Deconvolution of light sheet microscopy recordings

We developed a deconvolution software for light sheet microscopy that uses a theoretical point spread function, which we derived from a model of image formation in a light sheet microscope. We show that this approach provides excellent blur reduction and enhancement of fine image details for image stacks recorded with low magnification objectives of relatively high NA and high field numbers as e.g. 2x NA 0.14 FN 22, or 4x NA 0.28 FN 22. For these objectives, which are widely used in light sheet microscopy, sufficiently resolved point spread functions that are suitable for deconvolution are difficult to measure and the results obtained by common deconvolution software developed for confocal microscopy are usually poor. We demonstrate that the deconvolutions computed using our point spread function model are equivalent to those obtained using a measured point spread function for a 10x objective with NA 0.3 and for a 20x objective with NA 0.45.


Additional methods
Software. We used MATLAB (Math Works, Germany) to implement our deconvolution tool and compiled it into a stand-alone Windows application using the MATLAB compiler. The source code, as well as the compiled version (requires 64 bit Windows version and at least 8 GB of RAM) can be downloaded from (http://www/xxx). Running the program requires the prior installation of the MATLAB Runtime libraries, which can be obtained free of charge e.g. from https://www.mathworks.com/products/compiler/mcr. The program ("LsDeconv.exe") can either be started from a windows console window (see the attached README.TXT file for command line parameters), or launched using a simple graphical user interface (LsDeconvGUI.exe). The deconvolution tool splits image stacks that are too big to fit into the RAM automatically into separate blocks so that even very large data sets can be processed (up to ~30 GB tested). As a single limitation, at least one entire z-layer must fit into the RAM after splitting the data into blocks, i.e. if the deconvolution is e.g. split into 3 x 4 x 5 (x y z) blocks, at least 3 x 4 = 12 data blocks must fit into the RAM for final stitching. For a computer equipped with 32 GB RAM this limits the size of a single camera image to approximately 8000 pixel x 8000 pixel. There is no limitation for the number of images in z-direction. solids, order no. F8811 Thermo Fisher Scientific, Austria) were embedded in gelatin. We found that gelatin from pork skin (Sigma-Aldrich, Austria, order no. G1890.~4% in water) exhibits higher transparency and less stray light generation than the more common embedding media agar or agarose. For preparing the gelatin blocks, the original vial containing 10 ml bead emulsion was carefully vortexed and a 1:100 pre-dilution in water was prepared. 2 g gelatin were dissolved in 50 ml boiling water. After cooling down to about 60°C, 2µl of the pre-diluted bead suspension were added and the mixture was carefully stirred on a magnetic stirrer. Histology forms of 7 x 7 x 5 mm 3 size, made from polystyrene (Plano GmbH, Germany, order-no. 2747-1) were filled with the mixture and stored in the fridge for at least 30 min to let the gelatin polymerize. The forms were wrapped into a piece of wet tissue to prevent them from drying and stored at 4°C. Before The GFP expressing drosophila melanogaster depicted in Fig. 3a was prepared and chemically cleared as described in 2 . The mouse embryo shown in Fig. 3b and Fig. 4a was prepared, immune-stained and rendered transparent as described in 3 . The GFP-expressing mouse hippocampus presented in Fig. 4b was prepared and chemically cleared as described in 4 .
The whole mouse from which the head is depicted in Fig. 4c was prepared and entirely chemically cleared as described in 5 . The whole brain of a GFP expressing mouse used for Fig. 4D was prepared and chemically cleared according to 6 .

Additional Results
Comparison of our program with DeconvolutionLAB using the PSF-generator plugin.
We compared the performance of our deconvolution program with the DeconvolutionLAB 7 deconvolution tool available as a plugin for ImageJ 8 (http://bigwww.epfl.ch/deconvolution/). The PSFs used for deconvolution were obtained using the PSF-generator 9 plugin available for ImageJ (http://bigwww.epfl.ch/algorithms /psfgenerator/). With our approach, a distinct improvement in image quality was visible (as already evident by Fig. 4A). However, the results obtained with DeconvolutionLab utilizing two different PSF models developed for confocal and wide-field microscopy (Gibson-Lanni 10 and Born and Wolf 9 ) calculated with the PSF-generator plugin were unsatisfactory. (Figure S1). This strongly suggest that for deconvolving light sheet microscope recordings with low magnification objectives existing programs designed for confocal or widefield microscopy are inappropriate. Noticeably, the quality of Fig. S1 c1, c2, and d2 is even worse compared to the original image. We further found that our program (compiled MATLAB code) runs significantly faster than DeconvolutionLab (Figure 1). Figure S1: Comparison of our deconvolution program with DeconvolutionLAB applying two different PSFs obtained with the ImageJ PSF-generator plugin. a) Singleoptical slice from the stack used for generating Figure 4A (Zeiss Fluar 2.5x, NA 0.12, Carl Zeiss, Germany). b) Same optical slice after deconvolution with our deconvolution program and a modeled PSF according to eq. 15 in the main article. (10 iteratations, no damping). c1-c4: Same image as in a and b deconvolved with DeconvolutionLAB 7 using the Landweber 11 algorithm (C1, D1), or the RL algorithm (c2, d2), respectively. The PSFs were modeled with the ImageJ PSF-generator 9 using the Gibson-Lanny model (c1, c2) or the Born and Wolf model (d1, d2). In all cases the number of iterations was fixed to ten rounds and no damping or pre-processing was used. Required

Change of deconvolution efficacy along the light sheet propagation axis
We determined the mean squared error (MSE) between original and deconvolved image stack within six equally sized stripes along the light sheet propagation axis (Figure S3). We found that after 30 iterations of RL-deconvolution, the mean squared differences are highest in the center position, corresponds to the location of the beam waist of the illumination light sheet (Figure 1a).
The curve reflects the broadening of the light sheet with increasing distances of the focus. The light sheet was generated using a single cylindrical lens of 80 mm focal length and a 6 mm wide slit aperture. Figure S3: Variation of deconvolution efficacy along the light sheet propagation axis. A) 3D reconstruction of the same data set as depicted in Figure S2 (2x, NA 0.14). The MSE was quantified between original and deconvolved image stack and plotted along five vertical stripes along the light sheet propagation axis. B) Same as in a, but for the data set shown in Figure 1b

Comparison of deconvolution results with other image enhancement methods
We compared the results obtained by our deconvolution algorithm using a computed PSF with two other image enhancement techniques frequently used in computational post-processing of microscopy data: a) rolling ball background subtraction 13 and b) contrast limited histogram equilibration (CLAHE) 14 (Figure S4). Compared to deconvolution both techniques have the advantage that they are computationally less expensive and therefore can be performed almost in real time.
Alternatively to deconvolution we processed the image stack of the mouse embryo depicted in Fig. 4 by the rolling ball background filter 15   Deconvolution obtained using a modelled PSF. Although, a and b provide an obvious improvement in image sharpness and detail (compare Fig. 4a in the main text), superior results are obtained by deconvolution (c).

Supplemental videos
Video S1 Same mouse embryo as depicted in Fig. 4a. The left side of the video shows a 3D-reconstruction obtained from the non-deconvolved data set. The right side shows the same data set after deconvolution. For final contrast enhancement both data sets were subjected to contrast-limited histogram equilibration using identical sets of parameters (CLAHE). Nerve fibers are highlighted by NF-160 fluorescence labelling. The 3D-reconstructions were obtained from 667 slices recorded using a 2.5x objective (Zeiss FLUAR 2.5x, Carl Zeiss, Germany) with an NA of 0.12 and a 0.5x post magnification.

Video S2
Whole EGFP expressing mouse brain that has been chemically cleared with the same technique as in Fig. 4d. The left side of the video shows a 3D-reconstruction obtained from the nondeconvolved data set. The right side shows the same data set after deconvolution. For final contrast enhancement both data sets were subjected to contrast-limited histogram equilibration using identical sets of parameters (CLAHE). Reconstructions were obtained from 2520 slices with 2560 x 2160 pixel resolution . For imaging a 2x objective (XLFLUOR 2x, Olympus, Germany) with an NA of 0.14 and a 0.5x post magnification was used.