Abstract

Ptychographic coherent X-ray diffractive imaging (PCDI) has been combined with nano-focus X-ray diffraction to study the structure and density distribution of unstained and unsliced bacterial cells, using a hard X-ray beam of 6.2keV photon energy, focused to about 90nm by a Fresnel zone plate lens. While PCDI provides images of the bacteria with quantitative contrast in real space with a resolution well below the beam size at the sample, spatially resolved small angle X-ray scattering using the same Fresnel zone plate (cellular nano-diffraction) provides structural information at highest resolution in reciprocal space up to 2nm−1. We show how the real and reciprocal space approach can be used synergistically on the same sample and with the same setup. In addition, we present 3D hard X-ray imaging of unstained bacterial cells by a combination of ptychography and tomography.

© 2012 OSA

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2012

A. Diaz, P. Trtik, M. Guizar-Sicairos, A. Menzel, P. Thibault, and O. Bunk, “Quantitative x-ray phase nanotomography,” Phys. Rev. B85, 020104 (2012).
[CrossRef]

2011

T. H. Jensen, M. Bech, O. Bunk, M. Thomsen, A. Menzel, A. Bouchet, G. L. Duc, R. Feidenhans’l, and F. Pfeiffer, “Brain tumor imaging using small-angle x-ray scattering tomography,” Phys. Med. Biol.56, 1717–1726 (2011).
[CrossRef] [PubMed]

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salome, and C. David, “High- efficiency fresnel zone plates for hard x-rays by 100 kev e-beam lithography and electroplating,” J. Synchrotron Radiat.18, 442–446 (2011).
[CrossRef] [PubMed]

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, and T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B83, 214109 (2011).
[CrossRef]

M. Guizar-Sicairos, A. Diaz, M. Holler, M. S. Lucas, A. Menzel, R. A. Wepf, and O. Bunk, “Phase tomography from x-ray coherent diffractive imaging projections,” Opt. Express19, 21345–21357 (2011).
[CrossRef] [PubMed]

2010

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic x-ray computed tomography at the nanoscale,” Nature467, 436–439 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von Knig, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12, 035017 (2010).
[CrossRef]

A. Schropp, P. Boye, J. M. Feldkamp, R. Hoppe, J. Patommel, D. Samberg, S. Stephan, K. Giewekemeyer, R. N. Wilke, T. Salditt, J. Gulden, A. P. Mancuso, I. A. Vartanyants, E. Weckert, S. Schoder, M. Burghammer, and C. G. Schroer, “Hard x-ray nanobeam characterization by coherent diffraction microscopy,” Appl. Phys. Lett.96, 091102 (2010).
[CrossRef]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110, 325–329 (2010).
[CrossRef] [PubMed]

S. Gorelick, V. A. Guzenko, J. Vila-Comamala, and C. David, “Direct e-beam writing of dense and high aspect ratio nanostructures in thick layers of PMMA for electroplating,” Nanotechnology21, 295303 (2010).
[CrossRef] [PubMed]

K. Nygård, O. Bunk, E. Perret, C. David, and J.F. van der Veen, “Diffraction gratings as small-angle X-ray scattering calibration standards,” J. Appl. Cryst.43, 350–351 (2010).
[CrossRef]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA107, 529–534 (2010).
[CrossRef]

K. Giewekemeyer, H. Neubauer, S. Kalbfleisch, S. P. Krüger, and T. Salditt, “Holographic and diffractive x-ray imaging using waveguides as quasi-point sources,” New J. Phys.12, 035008 (2010).
[CrossRef]

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. USA107, 7235–7239 (2010).
[CrossRef] [PubMed]

2009

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11, 123016 (2009).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109, 338–343 (2009).
[CrossRef] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109, 1256–1262 (2009).
[CrossRef] [PubMed]

P. Kraft, A. Bergamaschi, C. Broennimann, R. Dinapoli, E. F. Eikenberry, B. Henrich, I. Johnson, A. Mozzanica, C. M. Schleputz, P. R. Willmott, and B. Schmitt, “Performance of single-photon- counting pilatus detector modules,” J. Synchrotron Radiat.16, 368–375 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, C. M. Kewish, A. Menzel, O. Bunk, and F. Pfeiffer, “Contrast mechanisms in scanning transmission x-ray microscopy,” Phys. Rev. A80, 043813 (2009).
[CrossRef]

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic fresnel coherent diffractive imaging,” Phys. Rev. A80, 063823 (2009).
[CrossRef]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation-damage in x-ray diffraction microscopy,” J. Electron Spectrosc.170, 4–12 (2009).
[CrossRef]

2008

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy108, 481–487 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science321, 379–382 (2008).
[CrossRef] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys.4, 394–398 (2008).
[CrossRef]

M. Guizar-Sicairos, S.T. Thurman, and J.R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33, 156–158 (2008).
[CrossRef] [PubMed]

2007

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett.98, 034801 (2007).
[CrossRef] [PubMed]

A. Gourrier, W. Wagermaier, M. Burghammer, D. Lammie, H. S. Gupta, P. Fratzl, C. Riekel, T. J. Wess, and O. Paris, “Scanning x-ray imaging with small-angle scattering contrast,” J. Appl. Crystallogr.40, 78–82 (2007).
[CrossRef]

2006

M. Eltsov and J. Dubochet, “Rebuttal: Ring-like nucleoids and dna repair in deinococcus radio-durans,” J. Bacteriol.188, 6052 (2006).
[CrossRef]

M. Eltsov and J. Dubochet, “Study of the deinococcus radiodurans nucleoid by cryoelectron microscopy of vitreous sections: supplementary comments,” J. Bacteriol.188, 6053–6058 (2006).
[CrossRef] [PubMed]

A. Minsky, E. Shimoni, and J. Englander, “Rebuttal: study of the deinococcus radiodurans nucleoid,” J. Bacteriol.188, 6059 (2006).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett.97, 025506 (2006).
[CrossRef] [PubMed]

H. N. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A23, 1179–1200 (2006).
[CrossRef]

2005

M. Eltsov and J. Dubochet, “Fine structure of the deinococcus radiodurans nucleoid revealed by cryoelectron microscopy of vitreous sections,” J. Bacteriol.187, 8047–8054 (2005).
[CrossRef] [PubMed]

J. Zimmerman and J. Battista, “A ring-like nucleoid is not necessary for radioresistance in the deinococcaceae,” BMC Microbiol.5, 17 (2005).
[CrossRef] [PubMed]

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA102, 15343–15346 (2005).
[CrossRef] [PubMed]

2004

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett.85, 4795–4797 (2004).
[CrossRef]

2003

G. Morrison, W. Eaton, R. Barrett, and P. Charalambous, “STXM imaging with a configured detector,” J. Phys. IV France104, 547–550 (2003).
[CrossRef]

S. Levin-Zaidman, J. Englander, E. Shimoni, A. K. Sharma, K. W. Minton, and A. Minsky, “Ringlike structure of the deinococcus radiodurans genome: a key to radioresistance?,” Science299, 254–256 (2003).
[CrossRef] [PubMed]

2000

O. Paris, D. Loidl, H. Peterlik, M. Muller, H. Lichtenegger, and P. Fratzl, “The internal structure of single carbon fibers determined by simultaneous small- and wide-angle scattering,” J. Appl. Crystallogr.33, 695–699 (2000).
[CrossRef]

1999

S. Rinnerthaler, P. Roschger, H. F. Jakob, A. Nader, K. Klaushofer, and P. Fratzl, “Scanning small angle x-ray scattering analysis of human bone sections,” Calcified Tissue Int.64, 422–429 (1999).
[CrossRef]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature400, 342–344 (1999).
[CrossRef]

1998

1997

P. Fratzl, H. F. Jakob, S. Rinnerthaler, P. Roschger, and K. Klaushofer, “Position-resolved small-angle x-ray scattering of complex biological materials,” J. Appl. Crystallogr.30, 765–769 (1997).
[CrossRef]

1988

J. Dubochet, M. Adrian, J.-J. Chang, J.-C. Homo, J. Lepault, A.W. McDowall, and P. Schultz, “Cryo-Electron microscopy of vitrified specimens,” Q. Rev. Biophys.21, 129–228 (1988).
[CrossRef] [PubMed]

1985

1982

Abbey, B.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic fresnel coherent diffractive imaging,” Phys. Rev. A80, 063823 (2009).
[CrossRef]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys.4, 394–398 (2008).
[CrossRef]

Adrian, M.

J. Dubochet, M. Adrian, J.-J. Chang, J.-C. Homo, J. Lepault, A.W. McDowall, and P. Schultz, “Cryo-Electron microscopy of vitrified specimens,” Q. Rev. Biophys.21, 129–228 (1988).
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Barrett, R.

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Supplementary Material (2)

» Media 1: AVI (7973 KB)     
» Media 2: MPG (22799 KB)     

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Figures (10)

Fig. 1
Fig. 1

Schematic of the experimental setup used for X-ray cellular nano-diffraction and PCDI accentuating the important parameters: 1. gap of the source slit S0, which controls the flux and coherence properties of the beam, 2. the distance Z0 between the zone plate optics (FZP) and the sample, which defines the size of the beam at the cellular specimen, and 3. the detector distance Z12 with respect to the sample, which determines sampling of the recorded diffraction pattern and attainable diffraction angle. For different choices of these three parameters the biological specimen can then be translated in the XY – directions and additionally be rotated with respect to ϕ. In detail, the beamline setup consists of the X-ray undulator (period 19mm) source (S), horizontal and vertical slits (S1–S4), Si(111) monochromator (LN2-cooled), fast shutter (FS), filter (Fi), central stop (CS), order sorting aperture (OSA) and focus (F) with bacterial specimen. Flight tube and beamstops are not shown.

Fig. 2
Fig. 2

(a) Phase from ‘ePIE’ reconstruction of the tantalum test structure. Scan points are indicated as magenta points. A fit of the error function to one of the edges of the line scans yields a line-spread function with FWHM-values of 16nm in the vertical direction and 17nm in the horizontal direction. The inner part of (a) is shown in (c). (b) Complex representation of reconstructed probe at the plane of the sample (top) and horizontal and vertical line scans through the centre of the back-propagated probe (bottom) (cf. Media 1). The white dashed lines highlight the position of the different focal positions. (d) (top) Gaussian fits (solid red lines) to the peaks of the line scans of the probe intensity are depicted below together with the data from the line scans (black dots). We obtain FWHM-values of 87nm in the vertical direction, and 93nm in the horizontal direction. (d) A typical diffraction pattern of the PCDI dataset (log-scale) is shown in the lower part.

Fig. 3
Fig. 3

The PRTFs of the ptychographic reconstruction of the resolution test chart and of a single projection of cells (Fig. 4(b)) are depicted in (a), green curve and blue curve respectively. In addition, the PRTF of the test sample according to an average over a single scan point is shown as red curve (cf. Eq. (2)). The high frequency ranges of the azimuthally averaged power spectral densities (PSD) of the reconstructed phase distributions are displayed in (b). Real space half-periods of 50nm, 25nm and 15nm are indicated as dashed, solid and dashed-dotted black lines, respectively. Legend of (b) is legend in (a).

Fig. 4
Fig. 4

(a)–(c) Phase reconstructions of D. radiodurans (‘DM’ - algorithm) showing dark areas, which we attribute to DNA rich regions. (d) 3D visualisation of the tomographic reconstruction of the set of projection images such as seen in (b) (cf. Media 2). The tomographic reconstruction is shown at three different angles. A magenta label in the tomogram (front-view) depicts voxel-regions which have been used to estimate the mass density ρc in the high-density regions of the bacterial specimen (red). We obtained <ρc> ≈ 1.6g/cm3. (a), (b) same colorbar as in (c).

Fig. 5
Fig. 5

Sample region A - coherent setting: differential phase contrast (a), (c) and darkfield (b), (d) of cells are shown for the mesh scans A1 (top) and A2 (bottom) - (cf. Table 2). The colorbar in (c) denotes the movement of the first moment whereas in (d) the grey scale denotes the ratio of scattered to unscattered photons, ns and n0 respectively. The intensity of the beam from the ptychographic reconstruction of the Siemens star (cf. Fig. 2) after back propagation of 1mm into its focus is visualized on top of the darkfield (d). Note, that the propagation of 1mm corresponds to the lateral displacement of the sample between the two different measurements (±100μm due to an uncertainty of the position on the sample holder with respect to the curvature of the polyimide foil). The centre of the reconstructed beam is chosen to be at the cell-position of A4 (cf. Fig. 6). Sample region B - incoherent setting: a section of the scan B1 is shown as darkfield (f) and differential phase contrast (e). The position of the cell diffraction of B3 is indicated on top of the incoherent darkfield as red circle (f). Sample region B - coherent setting: darkfield (h) and phase contrast (g) of a corresponding coherent mesh scan B2 are shown. Numerical simulations C: synthetic cell sample (top) and calculated differential phase contrast images (below) according to Eq. (1) using the back propagated probe (cf. Fig. 2) at different positions on the optical axis. The distance of propagation is displayed and the corresponding intensity of the probe is visualised as an overlay using the same colorbar as in (d).

Fig. 6
Fig. 6

Sample region A - coherent setting: (top) Diffraction data of A2 and A3 (cf. Table 2). The sets of diffraction patterns were segmented into areas with Σ1 and without cell signal Σ2 using the differential phase contrast image of A2 (see inset). The difference between the two classes of diffraction sets averaged according to their set size is depicted next to the legend in the top right corner for A2. Diffraction signals were obtained by azimuthally averaging each diffraction pattern of a scan and thereafter averaging according to their segmentation. The segmented diffraction curves of A2 are shown and the difference signals are presented for both scans in combination with their power-law fits. Exponents of ν = −3.2 and ν = −3.7 were obtained for A2 and A3, respectively. (Bottom) presents the results of A4 (cf. Fig. 5(d)). The diffraction signals obtained after azimuthally averaging are shown in the graph. The difference between the diffraction data of the cell material and of the sample holder is depicted in the lower left corner. A slightly modified power-law yields an exponent of ν = −3.6. In both graphs the points q = q ≡ (c/a)1/ν are marked.

Fig. 7
Fig. 7

Sample region B - incoherent setting: incoherent diffraction curves were obtained from data B1 and B3 (cf. Table 2). The image segmentation of B1 according to areas with cell signal Σ1 and without cell signal Σ2 is shown as an inset. Power-law fits yield exponents of ν = −3.5 and ν = −3.8 for B1 and B3, respectively. The points q = q ≡ (c/a)1/ν are marked for both curves.

Fig. 8
Fig. 8

Photon surface densities ργ of diffraction datasets A2 (a), A3 (b), B1 (c) and ptychographic dataset (Fig. 4(a)) (d). The location of bacterial cells is indicated by black lines. (a)–(c) same colorbar as in (d).

Fig. 9
Fig. 9

(a) 2D PSD of ‘ePIE’ reconstruction of Siemens star test pattern. Note that the Siemens star structure can be clearly seen in the radial direction. (b) 2D PSD of ptychographic (‘DM’) reconstruction of D. radiodurans in Fig. 4(b). Scale bars correspond to spatial frequencies.

Fig. 10
Fig. 10

(a) Intensity of a model-probe exhibiting a dumbbell-shape. The calculated knife-edge scan along the horizontal direction is shown in (b). The white, dashed line in (a) indicates the region of highest focusing which is shown in (c) (solid, black line). The resulting Gaussian shape as estimated from the knife-edge scan is depicted as solid, red curve. (d) shows the intensity of the reconstructed probe at Δz = −0.686mm behind the plane of the sample. A white, dashed line indicates the part which has been used for estimating the beam width. The corresponding result of the calculated knife-edge scan is shown in (e). The FWHM values from calculated knife-edge scans are shown as function of distance to the sample plane in (f). The red and the blue curve denote horizontal and vertical beam-width, respectively. In addition, ϒ(Δz) is shown as solid, black curve which has been scaled arbitrarily for reasons of visualisation.

Tables (2)

Tables Icon

Table 1 Overview of PCDI data sets according to dwell time ΔT, grid spacing between adjacent rings Δr of a scan of one projection, fluence F of a single projection and dose estimations D of the whole reconstruction.

Tables Icon

Table 2 Overview of diffraction data sets according to dwell time ΔT, step size Δxy and number of scan points Nx × Ny within the rectangular mesh. In addition, Si filter thickness (BS denotes usage of beamstops instead of Si filter) and nominal gap of slits S0 are shown as well as the results from diffraction analysis for the exponent of the diffraction curves ν, highest scattering vector q and dose estimations D.

Equations (13)

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I j = | { Ψ j ( x ) } | 2 = | { P ( x x j ) S ( x ) } | 2 ,
PRTF ( | q | ) = I j PCDI j φ I j meas j φ = | { Ψ j it } | j φ I j meas j φ .
𝒫 ( O ( x ) ) : = { | O ( x ) | exp ( i min ( Arg ( O ( x ) ) , 0 ) ) x χ | O ( x ) | exp ( i γ Arg ( O ( x ) ) ) x χ ,
D = μ E ρ c 2 d S χ ( x ) ρ γ ( x ) 2 d S χ ( x ) .
Δ I ( | q | ) = I j ( q ) ϕ j Σ 1 I j ( q ) ϕ j Σ 2
ϒ ( Δ z ) : = 2 d S | 𝔉 { P } ( x , Δ z ) | 4 ,
ρ c ( r ) 2 u λ r 0 ϕ ( r ) ,
q : = ( c / a ) 1 / ν .
w ( x ) = { I 0 ( β 1 ( 2 x / L ) 2 ) / I 0 ( β ) , L / 2 x L / 2 0 , | x | > L / 2
K ( x , Δ z ) = x d x d y | 𝔉 { P } ( x , y , Δ z ) | 2 ,
x K ( x ) = | 𝔉 { P } ( x , y , Δ z ) | 2 d y 𝔓 α = 0 ( x ) .
| 𝔉 { P } ( x , y , Δ z ) | 2 = exp ( ( x μ ) 2 / ( 2 σ 2 ) ) / ( σ / 2 π ) f ( y )
K ( x , Δ z ) = C 0 2 ( 1 + erf ( x μ 2 σ ) ) ,

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