Laterally swept light-sheet microscopy enhanced by pixel reassignment for photon-efficient volumetric imaging

Abstract. In light-sheet fluorescence microscopy, the axial resolution and field of view are mutually constrained. Axially swept light-sheet microscopy (ASLM) can decouple the trade-off, but the confocal detection scheme using a rolling shutter also rejects fluorescence signals from the specimen in the field of interest, which sacrifices the photon efficiency. Here, we report a laterally swept light-sheet microscopy (LSLM) scheme in which the focused beam is first scanned along the axial direction and subsequently laterally swept with the rolling shutter. We show that LSLM can obtain a higher photon efficiency when similar axial resolution and field of view can be achieved. Moreover, based on the principle of image scanning microscopy, applying the pixel reassignment to the LSLM images, hereby named iLSLM, improves the optical sectioning. Both simulation and experimental results demonstrate the higher photon efficiency with similar axial resolution and optical sectioning. Our proposed scheme is suitable for volumetric imaging of specimens that are susceptible to photobleaching or phototoxicity.


Introduction
Light-sheet fluorescence microscopy has become an indispensable tool for biological imaging because of its high spatiotemporal resolution and low phototoxicity. [1][2][3] It eliminates the out-of-focus excitation by illuminating the specimen from the side with a sheet of light. 4,5 Therefore, most of the excited fluorophores can be collected by the detection camera. This excitation and detection scheme and the exclusion of pinholes significantly reduce photobleaching and phototoxicity, which makes it suitable for long-term imaging. In addition, the thin light sheet improves optical sectioning and provides better axial resolution. However, generating a thin and uniform light sheet is difficult because the thickness and field of view (FoV) limit each other. 6 For a typical Gaussian light sheet, the light sheet only covers a region of ∼2 Rayleigh lengths, which is quadratically proportional to its thickness.
Propagation invariant beams can persist at a thin thickness over an arbitrarily long distance, including Bessel beams [7][8][9] and Airy beams, 10,11 while the conflict between light-sheet thickness and FoV remains. Moreover, these nondiffractive beams contain more sidelobes, which will introduce more out-of-focus illumination and increase phototoxicity. 12 Another method is to use multiple light sheets with swept focus 13 or tiled beams. [14][15][16][17] Swept focus light-sheet microscopy (SFLM) generates a virtual light sheet with a higher aspect ratio. However, multiple beams also introduce more sidelobes, which decrease the axial resolution and worsen the optical sectioning.
A slit can efficiently reject the sidelobes of the excitation beams. In light-sheet microscopy, the rolling shutter of sCMOS cameras can synchronize with the beam scanning and naturally serve as the slit. For example, the rolling shutter can eliminate the sidelobes of Gaussian beams 18 or Bessel beams 19 in digital scanned light-sheet microscopy. While the conflict between light-sheet thickness and FoV remains in these methods, axially swept light-sheet microscopy (ASLM) uses the synchronized rolling shutter of a camera to image only the in-focus region of a light sheet so that an arbitrarily large FoV with optimal axial resolution can be achieved. 20,21 However, like the pinhole in confocal microscopes, the slit or the rolling shutter rejects many fluorescent signals and sacrifices the photon efficiency of lightsheet microscopy. As shown in Fig. 1(a), a Gaussian beam is first laterally scanned and subsequently axially swept in synchronization with the rolling shutter of the sCMOS camera. The fluorescence signal outside the rolling shutter is rejected, so a larger imaging FoV occurs at the price of less photon efficiency.
Imaging scanning microscopy (ISM) can achieve the optimal resolution of confocal microscopy without sacrificing the efficiency of photon collection. 22,23 Array detectors are used in ISM to record images at each scan position. Each pixel of the array can act as a confocal pinhole to simultaneously acquire many confocal images. Then, these confocal images are reassembled through pixel reassignment, either computer-based or opticsbased. 24 The final image has the optimal resolution and optical sectioning of the confocal microscopy but with no light loss. We anticipate that the same principle can be applied to light-sheet microscopy with a swept focus. A series of images at different illumination foci can be acquired and reassembled with pixel reassignment. The final image should achieve improved axial optical sectioning with little loss of fluorescent signals. Thus, the tradeoff between light-sheet thickness and FoV can be decoupled without sacrificing the photon efficiency of fluorescent signals.
Here, we present the laterally swept light-sheet (LSLM) scheme, which is first scanned along the axial direction and subsequently laterally swept [ Fig. 1(a)]. Compared with ASLM, this setup has two primary advantages. First, the excitation light is more constrained after axial scanning, so the majority of the excited fluorescence is within the rolling shutter and can be collected by the detection pixels. Second, the full width at halfmaximum (FWHM) of the beam profile is much smaller than that of the ASLM, which makes it possible to adopt the ISM concept with pixel reassignment. In this paper, we systematically compare the ASLM and LSLM with simulation studies Fig. 1 Schematic comparison between the ASLM and LSLM. (a) In the ASLM, a focused Gaussian beam is first laterally scanned that generates a light sheet perpendicular to the direction of beam propagation. Afterward, the focus of the Gaussian beam is axially swept in synchronization with the rolling shutter of the camera. In the LSLM, a Gaussian beam is first axially scanned that forms a "light needle" along the direction of beam propagation. Then, the beam is laterally swept in synchronization with the camera. Here, the axial direction is along the propagation of the beam and the lateral direction is perpendicular to the propagation of the beam. With the rolling shutter, only the region excited by the in-focus, thin light sheet is imaged by the camera. (b) Comparison of light sheets generated by lateral scanning of the ASLM and axial scanning of the LSLM. The images on the Y -Z plane show the cross section of the light sheet, and the yellow dashed lines indicate the rolling shutter. With the same rolling shutter, the ASLM shows better axial optical sectioning, but the LSLM contains more excitation power in the shutter region, which is more photon-efficient. and experiments to demonstrate that the LSLM shows better axial resolution than the ASLM when a high photon efficiency is required, particularly for the ISM-enhanced LSLM (iLSLM).

Principle of the LSLM
The scanning schematics of the ASLM and LSLM are compared in Fig. 1(a). In the ASLM, the lateral scanning of the Gaussian beams improves the axial resolution in the in-focus region. However, because the rolling shutter is applied perpendicular to the beam propagation direction, a large region of a specimen outside of the rolling shutter is excited, while the emitted fluorescence is not detected by the camera. When the fluorophores are widely distributed and excited by the light sheet, only the fluorescence within the rolling shutter can be detected, and the fluorescence outside the rolling shutter is wasted. A larger entire imaging FoV corresponds to a lower efficiency of fluorescence detection. When the rolling shutter becomes narrower, a higher axial resolution and better optical sectioning can be obtained at the cost of the lower collection efficiency of fluorescent signals. Therefore, the width of the rolling shutter is a balance between photon efficiency and axial resolution or optical sectioning.
In contrast, the Gaussian beams are first axially scanned in the LSLM, and the rolling shutter is applied along the beam propagation direction. Following the definition of the ASLM, 20,21,25 we set the direction of the rolling shutter as the Y axis and term the beam propagation as the axial scanning direction. From the beam profiles along the Y axis [ Fig. 1(b)], we find that the power of the LSLM light sheet is more constrained within the rolling shutter, which should be more photonefficient. To quantitatively compare the performance between the ASLM and LSLM, we conduct theoretical simulations based on the scalar propagation model considering a coherent, monochromatic, and medium numberical aperture (N.A.) imaging system. The simulation was performed based on the beam simulator software developed by Remacha et al. 6 Briefly, the beam intensity distribution is where Eðx; z; yÞ is the electricity distribution. Eðk x ; k z Þ is the electricity distribution in the back focus plane (BFP). y is the position along the propagation direction with Δy from the focus.
where n is the refraction index, and k 0 ¼ 2π∕λ is the vacuum wavenumber. For a Gaussian beam, the amplitude at the BFP can be considered as where N.A. is the numerical aperture of the excitation objective. In Fig. 2, we set N.A. = 0.3, n ¼ 1.33, λ ¼ 473 nm, and the imaging FoV is 300 μm × 300 μm in the simulation, which is consistent with our experimental settings. The simulation with N.A. = 0.5 ( Although the axial FWHM of the LSLM is close to that of the ASLM, the axial scanning in the LSLM will introduce larger sidelobes in the "light needle" [ Fig. 2(d)], and the problem of sidelobes will become more severe when the scanning FoV increases. The optical sectioning width (OS), which is defined as the range containing 63% (obtained by 1 − 1∕e) of the detected beam power, 12 is OS ASLM ¼ 0.69 μm, OS LSLM ¼ 2.32 μm, and OS SFLM ¼ 8.46 μm, respectively. In contrast, the light-sheet thickness of laterally scanned beams in the ASLM is diffraction-limited. In summary, both the LSLM and ASLM show approximately tripled axial resolution of the conventional SFLM, and both have thinner optical sectioning. While the LSLM still has a similar axial resolution to the ASLM, the LSLM has worse optical sectioning than the ASLM. However, the FWHM of the axial scanning beams is close to the diffraction limit on both the Y axis and Z axis, so the pixel reassignment can effectively eliminate the sidelobe effect of the LSLM.

Pixel Reassignment Increases the Optical Sectioning of the LSLM
The photon efficiency is related to the energy ratio of the detected fluorescence within the rolling shutter to all the emitted fluorescence throughout the FoV. The relationship between the energy ratio and the width of the rolling shutter is plotted in Fig. 2(f). In addition, the relationships between the axial FWHM and the rolling shutter width are plotted in Fig. 2(g). A larger rolling shutter will result in a higher photon efficiency but worse axial resolution and optical sectioning. To fairly compare the ASLM and LSLM, we plot their axial resolutions corresponding to the same energy ratio in Fig. 2(h). When a high energy ratio or photon efficiency is required, LSLM shows about 9% improvement in the axial resolution compared to the ASLM in terms of the axial FWHM. For example, the highlighted regions in Figs. 2(a) and 2(b) indicate the appropriate shutter widths of 86.0 μm for the ASLM and 3.6 μm for the LSLM, within which they both have an energy ratio of ∼50% and an axial FWHM of ∼1.2 μm When an energy ratio above 18% (10%, N.A. = 0.5) is desired, the LSLM creates a thinner axial FWHM than the ASLM. Nevertheless, the optical sectioning of the LSLM is about three times thicker than that of the ASLM, so we will try to eliminate the sidelobe effect in the LSLM with pixel reassignment. Since the LSLM has a comparable resolution along the scanning axis to the detection point spread function (PSF), pixel reassignment based on the ISM principle can increase the axial resolution and improve optical sectioning. In this work, we only apply the digital pixel reassignment to the multiple raw images, so that the imaging results of the ASLM, LSLM, and iLSLM are processed from the same raw data to guarantee a fair comparison. The drawback is that the digital pixel reassignment requires more raw images and takes a longer acquisition time.
In our experiments, 22 axial scanning and 30 lateral scanning are performed, acquiring 660 raw images for one scanning cycle. Nevertheless, the acquisition of the raw images at every focus is for a fair comparison of the ASLM, LSLM, and iLSLM. In real experiments, the axial scanning of the iLSLM can be performed within one exposure since the refreshing rate of the spatial light modulator (SLM) is fast enough. Therefore, only 30 images with lateral scanning are acquired for reconstruction with pixel reassignment, resulting in a 30-fold increase of the acquisition time. Optical ISM 24 can also achieve doubled spatial resolution. In the all-optical realization, the pixel reassignment is achieved by the descanning or rescanning of the emitted fluorescence. The drawback is that the scaling of the focused image is determined by the two-lens relay optics and is fixed. However, optical pixel reassignment can obtain the super-resolution image in one frame, which is in principle applicable and remains to be our future work.
The spatial resolution of ISM can be quantitatively described as 23 when the detected photon is reassigned to the excitation center by a factor of m ¼ σ 2 exc ∕ðσ 2 exc þ σ 2 det Þ. 24 The excitation PSF, detection PSF, and PSF of the ISM are approximated by Gaussian functions, and σ exc , σ det , and σ ISM are the corresponding standard deviations. To obtain a higher resolution in ISM (smaller σ ISM ), σ exc and σ det should be as small as possible. While σ det is determined by the detection objective and fixed, σ exc is determined by the beam type of the light sheet. For the ASLM, σ exc relates to the axial profile of the Gaussian PSF, which is much larger than that of the lateral profile. Therefore, the combination of the ISM and ASLM will slightly enhance the spatial resolution and optical sectioning due to the difference between σ exc and σ det . In comparison, the σ exc and σ det are close in the LSLM, which can better increase the spatial resolution.
To verify the performance of pixel reassignment in the LSLM, we simulate the ASLM and LSLM imaging of fluorescent beads in a 3D volume. We set N.A. = 0.3, n ¼ 1.33 for both excitation and detection, λ ¼ 473 nm and 525 nm for excitation and detection, respectively, voxel size of 720 nm, and imaging volume of 72 μm × 720 μm × 72 μm, which is consistent with our experimental settings. The bead size in the simulation is set to be one voxel. The first step of the simulation is the same for the ASLM and LSLM. A focused Gaussian beam is axially and laterally scanned to excite the specimen. A series of images are simulated in which each image is excited by a single-focus Gaussian light sheet. Therefore, the ASLM and LSLM results are generated from the same dataset and compared under identical conditions. Next, we simulate the lateral scanning of the ASLM by summing the laterally scanned images and simulate the axially scanned "light needle" of the LSLM by summing the axially scanned images, as illustrated in Fig. 1. The imaging process of the first step could be expressed as where I ASLM1 ðx; y − y s ; z − z s Þ and I LSLM1 ðx − x s ; y; z − z s Þ are the signals delivered by the imaging system after first scanning for the ASLM and LSLM, respectively. oðx; z; yÞ is the bead distribution, I ex ðx − x s ; z; y − y s Þ is the focused Gaussian beam for excitation at the lateral and axial scanning positions x s and y s , Ã means convolution and h det ðx; y; zÞ is the detection PSF.
Only the in-focus signal is captured by the camera, and a digital slit mask that serves as the rolling shutter is applied to each image during the second scanning where I ASLM2 ðx; y − y s ; z 0 − z s Þ and I LSLM2 ðx − x s ; y; z 0 − z s Þ are the recorded signals in the second scanning for the ASLM and LSLM, respectively. I ASLM1 ðx; y; z 0 − z s Þ and I LSLM1 ðx; y; z 0 − z s Þ are the signals on the detection focal plane after first scanning for the ASLM and LSLM. Sðx; y − y s Þ and Sðx − x s ; yÞ are the rolling shutters on the conjunction positions of excitations for the ASLM and LSLM, respectively. Finally, a 3D stack of images could be obtained considering all the scanning positions in which I ASLM ðx; y; z s Þ and I LSLM ðx; y; z s Þ are the final ALSM and LSLM images, respectively. For iLSLM, pixel reassignment is applied to LSLM images during the second scanning. The image is scaled down by a factor of m ¼ σ 2 exc ∕ðσ 2 exc þ σ 2 det Þ, which in practice is set to be 1/2 as σ exc and σ det are close in the LSLM, along the swept direction at each focus position. For the fluorophores with a large Stokes shift or with multiphoton excitation, the σ exc and σ det will be different because of the different excitation wavelengths and emission wavelengths, so the scaling factor should be chosen based on the equation. Then, the images are placed back in the same position and summed to obtain the final iLSLM image When all images are summed without a digital rolling shutter applied, the resulting image is equivalent to the SFLM image. The SFLM image collects more fluorescence signals but contains heavier sidelobes. Therefore, the photon efficiency of the ASLM and LSLM is calculated based on the SFLM image. Figures 3(a) and 3(b) show the simulated imaging results of fluorescence beads in the X-Y and X-Z planes. The upper part of Fig. 3(c) shows the profiles of the ASLM and iLSLM at 55% photon efficiency, and they have an axial FWHM of about 1.09 μm. The lower part of Fig. 3(c) shows the profiles of the ASLM and iLSLM at 80% photon efficiency, and the iLSLM has a higher axial resolution (FWHM iLSLM ¼ 1.15 μm) than the ASLM (FWHM ASLM ¼ 1.58 μm). We calculated the changes in the photon efficiency of the ASLM and iLSLM with increasing rolling shutter over the entire ratio range, and the results are shown in Fig. 3(d). As shown in Fig. 3(f), the iLSLM has a smaller axial FWHM than the ASLM at the same photon efficiency when the photon efficiency is higher than 55%. The "turning point" of 55% is related to the N.A. of the objective, but is not affected by the signal-to-noise ratio (SNR), according to further simulation studies in Fig. S2 in the Supplementary Material. Therefore, when the specimen is easy to photobleach or susceptible to phototoxicity, the iLSLM is a better choice than the ASLM.

Microscope Setup and Experimental Demonstration
We build a light-sheet microscope as shown in Fig. 4(a) that modulates the beam focus via a reflectively binary phase SLM. The SLM modulates the phase of the exciting light wave front and scans the beam in three dimensions. The pattern loaded for the SLM is calculated as described in previous work. 14,16 Briefly, we take the SLM as a thin focusable lens for axial scanning whose phase modulation function to achieve axial defocus Δy can be expressed as where x m and z m are the central coordinates of row m and column n of the SLM space pixel, respectively, k is the wavenumber of the incident beam, Δy is the axial focus shift, and f scan is the focal length of scan lens L2. For lateral scanning, the SLM can be considered as a grating. Therefore, we applied the beam tilt phase delay in the SLM. The function can be expressed as ϕ lateral ðx; zÞ ¼ kðx m sin θ x þ z n sin θ z Þ; (13) where θ x and θ z are the deflection angles of the beam in the x and z directions, respectively. We obtain the lateral coordinates ðx s ; z s Þ from the geometric relationship with the scanning deflection angle ðθ x ; θ z Þ, denoted as When the SLM is loaded with patterns without additional phase information, the beam is focused at the focus of the scan lens, as shown in Fig. 4(b). By loading the SLM with different patterns with additional phase information, we achieve 3D focus scanning, as shown in Figs. 4(c) and 4(d).
The LSLM and ASLM results are generated from the same dataset that consists of single-focus images. Then, we process the raw images following Eqs. (4)- (11) to obtain the LSLM, ASLM, and SFLM results. Figures 5(a) and 5(b) show the experimental imaging of 200 nm fluorescence beads (F8888, Thermofisher) in the X-Y and X-Z planes, when the photon  efficiencies of the ASLM and iLSLM are at 58%. In Fig. 5(a), the lateral resolution of the iLSLM can reach 1.43 μm. The upper part of Fig. 5(c) shows the profiles of the iLSLM (FWHM iLSLM ¼ 1.28 μm, OS iLSLM ¼ 2.69 μm) and ASLM (FWHM ASLM ¼ 1.35 μm, OS ASLM ¼ 2.04 μm) at a photon efficiency of 58%. The lower part shows the profiles of the iLSLM (FWHM iLSLM ¼ 1.60 μm, OS iLSLM ¼ 2.99 μm) and ASLM (FWHM ASLM ¼ 2.19 μm, OS ASLM ¼ 2.91 μm) when the photon efficiency reaches 80%. The experimental results are consistent with the simulation results, which demonstrates that the ISM method can effectively improve the axial resolution and optical sectioning of the LSLM. Similarly, we analyze the relationship among the rolling shutter width, axial resolution, and photon efficiency in Figs. 5(d)-5(f). We further imaged the U2OS cells with the proposed scheme. Figure 5(g) shows the X-Y view of the U2OS cell, and Figs. 5(h)-5(i) compare the X-Z images of the ASLM and iLSLM under the same photon efficiencies of 53% and 80%. By analyzing the simulation results and experimental results, we can conclude that the iLSLM has a better axial FWHM and optical sectioning than the ASLM when the photon efficiency exceeds 55%.

Conclusions
We propose the iLSLM scheme, which is laterally swept lightsheet microscopy with pixel reassignment based on the principle of an image scanning scope. First, we illustrate the generation of an axially swept light sheet and a laterally swept light sheet and compare their beam profiles. The laterally swept light sheet is more constrained and avoids the excitation of the specimen outside the rolling shutter. When all the final results are processed from the same raw data, both the LSLM and ASLM are three Fei Su received her master's of medicine (MM) degree from West China Clinical Medical College, Sichuan University in 2018. Currently, she is a PhD student at the Institute for Biomedical Materials and Devices (IBMD), Faculty of Science University of Technology Sydney, Australia, and a visiting scholar in the Department of Biomedical Engineering, Southern University of Science and Technology. Her research interests include bioimaging, pathological diagnosis and techniques, time-resolved pathological detection technology, artificial intelligence diagnostic system, biochemistry, and molecular biology.
Xi Peng received his BS degree from Shanxi University in 1998 and his PhD from Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, in 2003. Currently, he is a professor at the College of Future Technology, Peking University, Beijing, China. He is the author of more than 80 journal papers and has written three book chapters. His current research interests include multimodality high-speed superresolution fluorescence microscopy, lensfree microscopy, and twophoton STED hybrid microscope.
Dayong Jin received his PhD from Macquarie University of Australia in 2007. Currently, he is a fellow of the Australian Academy of Technology and Engineering, and is the head of the Joint Research Centre for Biomedical Materials and Instruments, University of Technology, Sydney, and Southern University of Technology, China. He has published more than 230 academic papers. His current research interests include bioengineering optics, nanoprobe technology, biomedical diagnostics, precision optical instruments, and automation.
Karl Zhanghao received his BS degree from Peking University in 2012 and his PhD from Peking University and Georgia Institute of Technology. He is a research assistant professor in the Department of Biomedical Engineering, Southern University of Science and Technology. His research interests include super-resolution microscopy, multidimensional live-cell imaging, and fluorescence polarization microscopy.