Abstract

Stimulated emission depletion (STED) microscopy generates super-resolved images of single cells by point-wise depletion of fluorescence around a small focal volume. Scanned light sheet microscopy, on the other side, generates images line-wise by scanning a weakly focused laser beam through thousands of scattering cells. Here we address the question of whether fluorescence from an excitation beam can be depleted by a STED beam over tens of micrometers while propagating through scattering material. Therefore, we use two self-reconstructing Bessel beams in continuous wave mode with a different angular momentum for fluorescence excitation and depletion along a distance of 110 μm. We show that despite significant scattering at various arrangements of microspheres embedded in agarose gel and despite strong losses in spatial coherence, it is possible to generate a sufficiently good overlap of both beam intensities. Without affecting the self-healing capability of the illumination photons in the Bessel beam’s ring system, the emission of fluorescence photons thereof can be strongly suppressed. This results in a needle-like fluorescence distribution inside scattering media, providing new perspectives for fundamental principles and applications in microscopy and metrology.

© 2017 Optical Society of America

1. INTRODUCTION

The control of beam propagation and imaging through turbid media remains a great scientific and technical challenge—especially in life science applications, since measurement time is limited and high spatial resolution is required. The deeper light propagates through scattering media, the more ballistic photons change to diffusive photons, such that their propagation directions or, respectively, their wavefronts become randomly distorted. However, several approaches have shown that wavefronts and photon propagation directions can be corrected to form a tight focus behind scattering media, if the transition properties (matrix) of the medium at a fixed time point can be measured [1,2]. In a similar way, angular phase correlations (phase memory) can be exploited to image simple structures through strongly scattering, opaque media onto a detector when certain boundary conditions are met [35]. In this regime, where light propagation is governed by diffusive photons, subsequent imaging from many directions becomes very time-consuming and computationally elaborate—a situation that is incompatible with most investigations of living matter.

But, image acquisition time and computational efforts can be significantly reduced if the number of ballistic photons can be enhanced relative to the number of diffusive photons. Ballistic photons propagate through the object and to the camera nearly without scattering, thus generating different spectral distributions regarding temporal or spatial frequencies from diffusive photons. By exploiting such principles, the image contributions between ballistic and diffusive photons can be separated on the detection side by image postprocessing [6,7] or by time gating [8,9].

However, the ratio between ballistic and diffusive photons along the optical beam axis can also be increased by controlling the phase profile on the illumination side, an effect that was unexpected, based on the picture of incoherent photon migration. If the overall dimensions and the scattering strengths of the objects can be roughly estimated, then Bessel beams—preferably generated by computer controlled spatial light modulators (SLM)—have shown to self-reconstruct their intensity profile in scattering media [10] by an amazingly strong constructive photon interference along the central intensity lobe of the Bessel beam, thereby increasing the number of ballistic photons relative to the diffusive photons.

Bessel beams seem to be especially advantageous in light sheet-based microscopy, since they penetrate deeper into inhomogeneous media, and their central beam lobe is much narrower than that of a Gaussian beam having the same depth of field. However, the concentric ring system of the Bessel beam illuminates the object above and below the focal plane and thereby reduces contrast. Several approaches have been applied to minimize the fluorescence in the ring system, such as multiple photon excitation [11,12], confocal line detection [13] or arranging Bessel beams to a lattice, leading to destructive interference in the ring systems, if phase disturbances induced by the biological medium are moderate [14].

An alternative approach to reduce the fluorescence in the Bessel beams ring system and to generate a very thin light needle by the remaining central lobe of the Bessel beam is to use stimulated emission depletion (STED) [15]. This idea has been investigated theoretically in idealized homogeneous media [16] and in more realistic scattering media [17]. Related approaches have been presented recently by reducing the beam width of a Gaussian beam propagating through water with a second harmonic generated STED beam [18]. Attempts to reduce the width of a complete light sheet remain difficult [19,20], since enormous STED beam powers would be required for efficient fluorescence depletion. Using the much slower fluorescence depletion process of RESOLFT, the spatial resolution in detection direction could be increased strongly by reducing the width of each fluorescence layer in light sheet microscopy [21].

In this paper, we demonstrate that the STED principle can be applied point-wise and also line-wise along 120-μm-long, self-reconstructing Bessel beams. Furthermore, we show that the spatial overlap of two Bessel beams with different orbital angular momenta and the resulting fluorescence depletion efficiency remains surprisingly stable, despite propagation through different scattering media, which may offer new applications in optical metrology or in microscopy.

2. BASIC PRINCIPLE

The combination of these two microscopy techniques requires two different non-diffracting (self-reconstructing) beams, which have to overlap perfectly over a propagation length of typically Δz>100μm inside the object. Therefore, we use a 0th order (=0) Bessel beam with a thin lobe in the center of the surrounding ring system for fluorescence excitation and a higher order (=34) STED Bessel beam with zero intensity in the center of the ring system with the same periodicity for fluorescence depletion [see top inset in Fig. 1(a)]. The vanishing intensity in the STED beam center results from a phase singularity of the helical phase profile exp(iϕ˜), which is quantified by the charge number and counts the rotations of the k- vector around the Poynting-vector per wavelength. As shown in Fig. 1(a), both beams can be generated side by side by a single phase shaping element (SLM, Hamamatsu X10468-04).

 figure: Fig. 1.

Fig. 1. Schematic of measurement principle. (a) Two phase holograms are used to generate the excitation beam (blue arrow and frame) and the depletion beam (yellow), with intensities IEX(r) and IST(r). Both Bessel beams, differing in angular and radial momentum, are superimposed and focused by an objective lens onto a cluster of scattering spheres. After fluorescence depletion, a thin fluorescent light needle with intensity Itot(r) is generated and detected by a perpendicularly arranged objective lens (green arrow and frame). Theoretically obtained intensity line scans illustrate the depletion of the fluorescence in the Bessel beam’s ring system. (b) Numerical simulation of beam propagation and scattering at glass beads (in gray) by the excitation beam (in blue), the depletion beam (in orange) and the remaining needle-like fluorescence of the central beam lobe (in green).

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A. Description of Both Bessel Beams

The smaller the broadening of both beams during propagation, the narrower their radial angular spectrum widths Δkr. The smaller this radial momentum uncertainty, the more beam energy is carried in the Bessel beam’s ring system and the better the propagation stability (invariance). A perfect, but unrealistic Bessel beam has a thin annular Fourier spectrum, described by a delta function δ(krk0NA), and carries an infinite amount of energy in its ring system. A realistic Bessel beam has a smooth annular spectrum of thickness Δkr, and can be described by a 1D convolution (*) with a Gaussian function exp(kr2/Δkr2), where Δkr defines the amount of energy in the ring system. Hence the beams’ electric field spectra

E˜(kr,ϕ˜)E˜0·(δ(krk0NA)*exp(kr2/Δkr2))·exp(iϕ˜)
for fluorescence excitation (=0) and fluorescence depletion (>0) are expressed by the radial wave numbers kr=kx2+ky2, with |kcntkr|12Δkr, where the central ring radius kcnt=2πλNA is defined by the beam focusing numerical aperture NA. For an object illumination over the length Δz, the Bessel beam’s depth of field (FWHM) should be Δz as well, and it can be controlled by the width of the annular spectrum [22]. This can be optimally achieved with the SLM [17] by choosing NAEX=0.2 at an excitation wavelength of λEX=491nm, and NAST=0.26 at a depletion wavelength of λST=560nm. The angular spectral widths chosen for both beams were Δkr=2·1ϵ1+ϵ·kcnt=0.27·kcnt, with ϵ=2kcntΔkr2kcnt+Δkr=0.76 being the ratio of the outer to the inner radius of a hard edge annular aperture [22].

From the angular spectra, the electric field in the beam center is obtained, which is described by the Bessel function J of order , where the radial Bessel side lobes are damped by the Gaussian function:

E(r,ϕ)A·J(k0NA·r)·exp(r2·Δkr2)·exp[i(ϕ+kzz)].

Figure 1(a) shows side by side the intensities of the excitation beam IEX(r,ϕ,z)=|E=0(r,ϕ,z)|2 and the STED beam IST(r,ϕ,z)=|E=3(r,ϕ,z)|2, which depletes the fluorescence only in the ring system, provided both beams are well adjusted relative to each other with help of the SLM. In the ideal case, fluorescence is emitted only in the central main lobe, such that a thin light needle is generated even inside a scattering medium [see cluster of spheres in Fig. 1(b)].

The overlap between both beams can be optimized by maximizing the product of both intensity cross-sections, ρ(,α)=1A·r0rmaxIEX(r)·IST(r,,α)rdr, which are integrated over the extent of their ring systems defined by the radii r0 and rmax, with IEX(r0)=0. It turned out that the beam parameters in the absence of scatterers were α=(NAST/λST)/(NAEX/λEX)=1.1 and helicity =3 [17].

B. Quantifying Fluorescence and Depletion

The scenario illustrated in Fig. 1(b) is obtained from a computer simulation using the beam propagation method (BPM) [23,24] for two Bessel beams propagating through a cluster of spheres. The excitation beam intensity (in blue) and the depletion beam intensity (in orange), both distorted by scattering at the spheres, define the space variant depletion efficiency η(r), which defines the remaining fluorescence (in green).

The resulting fluorescence F(r)Cext(r)·Qfl·η(r)·IEX(r) is approximately proportional to the extinction cross-section Cext(r) and the quantum efficiency Qfl of the fluorophores and to the excitation intensity IEX(r) and the probability for spontaneous emission η(r). A good expression for this space variant distribution is η(r)=Isat/(Isat+IST(r)) [25], which depends on the intensity of the STED beam IST(r) and the saturation intensity Isat=(hc·kfl)/(σSTλST) at which the rates of depletion κST and fluorescence κfl equal each other [see inset of Fig. 1(a)]. σST is the fluorophore-specific STED emission cross-section. Typical saturation intensities are in the range of Isat1020mW/μm2.

During propagation, both beams are scattered at the spheres, such that the total intensity of the beams is characterized by the interference of unscattered (index u) and scattered (index s) light, IEX(r)=|EEX,u(r)+EEX,s(r)|2 and IST(r)=|EST,u(r)+EST,s(r)|2. Both beams can be separated in an ideal unscattered term and an additive term due to scattering [24] such that IEX(r)=hEX,u(r)+hEX,s(r) and IST(r)=hST,u(r)+hST,s(r). Using the separation into unscattered and scattered beams for both excitation and depletion, the expected fluorescence can also be split into a term without and with scatterers:

F(r)=Fu(r)+Fs(r)Cext(r)·Qfl·(ηu(r)+ηs(r))·(hEX,u(r)+hEX,s(r))=Cext(r)·Qfl·[(ηuhEX,ugood)+(ηshEX,ubad+ηuhEX,sgood+ηshEX,sgood)].

Thus, the total fluorescence splits into four terms. In the absence of scatterers, the probability for spontaneous emission ηu(r)=Isat/(Isat+hST,u(r)) is determined by the ideal, unscattered STED beam hST,u(r). In the presence of scatterers, however, three additional terms occur, among which two terms are beneficial to the image quality and only one is bad, where scattered light from the STED beam depletes fluorescence from the center of the unscattered excitation beam.

The space-dependent fluorescence depletion efficiency QD(r)=1η(r)=IST(r)/(Isat+IST(r)) expresses the probability of the depletion process and can also be separated in terms of unscattered and scattered light:

QD(r)=1ηu(r)ηs(r)=(1+IsathST,u(r)+hST,s(r))1.

For large intensities of the STED beam, ISTIsat, the depletion efficiency reaches QD(r)1.

3. EXPERIMENTAL SETUP

The setup developed and constructed in our lab is based on two continuous wave (cw) lasers: a 25-mW excitation laser (Cobolt Calypso 04-01 491 nm) and a 2-W STED laser (MPB Communications, VFL-P-2000-560). As depicted in Fig. 2, both beams are first expanded and then combined by beam splitters such that their beam phases are modulated independently by the left and right halves of a SLM (Hamamatsu X10468-04) operating in reflection mode. After overlapping both beams, these are deflected with a galvanometric scan mirror and focused with the illumination objective (IO, NAill=0.35) to be scanned through the focal plane of the detection objective (DO, NAdet=1.0). This lens images the fluorescence light onto a sCMOS camera (Andor Neo 5.5). Coherent light from both lasers transmitted through the object is collected by a scattering objective lens (SO, NAsca=0.35) and projected onto the second camera (PhotonFocus DS1-D1024-80-CL-10), which enables analysis of the power spectra |E˜=0(kx,ky)|2 and |E˜=3(kx,ky)|2 of the transmitted beams and thus facilitates the alignment of both beams.

 figure: Fig. 2.

Fig. 2. Photos and sketch of the experimental setup. The excitation beam and the STED beam are projected onto the left and right halves of a SLM and are then superimposed by beam splitters (BS). The angular spectra of both beams are projected by a lens L1 onto a scanning mirror (SM) with zeroth order beam block (B). Two lenses (SL and TL) project the tilted angular spectra onto the back focal plane (BFP) of the IO, which focuses the Bessel beams into the sample chamber. The SO images the angular spectrum of the scattered laser light onto a camera (Camsca), whereas the fluorescence generated in the sample chamber is collected by the detection objective (DO) and imaged onto another camera (Camdet).

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4. RESULTS

In point scanning STED, the stronger the depletion efficiency and the reduction of the width of the point-spread function, the higher the intensity of the STED beam at the fluorophore, which is expressed as a multiple of the fluorophores saturation intensity, that is, ISTED/Isat6 in our case. This is achieved best with shorter laser pulses with high peak intensities, often leading to strong fluorophore bleaching. However, since we seek to achieve efficient depletion along the focus line with propagation lengths Δz>100μm, the challenge is different. Because the central maximum of the Bessel beam is much narrower than that of a comparable Gaussian beam, the goal is to suppress the fluorescence most efficiently in the ring system of the Bessel beam. This goal becomes more and more difficult the more strongly the two beams run out of phase relative to each other; they thereby generate new interference distributions along the propagation length. The decay of the depletion efficiency QD(x,y,Δz) with propagation length Δz therefore depends on the strength of the scattering and the loss of the phase correlations between the coherent photons in each beam. In the following, three different classes of the refractive index inhomogeneities are investigated.

A. Bessel Beam Depletion of Isolated Beads

In a first experiment, we imaged isolated 0.75-μm large, fluorescing polystyrene beads embedded in an agarose gel. These beads were smaller than the ring period of both Bessel beams. As illustrated in Fig. 3(a), a first scan was performed by moving a single bead in the lateral x-direction through the excitation Bessel beam (=0) alone, resulting in the fluorescence image (blue frame) displayed in Fig. 3(b). A second scan was performed with a STED Bessel beam (=3) alone, resulting in a fluorescence image indicating the central zero intensity (red frame). The third scan was performed with both beams switched on, resulting in a fluorescence image, where the intensity in the ring system is efficiently suppressed (green frame). This is quantified by four line scans shown in Fig. 3(c), where the fluorescence in the first Bessel ring with STED beam switched on is reduced by up to 80%. The usual subtraction of the fluorescence excited by the STED beam (see inset) has only a minor effect (curve shown in cyan). Figure 3(d) shows the mean depletion efficiency Q(xb), which varies both in space and with the STED intensity and was averaged over 19 beads, as well as the standard deviation from the mean. It is highest at the first ring of the Bessel beam and well below 20% in the beam center at xb=0. Fluorescence is not affected in a distance |xb|>5μm.

 figure: Fig. 3.

Fig. 3. Beam profiling. (a) A 0.75-μm fluorescent bead embedded in agarose gel is scanned laterally with different beams. (b) Resulting fluorescence images of the 0th order excitation Bessel beam (blue), the 3rd order STED Bessel beam (red) and the combination of both beams (green). (c) Fluorescence line profiles show fluorescence depletion only in the Bessel ring system and small fluorescence excitation by the STED beam itself, which is typically subtracted (-S) in postprocessing from the combination of both beams (Exc/STED-S). (d) Space-dependent probability for spontaneous emission Q(xb) averaged over 19 beads (solid line), and the standard deviation from the mean (shaded area).

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B. Resolution Enhancement in Bead Images

In a second experiment, we performed one sweep of the Bessel beams in lateral x-direction during the integration time of the camera and moved the bead cluster in detection direction yb to record a stack of images [see sketch in Fig. 4(a)]. The projected bead images in the yz-plane are shown in Fig. 4(b) and a magnification of two bead images in Fig. 4(c). The corresponding line scans in the detection direction in Fig. 4(d) reveal a significant reduction in the 1/e widths, which are on average nearly 50% with STED Bessel beam switched on [green profile in Fig. 4(e)]. It should be emphasized that the ring intensity oscillations visible in Fig. 3(c) are invisible in Fig. 4(d), since the elongated width of the point-spread function in detection direction has a strong averaging effect.

 figure: Fig. 4.

Fig. 4. Single bead imaging. (a) Different beams are scanned in lateral x-direction across isolated 0.75-μm beads. (b) Bead images in the yz-plane without (blue frame) and with (green frame) fluorescence depletion (STED). (c) Magnification of marked area in (b). (d) Normalized image intensity profiles F(y) without STED beam (blue), with STED beam (green), and the fluorescence bead image of the STED beam alone (red). (e) The 1/e Image widths δy(z) from different bead images at propagation distances between z=12 and z=42μm without (blue) and with (green) STED beam.

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The red fluorescence image profile from the STED beam, which is not the STED beam profile, has been normalized to F(y)=1 to visualize this effect.

C. Fluorescence Depletion Behind Two Large Scatterers

In a third experiment, we embedded unlabeled 8-μm glass spheres in a fluorescing gel, such that the fluorescence excited (at PEX=0.6mW) and depleted (at PST=1W) by the beams can be well examined. In the example presented in Fig. 5, different beams are incident from the left and are scattered at two spheres, which appear as black circular areas. The fluorescence image in Fig. 5(a) shows the propagation behavior of a conventional Gaussian beam (all beams have the same depth of field), which is strongly focused and deflected by the two spheres, such that no fluorescence signal is visible in the back part of the image along the optical axis.

 figure: Fig. 5.

Fig. 5. Beam self-reconstruction behind two 8-μm glass spheres. Images F(x,z) of propagating and scattering beams exciting fluorescence in a labeled agarose gel. Image width corresponds to a propagation length of 140 μm. Two unlabeled beads appear dark. (a) Fluorescence image of the Gaussian beam reveals its large diameter and strong deflection at the spheres. Two hypothetic round objects (yellow circles) are images in detection direction, indicated by two elongated PSFs. The real and the ideal images differ significantly. (b) Zeroth order Bessel beam reconstructs its intensity profile after scattering at both spheres. Hypothetic real images are more like the ideal images. (c) In combination with a 3rd order STED Bessel beam, the fluorescence in the ring system can be depleted, despite strong scattering with a reasonable efficiency, as indicated in (f) by the two line scans taken at z1=20μm and z2=90μm. Hypothetic real images resemble the ideal images as also visible in Fig. 5(d) without scatterers. (e) Distribution QD(x,z) illustrates the space-dependent efficiency of fluorescence depletion. Scale bar: 10 μm.

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The focal plane images F(x,z) in Fig. 5 approximate the fluorescence intensity within the object. Because the unscattered beams and the scatterers are both rotationally symmetric, it is valid to assume that the fluorescence distribution in the focal plane may also correspond to the fluorescence distribution perpendicular to it, that is, F(x,z)F(y,z). To illustrate the space-dependent appearance of two hypothetical roundish fluorescent objects (indicated by yellow circles) caused by the deflected and imperfect illumination, we took the hypothetic fluorescence image at z80μm in different heights along y relative to each other, but both within the depth of field of the detection PSF(y,z). The two resulting real and ideal roundish images taken in the (x, z) plane are completely different for Gaussian, Bessel and STED Bessel beams.

By exciting fluorescence with a 0th order Bessel beam, Fig. 5(b) shows that this beam self-reconstructs behind both spheres and is able to illuminate both hypothetic spheres differently, although a perfect beam would not illuminate the upper sphere, as shown in the ideal image. Figure 5(c) shows the result of additional fluorescence depletion with the self-reconstructing 3rd order Bessel beam, resulting in an efficient depletion, even behind the scatterers. This is demonstrated by the bright (right) and hardly (left) fluorescing images of the hypothetical objects and by the intensity line scans of Fig. 5(f). In the experimental imaging process, the convolution of the 3D detection point-spread function with the 3D fluorescence emission distribution results in a strong background generation and image blur. Therefore, we subtracted a Gaussian shaped background intensity from the Bessel beams [see dashed line in Fig. 5(f)] leading to an increase in contrast in the images of Figs. 5(b)5(d) (for details see Supplement 1 and Visualization 1). A 3D deconvolution was not possible, since the required 3D image was not available.

Whereas Fig. 5(d) illustrates the fluorescence F(r)C(r)·η(r)·IEX(r) generated by the excitation intensity IEX(r) and the depletion η(r)=Isat/(Isat+IST(r)) in the absence of scatterers, Fig. 5(e) displays the depletion efficiency QD(r)=1η(r) in the presence of scatterers according to Eq. (4). QD(r)=(FEX(r)Ftot(r))/FEX(r) is obtained by the images of the fluorescence distributions without and with depletion, FEX(r) and Ftot(r).

D. Beam Penetration and Fluorescence Depletion in Sphere Clusters

Most relevant to applications in metrology and microscopy is the situation where beams have to propagate through turbid media, often consisting of diffusing aerosols, water droplets, complex fluids or, in the extreme, inhomogeneous biological material. To investigate the nonlinear interplay between the two self-reconstructing Bessel beams and the resulting fluorescence depletion in strongly, but homogeneously, scattering media, we used 0.35-μm fluorescing spheres embedded in an agarose gel in different concentrations.

To avoid the strong averaging effect by the 3-D imaging process, the change of the beam cross-section and, thereby, the propagation behavior can be better investigated by using the beads both as coherent scatterers and as point-like fluorescing probes C(r)=C0·jδ(rrj) randomly distributed across the beam volume. A series of N=121 images was taken by moving the bead cluster through the beam. From this stack of images, the maximum selection (projection) was performed. In this way, the ring system of an averaged Bessel beam, and also the effect of the fluorescence depletion, can be well visualized and quantified, and the effective penetration depth into scattering media can be extracted.

The beam propagation behavior from left to right through the scattering medium is illustrated in Figs. 6(a)6(d) for two bead volume concentrations of c1=0.13% and c3=0.52%. The mean fluorescent response was also measured for a third volume concentration c2=0.26%, which is shown in Supplement 1. The 0th order Bessel beam excites fluorescence both in its narrow beam center and in the surrounding ring system. In combination with the 3rd order Bessel beam, the fluorescence in the ring system is also efficiently depleted after more than 100-μm propagation through the scattering medium. The result is a thin fluorescing light needle, which hardly spreads out. The third image shows the Gaussian beam with the same depth of field, revealing the much broader beam diameter and a stronger decay in fluorescence. The fourth image displays the space variant depletion efficiency QD(x,z), according to Eq. (4), which is very small in the beam center and strongest at the location of the first Bessel ring. In order to compensate for the discrete nature and random position of the scatterers, a gliding average over a region of Δz=6μm has been performed before computing QD(x,z). Remarkably, the lateral periodic ring structure in the depletion efficiency is also visible by the parallel horizontal lines, indicating very good self-interference of the beam, despite a strong local phase disturbance induced by the scatterers.

 figure: Fig. 6.

Fig. 6. Beam propagation over 120 μm through a cluster of beads, fluorescence generation, and STED efficiency. Fluorescing polystyrene beads with 0.35-μm diameter are embedded in agarose gel at concentrations cvol=0.13% (left) and cvol=0.52% (right). Maximum projections of images revealing the intensity profile of (a) a single Bessel beam, (b) a Bessel beam with the STED beam and (c) a Gaussian beam. (d) Space varying depletion efficiency QD(x,z) derived from (b) reaching efficiencies at the first Bessel ring of up to 60%, which is shown by the bright yellow areas. Central parts of (a)–(d) are magnified in (e) and (f) for cvol=0.13% and cvol=0.52%, respectively. (g) Average depletion efficiencies along z in the center and the ring system for the three bead concentrations. (h) Fluorescence line profiles F(x,z0) at z0=30μm (solid line) and z0=75μm (dashed line), and corresponding depletion efficiencies QD(x,z0). Profiles are averaged over 60 pixels, that is, Δz6μm. (i) Axial fluorescence profiles F(x=0,z) for two different concentrations of scatterers averaged over the beam centers of the Bessel beam (left), the Bessel beam with STED (center) and the Gaussian beam (right). (j) Comparison of decay constants for all beam types at three different bead concentrations.

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The magnifications shown in Figs. 6(e) and 6(f) from the marked areas in the center of the beams allow a direct comparison of the four distributions FBe(x,z,IST=0), FBe(x,z,IST>0), FGa(x,z,IST=0) and QD(x,z,IST>0). The corresponding line scans (averaged over Δz6μm) at propagation distances of z=30μm and z=75μm are shown in Fig. 6(h). The decay of the fluorescence intensity Fj(rel) (with j=2,3 representing the respective volume concentrations) relative to the fluorescence intensity in the bead sample c1 is plotted in Fig. 6(i) along the propagation direction, averaged over the center of the Bessel beam. By exponentially fitting with exp((μjμ1)·z), one can extract the decay coefficients μj (or penetration depths dj=1/μj for the sample with volume concentration cj [see Figs. 6(i) and 6(j) and Supplement 1]. This fluorescence decay has been analyzed for the Bessel and the Gaussian beam and for the combination of both Bessel beams enabling the propagation variant STED effect. Figure 6(j) reveals that the average penetration depth of the Bessel beam is about 19% higher than the average penetration depth of the Gaussian beam. The penetration of the Bessel beam with the STED beam switched on is even about 27% higher than that of the Gaussian beam.

It can be seen from Fig. 6(h) that the 50% width (FWHM) Δx0.95μm of the Bessel beam with STED is three times narrower than the Gaussian beam over the whole propagation distance. The fluorescence decay for the Bessel beam (central lobe, position r0) with STED beam switched on is slightly smaller than without STED. We compared the unwanted depletion efficiency of QD(z,r0) <0.2 at the central lobe, relative to QD(z,r1) <0.6 along the lateral position ±r0 of the first ring [see Fig. 6(g)] and found a stronger decay in depletion efficiency along the first ring because of a loss of STED photons in this area mainly due to scattering. The scattered STED light also depletes the fluorescence in the central lobe, as described by Eq. (3). Further, it can be seen in Fig. 6(h) that the lateral profiles of the depletion efficiencies QD(x,z=30μm) and QD(x,z=75μm) still reveal a peak in depletion at the position of the first ring.

5. DISCUSSION AND CONCLUSION

In this study, we addressed the question of whether the propagation stability and the overlap of a 0th order and 3rd order Bessel beam propagating in inhomogeneous materials can exploit the STED principle for the generation of thin fluorescent light needles.

We discuss the design of the experiments, the unexpected nature of the results and how they can be explained, and what is necessary to apply these principles to light sheet microscopy or other optical measurement technologies.

Light sheet microscopy (LSM) has its main advantages in the fast and efficient acquisition of large 3D data stacks, where fluorescence bleaching is minimized through an efficient photon budget. STED microscopy, on the other hand, is a point scanning technique with modest acquisition speed, strong fluorescence bleaching, and very high spatial resolution (mostly in 2D images). The combination of these two techniques could result in an advantageous compromise regarding imaging speed, resolution, contrast, and bleaching. Since a very good overlap between the excitation and depletion beam, even in inhomogeneous media, is required, Bessel beams with their extraordinary propagation stability are much better suited than Gaussian beams [6,13]. The Bessel STED beam, however, must have sufficient power to be distributed over the volume of the first rings of the Bessel beam. It has been shown in many publications that the fluorescence depletion (and thereby the width of the illumination focus) can be increased with a higher STED intensity. To verify that this is also true for fluorescence depletion along a line (and not a point) was not the intention of the study. The application of a cw power of PST=1W, available in our STED beam—resulting in a ratio of IST/Isat6—was already so high that bleaching was an issue in some experiments. Hence, the main intention of our study was to demonstrate that efficient fluorescence excitation and depletion is possible along a line, even in large, inhomogeneous media. Our results indicate that the usage of higher intensities should not result in thinner light needles (the beam’s central lobe is only little affected by depletion) but generate less background through a more efficient fluorescence depletion in the ring system. In this way, thin and propagation stable light needles should be possible that can be scanned laterally in the plane of focus to achieve extraordinary image quality through very thin light sheets in LSM. This cannot be achieved with the cw beam photon densities available in our configuration, but it could be achieved with a pulsed STED setup with a sufficiently low repetition rate. This, however, usually comes with increased costs and complexity of the optical setup. If imaging speed is less of an issue then fluorophore bleaching, it is useful to replace the STED principle by the RESOLFT principle using switchable fluorophores [21], when their switching speed will have been improved in the future.

Our experimental concept of using a single SLM for the parallel and independent manipulation of the phases of both illumination beams turned out to be quite advantageous. By observing the propagation behavior in a fluorescing solution in the object plane and by recording their transmitted angular (Fourier) spectra, the SLM turned out to be the best solution to control the overall overlap of both beams. In a recent theory study, we evaluated the optimal beam parameters numerically, and these parameters were also optimal in the experiments with beam propagation lengths of at least 100 μm. In conventional point scanning STED, the beam overlap length is less than 1 μm, and the STED beam consists of only one ring. For line STED, focusing lenses with numerical apertures in the range of NA=0.20.3 are required and epsilon values ϵ<0.8 that do not distribute too high photon energies in the Bessel beams’ ring systems (ideally<30%). Using these beam parameters, we found that our depletion efficiencies of QD=0.60.8, achieved in the important first Bessel ring, coincide well with those predicted by our theory study. As predicted by the theory and confirmed in our experiments, fluorescence depletion in the second and outer rings dropped to QD=0.30.5, provided that scattering or the propagation length were small (Figs. 36). For imaging applications, it might be helpful to use confocal line detection (i.e., a rolling shutter of a camera) to additionally block the remaining fluorescence emitted from the outer beam rings.

The space variant depletion efficiency. The most striking results in this paper are the self-reconstructing properties of both Bessel beams and the resulting fluorescence distribution. Figures 5(a) and 5(b) demonstrate the known effect that Gaussian beams are strongly deflected by larger refractive index inhomogeneities, while Bessel beams remain propagation stable. Phase shifts induced from obstacles, such as glass spheres, can easily displace a constructive beam interference by a fraction of a wavelength. It is, therefore, surprising that the electric field and the intensity overlaps of both beams are so precise, even after strong scattering, that efficient fluorescence depletion occurs only at the desired positions. The intensity distributions of each first ring in both the excitation and the STED beam, in Figs. 5(c)5(e), reveal that the central Bessel lobe is hardly depleted, while the first ring at around z=90μm is significantly depleted, especially on the upper side. Exemplarily, the significance for potential imaging applications can be illustrated by two hypothetical objects, one within the main lobe, and another within the first side lobe (first ring). In a Gaussian beam with limited optical sectioning (spatial resolution), both objects would be illuminated and detected with nearly the same low intensity while with a Bessel beam with a similar bright intensity. However, only by switching on the STED Bessel beam are the intensities of both objects clearly different and can be separated with superior optical sectioning. An additional effect is important, when the beam intensities can be separated in unscattered and scattered parts: according to Eq. (3), the fluorescence terms due to scattering, Fs(ηshEX,u+ηuhEX,s+ηshEX,s), destroy the desired fluorescence of the unscattered illumination beam hEX,u(r) by the scattered STED beam hST,s(r) or the term ηs(r)=Isat/(Isat+hST,s(r)). Therefore, the propagation stability (little scattering and deflection) of the STED beam is of utmost importance.

The beam propagation through a homogeneous distribution of scatterers, illustrated in Fig. 6, shows once more that beam spreading is much larger with Gaussian beams than with Bessel beams. While the decay of the central Bessel lobe is hardly affected by the depletion beam, even in large propagation distances z=75μm [Fig. 6(h)], the decay of fluorescence depletion in the first ring is smaller than the decay along the centers of other beams. This can be explained by the dependency of the depletion efficiency according to Eq. (4), which decays non-exponentially, as visible in the depletion behavior QD(r0,z) at the location r0 of the first ring. This effect demonstrates that the nonlinear interaction of different beams can result in beneficial ratios of excitation and depletion rates when acting on the same fluorophores. These two rates—and thereby the STED efficiency—are heavily influenced by the local phase differences of the incident photons.

Despite the strong scattering of the beams during propagation through inhomogeneous media, resulting in individual and relative phase delays of photons (or plane waves) and thereby in spatial shifts of the interference intensities, the STED principle along a 100-μm-long line works surprisingly well. The resulting fluorescence light needles are unexpectedly propagation stable in inhomogeneous media and may open a range of new applications in bio-photonic and related technologies.

Funding

Bundesministerium für Bildung und Forschung (BMBF) (0315690A); Deutsche Forschungsgemeinschaft (DFG) (RO 3615/8).

Acknowledgment

The authors thank Tobias Meinert, Luis Köbele, and Florian Fahrbach for helpful comments on the paper. C. G. K. constructed the setup, performed experiments and simulations, analyzed the data, and prepared most of the figures. A. R. initiated and supervised the project, developed the theory together with C. G. K. and wrote the paper.

 

See Supplement 1 for supporting content.

REFERENCES

1. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010). [CrossRef]  

2. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012). [CrossRef]  

3. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012). [CrossRef]  

4. B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015). [CrossRef]  

5. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988). [CrossRef]  

6. T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016). [CrossRef]  

7. J. Li, D. R. Beaulieu, H. Paudel, R. Barankov, T. G. Bifano, and J. Mertz, “Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor,” Optica 2, 682–688 (2015). [CrossRef]  

8. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).

9. L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991). [CrossRef]  

10. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010). [CrossRef]  

11. F. O. Fahrbach, V. Gurchenkov, K. Alessandri, P. Nassoy, and A. Rohrbach, “Light-sheet microscopy in thick media using scanned Bessel beams and two-photon fluorescence excitation,” Opt. Express 21, 13824–13839 (2013). [CrossRef]  

12. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011). [CrossRef]  

13. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012). [CrossRef]  

14. B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014). [CrossRef]  

15. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994). [CrossRef]  

16. P. Zhang, P. M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22, 12398–12409 (2014). [CrossRef]  

17. C. Gohn-Kreuz and A. Rohrbach, “Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle,” Opt. Express 24, 5855–5865 (2016). [CrossRef]  

18. T. Scheul, I. Wang, and J.-C. Vial, “STED-SPIM made simple,” Opt. Express 22, 30852–30864 (2014). [CrossRef]  

19. M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011). [CrossRef]  

20. M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015). [CrossRef]  

21. P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

22. F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express 18, 24229–24244 (2010). [CrossRef]  

23. M. D. Feit and J. A. Fleck Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978). [CrossRef]  

24. A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. 34, 3041–3043 (2009). [CrossRef]  

25. M. Leutenegger, C. Eggeling, and S. W. Hell, “Analytical description of STED microscopy performance,” Opt. Express 18, 26417–26429 (2010). [CrossRef]  

References

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  1. S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
    [Crossref]
  2. M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
    [Crossref]
  3. J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
    [Crossref]
  4. B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
    [Crossref]
  5. I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
    [Crossref]
  6. T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016).
    [Crossref]
  7. J. Li, D. R. Beaulieu, H. Paudel, R. Barankov, T. G. Bifano, and J. Mertz, “Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor,” Optica 2, 682–688 (2015).
    [Crossref]
  8. M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).
  9. L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
    [Crossref]
  10. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
    [Crossref]
  11. F. O. Fahrbach, V. Gurchenkov, K. Alessandri, P. Nassoy, and A. Rohrbach, “Light-sheet microscopy in thick media using scanned Bessel beams and two-photon fluorescence excitation,” Opt. Express 21, 13824–13839 (2013).
    [Crossref]
  12. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
    [Crossref]
  13. F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
    [Crossref]
  14. B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
    [Crossref]
  15. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
    [Crossref]
  16. P. Zhang, P. M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22, 12398–12409 (2014).
    [Crossref]
  17. C. Gohn-Kreuz and A. Rohrbach, “Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle,” Opt. Express 24, 5855–5865 (2016).
    [Crossref]
  18. T. Scheul, I. Wang, and J.-C. Vial, “STED-SPIM made simple,” Opt. Express 22, 30852–30864 (2014).
    [Crossref]
  19. M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011).
    [Crossref]
  20. M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015).
    [Crossref]
  21. P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).
  22. F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express 18, 24229–24244 (2010).
    [Crossref]
  23. M. D. Feit and J. A. Fleck, “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978).
    [Crossref]
  24. A. Rohrbach, “Artifacts resulting from imaging in scattering media: a theoretical prediction,” Opt. Lett. 34, 3041–3043 (2009).
    [Crossref]
  25. M. Leutenegger, C. Eggeling, and S. W. Hell, “Analytical description of STED microscopy performance,” Opt. Express 18, 26417–26429 (2010).
    [Crossref]

2016 (3)

T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016).
[Crossref]

C. Gohn-Kreuz and A. Rohrbach, “Light-sheet generation in inhomogeneous media using self-reconstructing beams and the STED-principle,” Opt. Express 24, 5855–5865 (2016).
[Crossref]

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

2015 (3)

M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015).
[Crossref]

J. Li, D. R. Beaulieu, H. Paudel, R. Barankov, T. G. Bifano, and J. Mertz, “Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor,” Optica 2, 682–688 (2015).
[Crossref]

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
[Crossref]

2014 (3)

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

P. Zhang, P. M. Goodwin, and J. H. Werner, “Fast, super resolution imaging via Bessel-beam stimulated emission depletion microscopy,” Opt. Express 22, 12398–12409 (2014).
[Crossref]

T. Scheul, I. Wang, and J.-C. Vial, “STED-SPIM made simple,” Opt. Express 22, 30852–30864 (2014).
[Crossref]

2013 (1)

2012 (3)

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref]

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

2011 (2)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011).
[Crossref]

2010 (4)

F. O. Fahrbach and A. Rohrbach, “A line scanned light-sheet microscope with phase shaped self-reconstructing beams,” Opt. Express 18, 24229–24244 (2010).
[Crossref]

M. Leutenegger, C. Eggeling, and S. W. Hell, “Analytical description of STED microscopy performance,” Opt. Express 18, 26417–26429 (2010).
[Crossref]

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

2009 (1)

2006 (1)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).

1994 (1)

1991 (1)

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[Crossref]

1988 (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[Crossref]

1978 (1)

Alessandri, K.

Alfano, R. R.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[Crossref]

Balázs, B.

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

Barankov, R.

Beaulieu, D. R.

Bembenek, J. N.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Besir, C.

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

Betzig, E.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Bifano, T. G.

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Boccara, A. C.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
[Crossref]

Bohme, R.

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Freund, I.

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M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015).
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M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011).
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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Goodwin, P. M.

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Hammer, J. A.

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M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015).
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M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011).
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P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

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B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
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P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

Hufnagel, L.

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Kim, J.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
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Kim, M.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
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Kräusslich, H.-G.

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
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Legant, W. R.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Lerosey, G.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
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Leutenegger, M.

Li, J.

Lippincott-Schwartz, J.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
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Liu, Z.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).

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T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016).
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Mertz, J.

Milkie, D. E.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
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Mimori-Kiyosue, Y.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Mitchell, D. M.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491, 232–234 (2012).
[Crossref]

Mullins, R. D.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Nassoy, P.

Norlin, N.

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

Palme, K. J.

T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016).
[Crossref]

Papadopoulos, I. N.

B. Judkewitz, R. Horstmeyer, I. M. Vellekoop, I. N. Papadopoulos, and C. Yang, “Translation correlations in anisotropically scattering media,” Nat. Phys. 11, 684–689 (2015).
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Park, Q.-H.

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
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Paudel, H.

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref]

Popoff, S. M.

S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
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Reymann, A.-C.

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
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Appl. Opt. (1)

Biophys. J. (1)

M. Friedrich, Q. Gan, V. Ermolayev, and G. S. Harms, “STED-SPIM: stimulated emission depletion improves sheet illumination microscopy resolution,” Biophys. J. 100, L43–L45 (2011).
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J Biomed. Opt. (1)

M. Friedrich and G. S. Harms, “Axial resolution beyond the diffraction limit of a sheet illumination microscope with stimulated emission depletion,” J Biomed. Opt. 20, 106006 (2015).
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Nat. Commun. (1)

F. O. Fahrbach and A. Rohrbach, “Propagation stability of self-reconstructing Bessel beams enables contrast-enhanced imaging in thick media,” Nat. Commun. 3, 632 (2012).
[Crossref]

Nat. Methods (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
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Nat. Photonics (2)

M. Kim, Y. Choi, C. Yoon, W. Choi, J. Kim, Q.-H. Park, and W. Choi, “Maximal energy transport through disordered media with the implementation of transmission eigenchannels,” Nat. Photonics 6, 583–587 (2012).
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Nat. Phys. (1)

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Nature (1)

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Opt. Express (6)

Opt. Lett. (2)

Optica (1)

Phys. Rev. Lett. (2)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
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S. M. Popoff, G. Lerosey, R. Carminati, M. Fink, A. C. Boccara, and S. Gigan, “Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media,” Phys. Rev. Lett. 104, 100601 (2010).
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Proc. Natl. Acad. Sci. USA (2)

P. Hoyer, G. de Medeiros, B. Balázs, N. Norlin, C. Besir, J. Hanne, H.-G. Kräusslich, J. Engelhardt, S. J. Sahl, S. W. Hell, and L. Hufnagel, “Breaking the diffraction limit of light-sheet fluorescence microscopy by RESOLFT,” Proc. Natl. Acad. Sci. USA 113, 3442–3446 (2016).

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. USA 103, 17137–17142 (2006).

Sci. Rep. (1)

T. Meinert, O. Tietz, K. J. Palme, and A. Rohrbach, “Separation of ballistic and diffusive fluorescence photons in confocal light-sheet microscopy of arabidopsis roots,” Sci. Rep. 6, 30378 (2016).
[Crossref]

Science (2)

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-Dimaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769–771 (1991).
[Crossref]

B.-C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A.-C. Reymann, R. Bohme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346, 1257998 (2014).
[Crossref]

Supplementary Material (2)

NameDescription
» Supplement 1       Supplementary Material
» Visualization 1       Propagation of four beams through glass spheres

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Figures (6)

Fig. 1.
Fig. 1. Schematic of measurement principle. (a) Two phase holograms are used to generate the excitation beam (blue arrow and frame) and the depletion beam (yellow), with intensities IEX(r) and IST(r). Both Bessel beams, differing in angular and radial momentum, are superimposed and focused by an objective lens onto a cluster of scattering spheres. After fluorescence depletion, a thin fluorescent light needle with intensity Itot(r) is generated and detected by a perpendicularly arranged objective lens (green arrow and frame). Theoretically obtained intensity line scans illustrate the depletion of the fluorescence in the Bessel beam’s ring system. (b) Numerical simulation of beam propagation and scattering at glass beads (in gray) by the excitation beam (in blue), the depletion beam (in orange) and the remaining needle-like fluorescence of the central beam lobe (in green).
Fig. 2.
Fig. 2. Photos and sketch of the experimental setup. The excitation beam and the STED beam are projected onto the left and right halves of a SLM and are then superimposed by beam splitters (BS). The angular spectra of both beams are projected by a lens L1 onto a scanning mirror (SM) with zeroth order beam block (B). Two lenses (SL and TL) project the tilted angular spectra onto the back focal plane (BFP) of the IO, which focuses the Bessel beams into the sample chamber. The SO images the angular spectrum of the scattered laser light onto a camera (Camsca), whereas the fluorescence generated in the sample chamber is collected by the detection objective (DO) and imaged onto another camera (Camdet).
Fig. 3.
Fig. 3. Beam profiling. (a) A 0.75-μm fluorescent bead embedded in agarose gel is scanned laterally with different beams. (b) Resulting fluorescence images of the 0th order excitation Bessel beam (blue), the 3rd order STED Bessel beam (red) and the combination of both beams (green). (c) Fluorescence line profiles show fluorescence depletion only in the Bessel ring system and small fluorescence excitation by the STED beam itself, which is typically subtracted (-S) in postprocessing from the combination of both beams (Exc/STED-S). (d) Space-dependent probability for spontaneous emission Q(xb) averaged over 19 beads (solid line), and the standard deviation from the mean (shaded area).
Fig. 4.
Fig. 4. Single bead imaging. (a) Different beams are scanned in lateral x-direction across isolated 0.75-μm beads. (b) Bead images in the yz-plane without (blue frame) and with (green frame) fluorescence depletion (STED). (c) Magnification of marked area in (b). (d) Normalized image intensity profiles F(y) without STED beam (blue), with STED beam (green), and the fluorescence bead image of the STED beam alone (red). (e) The 1/e Image widths δy(z) from different bead images at propagation distances between z=12 and z=42μm without (blue) and with (green) STED beam.
Fig. 5.
Fig. 5. Beam self-reconstruction behind two 8-μm glass spheres. Images F(x,z) of propagating and scattering beams exciting fluorescence in a labeled agarose gel. Image width corresponds to a propagation length of 140 μm. Two unlabeled beads appear dark. (a) Fluorescence image of the Gaussian beam reveals its large diameter and strong deflection at the spheres. Two hypothetic round objects (yellow circles) are images in detection direction, indicated by two elongated PSFs. The real and the ideal images differ significantly. (b) Zeroth order Bessel beam reconstructs its intensity profile after scattering at both spheres. Hypothetic real images are more like the ideal images. (c) In combination with a 3rd order STED Bessel beam, the fluorescence in the ring system can be depleted, despite strong scattering with a reasonable efficiency, as indicated in (f) by the two line scans taken at z1=20μm and z2=90μm. Hypothetic real images resemble the ideal images as also visible in Fig. 5(d) without scatterers. (e) Distribution QD(x,z) illustrates the space-dependent efficiency of fluorescence depletion. Scale bar: 10 μm.
Fig. 6.
Fig. 6. Beam propagation over 120 μm through a cluster of beads, fluorescence generation, and STED efficiency. Fluorescing polystyrene beads with 0.35-μm diameter are embedded in agarose gel at concentrations cvol=0.13% (left) and cvol=0.52% (right). Maximum projections of images revealing the intensity profile of (a) a single Bessel beam, (b) a Bessel beam with the STED beam and (c) a Gaussian beam. (d) Space varying depletion efficiency QD(x,z) derived from (b) reaching efficiencies at the first Bessel ring of up to 60%, which is shown by the bright yellow areas. Central parts of (a)–(d) are magnified in (e) and (f) for cvol=0.13% and cvol=0.52%, respectively. (g) Average depletion efficiencies along z in the center and the ring system for the three bead concentrations. (h) Fluorescence line profiles F(x,z0) at z0=30μm (solid line) and z0=75μm (dashed line), and corresponding depletion efficiencies QD(x,z0). Profiles are averaged over 60 pixels, that is, Δz6μm. (i) Axial fluorescence profiles F(x=0,z) for two different concentrations of scatterers averaged over the beam centers of the Bessel beam (left), the Bessel beam with STED (center) and the Gaussian beam (right). (j) Comparison of decay constants for all beam types at three different bead concentrations.

Equations (4)

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E˜(kr,ϕ˜)E˜0·(δ(krk0NA)*exp(kr2/Δkr2))·exp(iϕ˜)
E(r,ϕ)A·J(k0NA·r)·exp(r2·Δkr2)·exp[i(ϕ+kzz)].
F(r)=Fu(r)+Fs(r)Cext(r)·Qfl·(ηu(r)+ηs(r))·(hEX,u(r)+hEX,s(r))=Cext(r)·Qfl·[(ηuhEX,ugood)+(ηshEX,ubad+ηuhEX,sgood+ηshEX,sgood)].
QD(r)=1ηu(r)ηs(r)=(1+IsathST,u(r)+hST,s(r))1.

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