Implicitly Learned Neural Phase Functions for Basis-Free Point Spread Function Engineering

Abstract: Point spread function (PSF) engineering is vital for precisely controlling the focus of light in computational imaging, with applications in neural imaging, fluorescence microscopy, and biophotonics. The PSF is derived from the magnitude of the Fourier transform of a phase function, making the construction of the phase function given the PSF (PSF engineering) an ill-posed inverse problem. Traditional PSF engineering methods rely on physical basis functions, limiting their ability to generalize across the range of PSFs required for imaging tasks. We introduce a novel approach leveraging implicit neural representations that overcome the limitations of pixel-wise optimization methods. Our approach achieves a median MSSIM of 0.8162 and a mean MSSIM of 0.5634, compared to a median MSSIM of 0.0 and a mean MSSIM of 0.1841 with pixel-wise optimization when learning randomly generated phase functions. Our approach also achieves a median PSNR of 10.38 dB and a mean PSNR of 8.672 dB, compared to a median PSNR of 6.653 dB and a mean PSNR of 6.660 dB with pixel-wise optimization for this task.