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Supplemental Document High-contrast multifocus microscopy with a single camera and z-splitter prism: supplement S HENG X IAO, 1, * H OWARD G RITTON , 1 H UA -A N T SENG , 1 DANA Z EMEL , 1 X UE H AN , 1,2,3 AND J EROME MERTZ 1,2,3 1 Department of Biomedical Engineering, Boston University, 44 Cummington Mall, Boston, Massachusetts 02215, USA 2 Photonics Center, Boston University, 8 St. Mary’s St., Boston, Massachusetts 02215, USA 3 Neurophotonics Center, Boston University, 24 Cummington Mall, Boston, Massachusetts 02215, USA * Corresponding author: [email protected] This supplement published with The Optical Society on 22 October 2020 by The Authors under the terms of the Creative Commons Attribution 4.0 License in the format provided by the authors and unedited. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Supplement DOI: https://doi.org/10.6084/m9.figshare.12964487 Parent Article DOI: https://doi.org/10.1364/OPTICA.404678

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Page 1: High-contrast multifocus microscopy with a single camera

Supplemental Document

High-contrast multifocus microscopy with asingle camera and z-splitter prism: supplement

SHENG XIAO,1,∗ HOWARD GRITTON,1 HUA-AN TSENG,1 DANAZEMEL,1 XUE HAN,1,2,3 AND JEROME MERTZ1,2,3

1Department of Biomedical Engineering, Boston University, 44 Cummington Mall, Boston, Massachusetts02215, USA2Photonics Center, Boston University, 8 St. Mary’s St., Boston, Massachusetts 02215, USA3Neurophotonics Center, Boston University, 24 Cummington Mall, Boston, Massachusetts 02215, USA∗Corresponding author: [email protected]

This supplement published with The Optical Society on 22 October 2020 by The Authors underthe terms of the Creative Commons Attribution 4.0 License in the format provided by the authorsand unedited. Further distribution of this work must maintain attribution to the author(s) and thepublished article’s title, journal citation, and DOI.

Supplement DOI: https://doi.org/10.6084/m9.figshare.12964487

Parent Article DOI: https://doi.org/10.1364/OPTICA.404678

Page 2: High-contrast multifocus microscopy with a single camera

High-contrast multifocus microscopywith a single camera and z-splitterprism: supplementary material

This document provides supplementary information to “High-contrast multifocus mi-croscopy with a single camera and z-splitter prism,” Optica volume, first page (year),http://dx.doi.org/10.1364/optica.0.000000.

1. SYSTEM SETUP

The detailed system setup is shown in Fig. S1.For fluorescence imaging, the sample was Köhler illuminated by light from a blue LED (Thor-

labs M470L3) that was collimated by an aspherical condenser lens (Thorlabs ACL25416U-A) andfiltered by an excitation filter (F1, Chroma ET470/24m). The fluorescence signal was collectedand imaged to the z-splitter prism by a 4 f system consisting of a microscope objective and af1 = 200 mm tube lens. A dichromatic mirror (DM, Semrock FF495-Di03) and emission filter (F2,Chroma ET519/26m) were used to separate fluorescence from excitation light. The front surfaceof the z-splitter prism was imaged to the camera (Hamamatsu ORCA Flash4.0-LT) by another4 f system with de-magnification 3 ( f2 = 300 mm and f3 = 100 mm). Image acquisition wascontrolled using HCImage.

For both phase-contrast and darkfield imaging, an LED (Thorlabs M505L4) was imaged to theback focal plane of a condenser (Thorlabs ACL25416U-A), where a half circle (for phase imaging)or an annulus (for darkfield imaging) aperture was placed. This shaped illumination was thencollected by the condenser and focused onto the sample. The USAF resolution target image inFig. 1(k) of the main text was obtained by transmission imaging with an unobstructed condenser.

The materials and designs of the z-splitter prisms are detailed at the end of this document.They were assembled by gluing together a collection of off-the-shelf beamsplitters and right-angleprisms using UV curing adhesives (Norland NOA65).

2. EV-3D DECONVOLUTION OF SIMULATED DATA

Here, we compare the results of EV-3D deconvolution with standard RL-3D deconvolution onsimulated data. The ground-truth object is shown in Fig. S2(a), which is a pair of 3D syntheticmicrotubule spindles obtained from [1]. We assume the total sample volume is 512× 256× 128µm3, and pixel size is 1× 1× 1 µm3. We convolved this with a theoretical 3D Airy PSF, assumingNA = 0.8, wavelength λ = 0.5 µm, and refractive index n = 1. Poisson noise was applied to theblurred image assuming a maximum of 103 photons per pixel, which resulted in the blurred andnoisy image shown in Fig. S2(b).

To study effect of out-of-focus fluorescence, we selected the imaging volume VI to be a subsetof the total volume VEV . Specifically, VI spans only the depth range 80 to 110 µm (indicated bythe red rectangle in Fig. S2(a), with EDOF image shown in Fig. S2(f,g)), meaning a significantamount of background arose from outside VI . To better highlight the behavior of the differentalgorithms, we did not use regularization (η = 0), and we initialized with b0(~r /∈ VI) = 0. ForEV-3D, we extended the deconvolution volume by amount w above and below axially, whilethe lateral extension was set to 0. We measured the fidelity of the deconvolved image with anormalized cross-correlation coefficient defined as:

c =∑VI

(o∗ − o∗)(ok − ok)√[∑VI

(o∗ − o∗)2][∑VI(ok − ok)2]

(S1)

where o∗ is the ground truth object, ok is the deconvolution result after iteration k, and o∗ and ok

are the average intensities of o∗ and ok.RL-3D deconvolution attained a best solution after 28 iterations with a maximum correlation

c = 0.46. The resulting EDOF image is shown in Fig. S2(h), where a considerable amount ofout-of-focus background around the two central dense areas is still apparent. More iterationsdid not improve image quality but rather amplified noise. However, with EV-3D algorithm, the

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background was removed and the retrieved image exhibited higher fidelity. Our best solution isshown in Fig. S2(i), obtained with axial extension w = 40 µm both above and below, and outeriteration K = 200, and inner iteration N = 80. Under such conditions, the deconvolved imageexhibits a cross-correlation of 0.82 with the ground truth.

Insufficient axial extension w often led to residual background in the reconstructed image. InFig. S2(d), we plot the evolution of c as a function of outer iteration number K, with varyingextension w. It can be seen that with w = 5 µm, the algorithm only converged to a solution withc = 0.38. The deconvolved EDOF image (Fig. S2(j)) still exhibits a fair amount of background.However, with larger w > 20 µm, the algorithm consistently converged to a common solutionwith c > 0.80.

One way to increase the speed of the algorithm is to use a warm-start strategy. Here, wecould initialize as b1(~r /∈ VI) = b0(~r′), where~r′ = PVI (~r) is the projection of~r onto the set VI .Figure S2(e) shows the evolution of c as a function of outer iterations K, with the same simulationcondition as in Fig. S2(d). Compared to Fig. S2(d), we found that a warm start significantlyboosted the speed of convergence of the algorithm, such that in most cases only a few iterationswere needed to reach an optimum. With only 14 outer iterations, the algorithm attained animage quality of c = 0.82 (Fig. S2(k)). To attain a comparable image quality without warm start,hundreds of iterations were needed.

3. EFFECTS OF OUT-OF-FOCUS LIGHT ON RL-3D AND EV-3D DECONVOLUTION

Here, we compare the deconvolution results using both RL-3D and EV-3D algorithms on experi-mental data with a varying amount of background. We imaged a fluorescent lens-paper samplewith a 9-plane prism and 20× objective. The total 3D FOV was cropped to 480× 480× 9 pixels,corresponding to a 470× 470× 160 mm3 volume. The individual 9-plane images are shown inFig. S4(a), where most of the sample was contained within the imaging volume. Thus, little out-of-focus background originated from outside of the imaging volume VI . In this case, as expected,standard RL-3D deconvolution without volume extension works well in terms of removingout-of-focus blur. As a comparison, a similar result was obtained with EV-3D deconvolution (seefirst row of Fig. S4(b)).

However, results start to differ as one artificially reduces the number of focal planes availablefor deconvolution, which effectively increases the amount of out-of-focus background originatingfrom outside the reduced imaging volume VI . If only the middle 7 planes are used for deconvolu-tion (VI = 480× 480× 7 pixels), residual background begins to appear in the RL-3D deconvolvedimage. On the other hand, this background is not present when using EV-3D deconvolution(see second row of Fig. S4(b)). The situation for RL-3D continues to deteriorate as fewer focalplanes are made available for deconvolution, with spurious background becoming increasinglyapparent in the deconvolved images. With EV-3D deconvolution, however, this background isconsistently removed, leaving only in-focus fibre structures located within the reduced imagingvolume (bottom two rows of S4(b)).

For RL-3D deconvolution, we used 200 iterations for all cases (more iterations did not improvethe resulting image quality). For EV-3D deconvolution, we used outer iteration K = 20 andinner iteration N = 40. We extended the deconvolution volume to VEV = 580× 580× 19 pixels,regardless of how much we reduced the imaging volume VI . We did not use regularization in allcases.

4. SUPPLEMENTARY METHODS

A. Mouse Surgery and ImagingAll animal procedures were approved by the Boston University Institutional Animal Care andUse Committee. C57BL/6 female mice were used in all studies (Taconic; Hudson, NY). Micewere 8–12 weeks old at the start of the experiments. All surgical and implantation details havebeen described previously [2]. Briefly, mice first underwent surgery for implantation of a customimaging window and guide cannula. The window/guide assembly consisted of a stainless steelimaging cannula (OD, 3.17 mm; ID, 2.36 mm; height, 2 mm), fitted with a circular coverslip (size0; OD: 3 mm). The guide cannula (26 gauge; C135GS4; Plastics, Roanoke, VA) was fixed at a45° angle and terminated flush to the base of the imaging window allowing for post-surgicalviral delivery. The overlying cortical tissue was carefully aspirated away to expose the corpuscallosum which was carefully thinned until the underlying striatal tissue could be visualized bymeans of a surgical microscope. The imaging window was centered over the dorsal striatum (AP:

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+0.5, ML:1.8 mm, DV: -1.6). During the same surgery, an aluminum head-plate was attached tothe skull anterior to the imaging cannula that allowed for head fixation during recording.

Upon complete recovery, animals were injected with 1 µL AAV9-Syn-GCaMP7f.WPRE.SV40virus through the attached guide cannula using a 10 µL syringe (701N; Hamilton Company, Reno,NV) controlled by a microinfusion pump (UltraMicroPump3-4; World Precision Instruments,Sarasota, FL) fitted to a 33 gauge infusion cannula (C135IS4; Plastics, Roanoke, VA). The injectionoccurred at a speed of 100 nL/min. Virus was obtained from the Addgene (titer 1e13 GC/mL:104488-AAV9).

Following surgery and virus infusion mice underwent handling and habituation to a sphericaltreadmill imaging platform. Habituation to running on the spherical treadmill while headfixedoccurred over 3-4 days prior to imaging.

A single imaging session took approximately 8 minutes. Prior to the imaging session animalswere positioned on a spherical treadmill underneath the microscope. During the imaging, theanimals were headfixed under the objective while freely running the on the treadmill.

B. Fluorescent C. elegans Preparation and ImagingC. elegans strain QW1217 (zfIs124[Prgef-1::GCaMP6s]; otIs355[Prab-3::NLS::tagRFP]) expressingpan-neuronal GCaMP and nuclear-localized RFP were used for imaging. Before imaging, C.elegans were cultured in Nematode Growth Medium Agar (Carolina Biological Supply #173520)seeded with Escherichia coli K-12 (Carolina Biological Supply #124500) as food source in a 20°incubator for 7 days. For imaging, worms of all different stages were transferred to an imagingchamber of approximate size 2× 2× 1 mm3, within which the worms could be freely swimmingin water. The imaging chamber was then sealed with a coverslip and imaged using a 20× waterimmersion objective.

C. Sample Preparations for Phase and Darkfield ImagingLiving rotifers and Daphnia magna were purchased from Carolina Biological Supply (#133172,#133174 and #142330). Samples were prepared by transferring a droplet of culture medium intoan imaging well on a microscope slide. The samples were then mixed with water and sealed witha coverslip. For imaging Daphnia magna, the imaging well was approximately 1.5× 1.5× 1 mm3

in volume, carved from a 1 mm thick silicone sheet.Fixed samples of radiolaria, volvox, and dictydium were purchased from Carolina Biological

Supply (#296840, #296620 and #C297328). The samples were embedded in Eukitt with refractiveindex nsample = 1.51.

D. Image ProcessingThe FOV of each focal plane on the camera was first identified and cropped by imaging a uniformautofluorescent plastic slide (Chroma Technology). A USAF resolution target was then placedunder the microscope and imaged when focused at each of the focal planes. We estimatedaffine transforms for all the focal planes (referenced to the top plane), to account for the lateraltranslations due to cropping.

For 3D phase imaging, an additional reference image was captured without the sample. Thisimage was subtracted from all subsequent recordings to correct for phase gradients induced byimperfections in our z-splitter assembly.

All-in-focus images were fused from the 9-plane focal stack using ImageJ Extended-Depth-of-Field plugin [3]. Phase-contrast images are displayed using Matlab ’bone’ colormap, darkfieldimages are displayed using ImageJ ’green-fire-blue’ colormap.

E. Implementation of EV-3D AlgorithmThe core RL deconvolution algorithm used here is adapted from the Matlab deconvlucy function,which was based on an accelerated RL deconvolution algorithm [4]. Additional TV regularizationwas implemented according to [5]. We further accelerated the algorithm using Matlab GPU array.

The regularization parameter µ was typically set in the range 0 - 0.01. Other parametersincluding w, u and iteration counts K, N were all determined manually by visually inspectingthe deconvolution results. A general rule of thumb is that one needs to use increasing w withincreasing out-of-focus background. u should be determined based on the axial extent of thedeconvolution volume VEV , which affects the boundary artifacts after deconvolution (see Fig. S5).Larger u is needed for longer axial extents of VEV , due to the larger out-of-focus PSF size. For

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static samples, we used the warm-start initialization b1(~r /∈ VI) = b0(~r′). This was performedwith the Matlab padarray function with parameter ’replicate’.

The deconvolution is performed using either a 3D Airy PSF or a 3D Gaussian-LorentzianPSF. The Airy PSF is computed using DeconvolutionLab2 [1]. The Gaussian-Lorentzian PSF iscalculated as:

PSF(x, y, z) =π∆k2

1 + ξ2 exp [−π2∆k2(x2 + y2)

1 + ξ2 ] (S2)

where k = n/λ, ∆k =√

2NA · k, ξ = π∆k2z/2k, n is the refractive index of the medium, λ is thewavelength, and NA is the numerical aperture of the objective.

We note that our goal in applying deconvolution here is to remove out-of-focus background,rather than perform restorative deconvolution where one tries to enhance lateral high spatialfrequencies. As such, our algorithm is more robust to sample aberrations and PSF inaccuracies,since it relies more on the overall span of the defocused PSF than on the fine structure (high spatialfrequencies) of the in-focus PSF. As a result, satisfactory results were obtained with theoreticallyapproximated PSF models, without the need for precise experimental calibration.

A Matlab version of our EV-3D algorithm along with test data can be found at http://sites.bu.edu/biomicroscopy/resources/.

F. SBR Characterization of Fluorescent BeadsThe fluorescent bead sample was made by mixing 5 µm diameter fluorescent polystyrene micro-spheres (Phosphorex Inc.) in agarose gel. We define SBR for each bead as (µs − µb)/µb, where µsis the average intensity of the bead, µb is the average intensity within a 50 pixel (44 µm) radiusabout the bead (excluding regions of other in-focus beads). For deconvolution without axialextension (w = 0), corresponding essentially to RL-3D, and we used iteration number N = 120.We found that increasing the value of N here did not lead to higher SBR. For axial extensionw > 0, we used outer iteration K = 20 and inner iteration N = 40. We did not use regularizationfor either RL-3D and EV-3D algorithms.

G. Data Analysis for Calcium Imaging in a Mouse BrainFor mouse imaging, images from each focal plane were first cropped and registered, resultingin a 617× 617× 3 pixel volume. We used normcorre to correct for motion artifacts during theacquisition [6]. Specifically, we assumed the motion was rigid and the same across all focal planes,so motion estimated in only one of the 3 focal planes was applied to all.

For deconvolution, we expanded the imaging volume to 717× 717× 13 pixels and appliedEV-3D deconvolution on a frame-by-frame basis. We found that using a simulated Gaussian-Lorentzian PSF yielded slightly better results than an Airy PSF (see Fig. S6), which is likely dueto blurring induced by scattering in the brain tissue. The initial background was estimated bydeconvolving the overall time-averaged frames, where we used outer iteration count K = 20 andinner iteration count N = 20. For all later frames we employed the warm-start approach in whichwe initialized with the estimated background, and used an outer loop count K = 1 (the inner loopcount remained at N = 20). The regularization parameter for all frames was set to be η = 0.001.For RL-3D deconvolution, we used iteration count N = 60, regularization η = 0.001 and the sameGaussian-Lorentzian PSF.

The neuron segmentation was performed at each focal plane separately using a custom de-veloped deep learning segmentation routine (see Section H). For each region of interest (ROI),a time trace s(t) was obtained by summing the intensity of all pixels within the ROI. Signals ofneurons were merged across different planes if their spatial and temporal correlation were bothgreater than 0.5. We define ∆F/F = [F− Fbaseline]/Fbaseline, where Fbaseline is the time averagedintensity for a given ROI. A Matlab detrend function with linear fitting was applied to all ∆F/Ftraces to correct for photobleaching. For each trace, its SNR was calculated as SNR = (∆F/F)/σn,where σn is the noise, defined as the standard deviation of all points of ∆F/F values below90% percentile. We only used common time points when ∆F/F > 3σn for all cases (withoutdeconvolution, RL-3D deconvolution and EV-3D deconvolution) for statistics calculation in Fig.3(f,g).

H. Neuron SegmentationNeuron segmentation was performed with a customized deep learning network, based on U-net [7]. The training data were obtained from both our previously published GCaMP datasets(hippocampus and striatum) [8] and unpublished GCaMP datasets (striatum) [9]. For each dataset,

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we generated a projection image of max minus min intensity (max-min projection image), andmanually curated a mask containing all identified neurons as our ground truth, where the neuronpixels were labeled as one and the background pixels as zero. To normalize the pixel intensity ofeach projection image, we offset the intensity of each pixel in the image so that average intensity ofthe image was centered at zero, and then divided the offset intensity by the standard deviation ofthe intensity across the image. Finally, the projected images and the corresponding ground truthmasks were cropped into small patches of 32× 32 pixels as the training input for the network.During the training process, we randomly applied various image augmentations (vertical and/orhorizontal flip, rotation at 90, 180, and 270 degrees) to increase the robustness of the network.

To perform segmentation, we first generated the max-min projection images from datasets ob-tained from widefield multifocus microscopy, and normalized the projection images as describedabove. A moving window of 32× 32 pixels with 50% overlap in both vertical and horizontaldirections was applied to the images to generate the inference data, resulting in each individualpixel being inferred four times. For each pixel, the results from four inferences were averaged,and the pixel was classified as a neuron pixel if the averaged result was larger than 0.5, and as abackground pixel otherwise. The groups of connected neuron pixels were segmented as neurons,and were refined with a watershed transformation to obtain the final set of regions of interest.

The segmentation results are overlaid in Fig. 3(a) of the main text. For visualization, images inFig. 3(a) have been brightened using Matlab brighten function with beta = 0.25.

I. Data Analysis for C. elegans ImagingC. elegans video was captured at 30 Hz and cropped to VI = 580× 580× 9 pixels. For deconvo-lution, we used a lateral extension u = 40 pixels, and axial extension w = 4 pixels, resulting inthe deconvolution volume VEV = 660× 660× 17 pixels. We employed a warm-start approachwhere we initialized b(~r ∈ VEV −VI) using the deconvolution result from the previous frame. Todeconvolve the first frame, we used outer iteration count K = 20 and inner iteration count N = 40.For all later frames, we only iterated outer loop with K = 1 (the inner loop count remained atN = 40). We did not use regularization (η = 0).

C. elegans tracking was performed using ImageJ TrackMate plugin [10] on the deconvolvedvideo. The results were further refined manually by visual inspection. Z positions of the trajecto-ries were determined by calculating the center of mass of pixel values along the axial direction.C. elegans posture was analyzed using ImageJ Skeletonize3D plugin. The 3D image stacks werefirst binarized by thresholding, and then noise was removed using a series of image erosion anddilation operations. The resultant stacks were processed by ImageJ Skeletonize3D plugin forskeleton extraction.

REFERENCES

1. D. Sage, L. Donati, F. Soulez, D. Fortun, G. Schmit, A. Seitz, R. Guiet, C. Vonesch, andM. Unser, “DeconvolutionLab2: An open-source software for deconvolution microscopy,”Methods 115, 28–41 (2017).

2. H. J. Gritton, W. M. Howe, M. F. Romano, A. G. DiFeliceantonio, M. A. Kramer, V. Saligrama,M. E. Bucklin, D. Zemel, and X. Han, “Unique contributions of parvalbumin and cholinergicinterneurons in organizing striatal networks during movement,” Nat. Neurosci. 22, 586–597(2019).

3. B. Forster, D. Van De Ville, J. Berent, D. Sage, and M. Unser, “Complex wavelets for extendeddepth-of-field: A new method for the fusion of multichannel microscopy images,” Microsc.Res. Tech. 65, 33–42 (2004).

4. D. S. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl.Opt. 36, 1766–1775 (1997).

5. M. Laasmaa, M. Vendelin, and P. Peterson, “Application of regularized richardson–lucyalgorithm for deconvolution of confocal microscopy images,” J. Microsc. 243, 124–140 (2011).

6. E. A. Pnevmatikakis and A. Giovannucci, “NoRMCorre: An online algorithm for piecewiserigid motion correction of calcium imaging data,” J. Neurosci. Methods 291, 83–94 (2017).

7. O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedicalimage segmentation,” in International Conference on Medical image computing and computer-assisted intervention, (Springer, 2015), pp. 234–241.

8. A. I. Mohammed, H. J. Gritton, H.-a. Tseng, M. E. Bucklin, Z. Yao, and X. Han, “An integrativeapproach for analyzing hundreds of neurons in task performing mice using wide-fieldcalcium imaging,” Sci. Reports 6, 20986 (2016).

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9. S. P. Shen, H.-a. Tseng, K. R. Hansen, R. Wu, H. J. Gritton, J. Si, and X. Han, “Automatic cellsegmentation by adaptive thresholding (ACSAT) for large-scale calcium imaging datasets,”Eneuro 5 (2018).

10. J.-Y. Tinevez, N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y.Bednarek, S. L. Shorte, and K. W. Eliceiri, “TrackMate: An open and extensible platform forsingle-particle tracking,” Methods 115, 80–90 (2017).

11. J. Sun, S. J. Lee, L. Wu, M. Sarntinoranont, and H. Xie, “Refractive index measurement ofacute rat brain tissue slices using optical coherence tomography,” Opt. Express 20, 1084–1095(2012).

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Objective

f1

f2 f3

Δz

Camera

LE

D 1

z-splitter prism

DM

LED 2

F2

F1

Aperture

Condenser

Diffusser

(a)

(b)

Fig. S1. Setup for fluorescence imaging. f1 = 200 mm, f2 = 300 mm, f3 = 100 mm. DM,dichromatic mirror. (a) Illumination module for fluorescence imaging. (b) Illumination modulefor transmission, phase contrast and darkfield imaging.

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Sample Volume Blurred & Noisy Volume

(a) (b)

xy

yz

xz

Richardson Lucy iteration K

(c) (d) (e)

(f)

(g)

(h)

(i)

(j)

(k)

c

0 50 100 150 2000

0.5

1

(h)

c

0

0.5

1

c

0 25 50 750

0.5

1

w = 5 µmw = 10 µmw = 20 µmw = 30 µmw = 40 µm

EV-3D outer iteration K EV-3D outer iteration K

(i)

(j)

(k)

0 50 100 150 200

w = 5 µmw = 10 µmw = 20 µmw = 30 µmw = 40 µm

Fig. S2. (a) Sum projection of 3D simulated microtubule spindles. Red rectangle indicate thevolume VI for deconvolution. (b) Sum projection of 3D simulated microtubule spindles afterconvolution and applying Poisson noise. (c) Cross-correlation as a function of iterations for RL-3D algorithm. (d) Cross-correlation as a function of outer iteration K, with varying axial exten-sion w and fixed inner iteration N = 80. (e) Same as (d) but with warm start initialization. (f)Ground truth EDOF image over VI . (g) Blurred and noisy EDOF image before deconvolutionover volume VI . (h-k) EDOF of image of the deconvolution results with different parameters asindicated by the arrows in (c-e).

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(a) (b) (c)

(d) (e) (f)

Orig inal w = 0 w = 2

w = 4 w = 6 w = 8

- 55 µm

55 µm

Fig. S3. Color-coded EDOF image of thick fluorescent bead sample before deconvolution(a), after RL-3D deconvolution (b), and after EV-3D deconvolution with axial extensionw = 2, 4, 6, 8 pixels (c-f). Scale bar is 100 µm.

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(a)

(b)

9 p

lane

s7

pla

ne

s5

pla

ne

s3

pla

ne

s

Raw RL-3D EV-3D

Plane 1 Plane 2 Plane 3 Plane 4 Plane 5 Plane 6 Plane 7 Plane 8 Plane 9

- 82 µm

82 µm

Fig. S4. (a) Individual 9 plane images of a fluroescent lens-paper sample, where the entiresample was mostly contained within the 9-plane volume. (b) Comparison of color-coded EDOFimages before deconvolution (first column), after using RL-3D deconvolution (second column),and after using EV-3D deconvolution (third row). From top row to bottom row, original anddeconvolved images only using the middle 9, 7, 5, 3 plane images. Scale bar, 100 µm.

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+ Δz

(a)

(b)

(c)

(d)

0 - Δz

Fig. S5. Effect of lateral extension parameter u. (a) Raw images before deconvolution. (b) De-convolution results using EV-3D algorithm without laterally extending deconvolution volume,where boundary effects are apparent in the bottom regions of the images. (c) Deconvolutionresults using EV-3D algorithms with lateral extension u = 50 pixels, where the boundary ef-fects in (b) are no longer apparent. (d) Deconvolution results using RL-3D algorithms withoutlaterally extending deconvolution volume. The original image size is 616× 617× 3 pixels. Theaxial extension is w = 5 pixels for (b) and (c). Scale bar, 100 µm. ∆z = 110 µm.

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Origin

al

Gauss

ian P

SF

Airy

PS

F

+Δz -Δz0

(a)

(b)

(c)

Fig. S6. Comparison of deconvolution results using different PSF models. (a) Original im-age without deconvolution. (b) Deconvolution with EV-3D algorithm using 3D Gaussian-Lorentzian PSF model. (c) Deconvolution with EV-3D algorithm using 3D Airy PSF model.Scale bar, 100 µm. ∆z = 110 µm.

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(c)

(a)

(b)

Origin

al

RL-3

D

+ Δz 0 - Δz

EV

-3D

Fig. S7. Comparison of (max - min) projection images before deconvolution (a), after RL-3Ddeconvolution (b) and after EV-3D deconvolution (c). Scale bar, 100 µm. ∆z = 110 µm.

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500

250

Neuro

n Index

1(a)

0.5 1 1.5 2

x 104

50

100

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x 104

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Time / min

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Neuro

n Index

(b)

Fig. S8. Calcium traces of all 528 neurons over the entire 8 min recording before deconvolution(a) and after EV-3D deconvolution (b).

14

Page 16: High-contrast multifocus microscopy with a single camera

Fig. S9. Individual single-shot 9-plane images of radiolaria (a), volvox (b) and dictydium (c).Scale bars are 100 µm. ∆z = 25 µm.

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Page 17: High-contrast multifocus microscopy with a single camera

Dataset nsample Objective No. of Planes Total FOV Imaging Speed

Fig. 1(e-k) 1.33 Olympus UMPLFLN 20×W 9 N/A N/A

Fig. 2(b-e) 1 Mitutoyo Plan Apo 20× 9 0.47× 0.47× 0.16 mm 3 N/A

Fig. 2(f) 1.33 Olympus UMPLFLN 20×W 6 0.49× 0.49× 0.11 mm 3 N/A

Fig. 3 1.36 [11] Mitutoyo Plan Apo 10× 3 1.2× 1.2× 0.22 mm3 50 Hz

Fig. 4 1.33 Olympus UMPLFLN 20×W 9 0.51× 0.51× 0.18 mm3 30 Hz

Fig. 5(a) 1.33 Olympus UMPLFLN 10×W 9 1.1× 1.1× 0.71 mm3 30 Hz

Fig. 5(b) 1.33 Olympus UMPLFLN 40×W 9 280× 280× 44 µm3 30 Hz

Fig. 5(c,d) 1.33 Olympus UMPLFLN 40×W 6 280× 140× 28 µm3 100 Hz

Fig. 6(a-c) 1.51 Olympus UMPLFLN 20×W 9 0.52× 0.52× 0.2 mm3 N/A

Fig. 6(d,e) 1.33 Olympus UMPLFLN 10×W 9 1.1× 1.1× 0.71 mm3 30 Hz

Table S1. List of experimental conditions

16

Page 18: High-contrast multifocus microscopy with a single camera

1 2 3

Label Description Vendor Part No.1 12.5mm 30R/70T Standard Cube Beamsplitter Edmund Optics 68-5482 12.5mm VIS, Non-Polarizing Cube Beamsplitter Edmund Optics 49-0033 12.5mm, Uncoated, N-BK7 Right Angle Prism Edmund Optics 45-108

A A

B B

C C

D D

E E

F F

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:2:1 SHEET 1 OF 1

A4

WEIGHT:

3-plane prism17

Page 19: High-contrast multifocus microscopy with a single camera

AA

BB

SECTION A-A

SECTION B-B

1

1

2

2

2 3

333

3

Label Description Vendor Part No.1 12.5mm 30R/70T Standard Cube Beamsplitter Edmund Optics 68-5482 12.5mm VIS, Non-Polarizing Cube Beamsplitter Edmund Optics 49-0033 12.5mm, Uncoated, N-BK7 Right Angle Prism Edmund Optics 45-108

A A

B B

C C

D D

E E

F F

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:1:1 SHEET 1 OF 1

A4

WEIGHT:

6-plane prism18

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AA

BB

CC

SECTION A-A

SECTION B-B

SECTION C-C

2

1

1

1

2

2

3

3

333

3

3

3

2

4

Label Description Vendor Part No.

1 12.5mm 30R/70T Standard Cube Beamsplitter Edmund Optics 68-548

2 12.5mm VIS, Non-Polarizing Cube Beamsplitter Edmund Optics 49-003

3 12.5mm, Uncoated, N-BK7 Right Angle Prism Edmund Optics 45-108

4 70:30 (R:T) Non-Polarizing Beamsplitter Cube, 400 - 700 nm, 1/2" Thorlabs BS061

A A

B B

C C

D D

E E

F F

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:1:1 SHEET 1 OF 1

A4

WEIGHT:

9-plane prism19

Page 21: High-contrast multifocus microscopy with a single camera

AA

BB

CC

DD

SECTION A-A

SECTION B-B

SECTION C-C

SECTION D-D

2

1

1

1

1

2

2

2

2

3

3

3

33

3

3

3

3

3

3

1

4

Label Description1 30R:70T Cube Beamsplitter

2 50R:50T Cube Beamsplitter

3 Right Angle Prism

4 75R:25T Cube Beamsplitter

A A

B B

C C

D D

E E

F F

4

4

3

3

2

2

1

1

DRAWN

CHK'D

APPV'D

MFG

Q.A

UNLESS OTHERWISE SPECIFIED:DIMENSIONS ARE IN MILLIMETERSSURFACE FINISH:TOLERANCES: LINEAR: ANGULAR:

FINISH: DEBURR AND BREAK SHARP EDGES

NAME SIGNATURE DATE

MATERIAL:

DO NOT SCALE DRAWING REVISION

TITLE:

DWG NO.

SCALE:1:1 SHEET 1 OF 1

A4

WEIGHT:

12-plane prism20