Publication

Revisiting PSF models: theory and implementation

Michaël Unser, Daniel Sage
2026

Abstract

We present a unifying framework for point-spread function (PSF) models in high-numerical-aperture optical microscopy. Starting from the Richards-Wolf integral, we demonstrate the mathematical equivalence between Fourier-based and Bessel-based approaches as alternative parameterizations of the same propagation integral. This framework enables us to generalize correction factors such as Gibson-Lanni aberrations, apodisation, and arbitrary phase masks to both scalar and vectorial models. We provide an open-source PyTorch implementation that achieves high computational performance on both CPU and GPU. Our results show that Bessel propagators excel for axisymmetric pupils while Fourier propagators handle general cases. The library integrates seamlessly with deep learning workflows through automatic differentiation, facilitating applications in deconvolution, PSF engineering, and computational microscopy.

Official source

https://infoscience.epfl.ch/entities/publication/389f1c6b-95a6-4472-bb95-252e514dfa95

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Michaël Unser, Daniel Sage
2026

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/389f1c6b-95a6-4472-bb95-252e514dfa95

About this result

Related concepts (32)

Super-resolution microscopy

Super-resolution microscopy is a series of techniques in optical microscopy that allow such images to have resolutions higher than those imposed by the diffraction limit, which is due to the diffraction of light. Super-resolution imaging techniques rely on the near-field (photon-tunneling microscopy as well as those that use the Pendry Superlens and near field scanning optical microscopy) or on the far-field.

Confocal microscopy

Confocal microscopy, most frequently confocal laser scanning microscopy (CLSM) or laser scanning confocal microscopy (LSCM), is an optical imaging technique for increasing optical resolution and contrast of a micrograph by means of using a spatial pinhole to block out-of-focus light in image formation. Capturing multiple two-dimensional images at different depths in a sample enables the reconstruction of three-dimensional structures (a process known as optical sectioning) within an object.

Point spread function

The point spread function (PSF) describes the response of a focused optical imaging system to a point source or point object. A more general term for the PSF is the system's impulse response; the PSF is the impulse response or impulse response function (IRF) of a focused optical imaging system. The PSF in many contexts can be thought of as the extended blob in an image that represents a single point object, that is considered as a spatial impulse. In functional terms, it is the spatial domain version (i.e.

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Revisiting PSF models: theory and implementation

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