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research article

Revisiting PSF models: Unifying framework and high‐performance implementation

Liu, Yan  
•
Stergiopoulou, Vasiliki  
•
Chuah Wen Jie, Jonathan  
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November 4, 2025
Journal of Microscopy

Localisation 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 a 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 accurate 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 their 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 and allows 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 the efficient computation of a point‐spread function on CPU or GPU, which can then be included in simulation and optimisation pipelines.

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Type
research article
DOI
10.1111/jmi.70045
Author(s)
Liu, Yan  

EPFL

Stergiopoulou, Vasiliki  

EPFL

Chuah Wen Jie, Jonathan  

École Polytechnique Fédérale de Lausanne

Bezzam, Eric  

École Polytechnique Fédérale de Lausanne

Both, Gert‐Jan

Janelia Research Campus

Unser, Michaël  

EPFL

Sage, Daniel  

EPFL

Dong, Jonathan  

EPFL

Date Issued

2025-11-04

Publisher

Wiley

Published in
Journal of Microscopy
Article Number

jmi.70045

Subjects

localisation microscopy

•

open-source library

•

point-spread function

•

vectorial field propagation

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LIB  
LCAV  
FunderFunding(s)Grant NumberGrant URL

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

CRSII5_213521,PZ00P2_216211

Available on Infoscience
November 7, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/255627
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