3D space-variant modal deconvolution with computed point spread functions

TL;DR

This work tackles spatially varying, non-symmetric aberrations in microscopy by introducing a 3D space-variant Richardson-Lucy deconvolution that uses a modal PSF basis. PSFs are generated via ZEMAX and represented as $PSF(u-x,v-y,w-z,x,y,z)=\sum_i p_i(u-x,v-y,w-z)a_i(x,y,z)$, allowing $I=\sum_i o\,a_i\otimes p_i$ and RL updates to operate on a sum of invariant convolutions. The modes and coefficient fields are derived from sparsely sampled PSFs using CVEM or NNMF, with interpolation to continuous fields and normalization to ensure valid PSFs. Demonstrations on a z-splitter based multiplane microscope show that a small number of modes (≈10) capture most PSF variability, yielding clear improvements in SNR and image sharpness for bead and jellyfish samples, and highlighting the method's potential for measurement-free PSF modeling and parallelizable computation.}{

Abstract

Deconvolution is the most widely used aberration correction technique in microscopy, however most techniques assume that the aberrations are the same for each point in the image, which is rarely true. Methods for tracking spatially varying aberrations require burdensome calibration or computation, or require symmetries in the aberration patterns. Here, we expand on existing modal deconvolution methods to demonstrate 3D fluorescence deconvolution in imaging systems that exhibit no simple symmetry. Our method is based on a space-variant generalization of Richardson-Lucy deconvolution that makes use of ZEMAX\textsuperscript{\textregistered}-derived point spread functions without the requirement of guide stars or calibration measurements. We validate the performance of our method by applying it to snapshot multiplane imaging of both bead samples and biological specimens, and show that modal decomposition is a practical solution for deconvolving spatially varying aberrations that do not display clear symmetries.

Figures (4)

• Figure 1: (a-b) Conceptual comparison of regular convolution (a) with modal convolution (b). Modal convolution enables efficient convolution of objects with spatially varying PSFs. (c) Simulated image with spatially varying PSFs. (d) Illustration of PSFs, modes (red frame) and coefficient fields (green frame) corresponding to image from (c). (e) Workflow explaining the steps for calculating modes and coefficient fields from a series of PSFs.
• Figure 2: (a) Schematic of the multi-z widefield microscope used in this work. (b) Effect of the z-splitter prism on breaking the rotational symmetry of the aberrations in the reconstructed 3D volume. (c) Effect of field curvature on the spacing of the 9 z-planes compared to the design spacing. (d) Comparison between maximum intensity projections of experimental and simulated PSFs.
• Figure 3: (a-c) Images of bead samples deconvolved using a 1-mode (b) and 20-mode vRL (c) for 100 iterations with CV modes (the FOV is $0.936 \times 0.936$ mm). (d-l) Zoom-ins of individual PSFs, comparing raw (d-f), deconvolved with 1 mode (g-i) and 20 modes (j-l). (m-o) Estimated SNR for PSF in panels (d-l).
• Figure 4: (a-f) Maximum intensity z-projections of 3D volumes of a fixed larva sample. From the left: the raw widefield image (a), a vRL deconvolution using a single CV mode (b), a vRL deconvolution using 20 CV modes (c) and their corresponding zoom-ins (d-f). (g) Quantification of relative image quality for datasets from (a) compared to the raw data using Normalized Variance, and Brenner-Tennenbaum methods. (h-i) Comparison of Normalized Variance (h) and Brenner-Tennenbaum (i) image quality metrics for the datasets from (a-c) as a function of number of modes used for vRL with the CVEM (blue) and NNMF (green) methods.