Ganino and Guo's new algorithm speeds PSF synthesis by 4x

Estimating the point spread function (PSF) of an optical system typically requires solving a diffraction integral, which has no closed-form solution and is traditionally computed via Fast Fourier Transform (FFT) or Hankel Transform. In a new paper accepted to IEEE ICIP 2026, Nicholas Ganino and Qi Guo show that under defocus and spherical aberration, this integral admits an approximate closed-form solution by combining piecewise Bessel approximation with Gaussian-type integrals. This breakthrough allows them to build a PSF simulator with linear computational complexity in radial resolution, a significant improvement over conventional methods.

The proposed simulator, even in its un-optimized form, achieves up to a 2x speedup over Hankel-based integration and a 4x speedup over FFT-based approaches, while maintaining high fidelity to wave-optical PSFs. This efficiency gain enables practical large-scale depth-of-field synthesis for applications in computational photography, microscopy, and augmented reality. The work represents a notable advance in optical simulation, making PSF estimation more accessible for real-time and high-resolution imaging systems.