Revisiting PSF models: Unifying framework and high-performance implementation.

Area of Science:

• Optical imaging
• Computational microscopy
• Photonic modeling

Background:

• Accurate point-spread function (PSF) models are essential for advanced imaging techniques like localisation microscopy.
• Existing models for light propagation in high numerical aperture systems, based on Fourier transforms or Bessel integrals, lack comprehensive comparison.
• Current software implementations in Java or MATLAB limit integration with modern deep learning frameworks.

Purpose of the Study:

• To systematically revisit and compare Fourier and Bessel approaches for PSF modeling.
• To develop a unifying theoretical framework proving the equivalence of these methods.
• To provide a high-performance, open-source library for efficient PSF computation compatible with deep learning.

Main Methods:

• Derivation from the Richards-Wolf integral to establish a unifying framework.
• Mathematical proof of the equivalence between Fourier and Bessel strategies.
• Development of an open-source library using PyTorch for high-performance computation on CPU/GPU.

Main Results:

• Demonstrated equivalence between Fourier and Bessel PSF modeling strategies.
• Introduced correction factors applicable to both approaches.
• Benchmarked accuracy and computational speed, showing Bessel is optimal for axisymmetric beams and Fourier for general cases.

Conclusions:

• The developed PyTorch library enables efficient and accurate PSF computation.
• Provides the first in-depth comparison of existing PSF models.
• Facilitates integration of PSF modeling into deep learning-based simulation and optimization pipelines.