n γ ^ n + n , n ( Δ τ n + n , n ) S n + n , n ] ,
Δ τ n + n , n τ n + n τ n ,
γ ^ n + n , n ( τ ) T ν [ S ( ν ) a n + n ( ν ) a n * ( ν ) ] S ( ν ) a n + n ( ν ) a n * ( ν ) d ν ,
 
S n + n , n S ( ν ) a n + n ( ν ) a n * ( ν ) d ν .
γ ^ n + n , n ( Δ τ n + n , n ) = exp [ 2 π i ν 0 ( Δ τ n + n , n ) ] .
I self ( x 2 , y 2 ) S ( ν 0 ) n μ ^ n b n ( ν 0 ) exp ( 2 π i n x 2 d 2 ) .
V = μ ^ 1 [ n γ ^ n + 1 , n ( Δ τ n + 1 , n ) S n + 1 , n ] μ ^ 0 [ n γ ^ n , n ( 0 ) S n , n ] ,
= μ ^ 1 [ n γ ^ n + 1 , n ( Δ τ n + 1 , n ) S n + 1 , n ] n S n , n .
V = μ ^ 1 [ γ ^ 1 , 0 ( Δ τ 1 , 0 ) S 1 , 0 ] n S n , n ,
T n ( x 1 Δ x n ) exp ( 2 π i Φ ^ n ( x 1 , y 1 , ν ) ,
Φ ^ n ( x 1 , y 1 , ν ) Φ ^ ( x s n p s d 1 , y s , ν ) ,
= { Φ ^ ( R s R 1 ( x 1 Δ x n ) , R s R 1 y 1 , ν ) ( 0 < R s R 1 ) Φ ^ ( R s R 1 x 1 R 2 R s R 2 R 1 Δ x n , R s R 1 y 1 , ν ) ( R 1 R s R 2 )
p s { p R s R 1 ( 0 < R s R 1 ) p R 2 R s R 2 R 1 ( R 1 R s R 2 ) ,
a n exp ( 2 π i Φ ^ n ( x 1 , y 1 , ν ) ) .
Φ ^ n ( x s , y s , ν ) = Φ ^ n ( x s , y s , ν 0 ) ( ν ν 0 + C n ( x s , y s , ν ) ) ,
I self ( x 2 , y 2 ) n μ ^ n exp ( 2 π i n x 2 d 2 )
× n S ( ν ) a n + n ( ν ) a n *
× exp [ 2 π i ( Φ ^ n + n ( ν 0 ) C n + n ( ν ) Φ ^ n ( ν 0 ) C n ( ν ) ) ]
× exp [ 2 π i ν ( Δ τ n + n , n + Δ τ s , n + n , n ) ] d ν ,
τ s , n = Φ ^ n ( ν 0 ) ν 0 ,
Δ τ s , n + n , n τ s , n + n τ s , n .
I self ( x 2 , y 2 ) n μ ^ n exp ( 2 π i n x 2 d 2 ) [ n γ ^ n + n , n ( Δ τ n + n , n + Δ τ s , n + n , n ) S n + n , n ] ,
γ ^ n + n , n ( τ ) T ν [ S ( ν ) a n + n ( ν ) a n * ( ν ) exp [ 2 π i ( Φ ^ n + n ( ν 0 ) C n + n ( ν ) Φ ^ n ( ν 0 ) C n ( ν ) ) ] ] S ( ν ) a n + n ( ν ) a n * ( ν ) exp [ 2 π i ( Φ ^ n + n ( ν 0 ) C n + n ( ν ) Φ ^ n ( ν 0 ) C n ( ν ) ) ] d ν ,
S n + n , n S ( ν ) a n + n ( ν ) a n * ( ν ) exp [ 2 π i ( Φ ^ n + n ( ν 0 ) C n + n ( ν ) Φ ^ n ( ν 0 ) C n ( ν ) ) ] d ν .
V s = μ ^ 1 [ n γ ^ n + 1 , n ( Δ τ n + 1 , n + Δ τ s , n + 1 , n ) S n + 1 , n ] n S n , n .
V s V = n S n , n n S n , n n γ ^ n + 1 , n ( Δ τ n + 1 , n + Δ τ s , n + 1 , n ) S n + 1 , n n γ ^ n + 1 , n ( Δ τ n + 1 , n ) S n + 1 , n
V s = μ ^ 1 [ S 1 , 0 γ ^ 1 , 0 ( Δ τ 1 , 0 + Δ τ s , 1 , 0 ) + S 0 , 1 γ ^ 0 , 1 ( Δ τ 0 , 1 + Δ τ s , 0 , 1 ) ] n S n , n ,
V s V = n S n , n n S n , n S 1 , 0 γ ^ 1 , 0 ( Δ τ 0 , 1 + Δ τ s , 0 , 1 ) + S 0 , 1 γ ^ 0 , 1 ( Δ τ 1 , 1 + Δ τ s , 1 , 1 ) S 1 , 0 γ ^ 1 , 0 ( Δ τ 0 , 1 ) + S 0 , 1 γ ^ 0 , 1 ( Δ τ 1 , 1 ) .
S ( ν ) c 1 ( ν ) ,
S ( ν ) c 1 α ( ν ) ϵ ( ν ) exp [ 4 π J [ Φ ^ n ( ν ) ] ] ,
| Δ P | > π 2 ν 0 Δ ν ,

Metrics