Computational Comparison and Validation of Point Spread Functions for Optical Microscopes

Point spread function (PSF) is quite important in modern computational microscopy techniques. Various approaches for measuring and modeling point spread functions have been proposed for both fluorescence and label-free microscopes. Among the various PSF candidates, it is often difficult to evaluate which PSF best suits the microscope and the experimental conditions. Visual qualification is often applied because there are hardly any techniques to quantify the quality of PSF as a basis for comparing different candidates and selecting the best one. To address this gap, we present a validation scheme based on the concept of confidence interval to evaluate the quality of fit of the PSF. This scheme is rigorous and supports precise validation for any microscope's PSF irrespective of their complexity, improving the performance of computational nanoscopy on them. We first demonstrate proof-of-principle of our scheme for a complex but practical label-free coherent imaging setup by comparing a variety of scalar and dyadic PSFs. Next, we validate our approach on conventional scalar PSFs using fluorescence based single molecule localization microscopy which needs PSF to compute the locations of single molecules. Lastly, we demonstrate how the scheme can be used in practice for challenging scenarios using images of gold nanorods placed on and illuminated by a photonic chip waveguide imaged using a label-free dark-field microscopy setup. Through these experiments, we demonstrate the generality and versatility of our PSF validation approach for the microscopy domain.