Revisiting PSF models: unifying framework and high-performance implementation

TL;DR

This paper unifies different PSF modeling approaches in microscopy, providing a theoretical framework and a high-performance, open-source PyTorch library for accurate and efficient PSF computation suitable for deep learning applications.

Contribution

It establishes the equivalence of Fourier and Bessel PSF models, introduces correction factors, and offers a GPU-accelerated implementation for improved microscopy simulations.

Findings

Bessel strategy is optimal for axisymmetric beams

Fourier approach is more versatile for general scenarios

Open-source library enables fast PSF computation on CPU and GPU

Abstract

Localization microscopy often relies on detailed models of point spread functions. For applications such as deconvolution or PSF engineering, accurate models for light propagation in imaging systems with high numerical aperture are required. Different models have been proposed based on 2D Fourier transforms or 1D Bessel integrals. The most precise ones combine a vectorial description of the electric field and precise aberration models. However, it may be unclear which model to choose, as there is no comprehensive comparison between the Fourier and Bessel approaches yet. Moreover, many existing libraries are written in Java (e.g. our previous PSF generator software) or MATLAB, which hinders the integration into deep learning algorithms. In this work, we start from the original Richards-Wolf integral and revisit both approaches in a systematic way. We present a unifying framework in which we prove the equivalence between the Fourier and Bessel strategies and detail a variety of correction factors applicable to both of them. Then, we provide a high-performance implementation of our theoretical framework in the form of an open-source library that is built on top of PyTorch, a popular library for deep learning. It enables us to benchmark the accuracy and computational speed of different models, thus allowing for an in-depth comparison of the existing models for the first time. We show that the Bessel strategy is optimal for axisymmetric beams while the Fourier approach can be applied to more general scenarios. Our work enables efficient PSF computation on CPU or GPU, which can then be included in simulation and optimization pipelines.