Evaluation of the phase diversity algorithm for noise statistics error and diversity function combination

Abstract

This paper will analyze the performance degradation of the phase diversity algorithm due to error in modeling the noise statistics. In other words, it will answer the question: "What is the level of degradation, if any, when the true noise statistics is Gaussian (Poisson) but is modeled as Poisson (Gaussian) in the likelihood function?" Furthermore, many phase diversity studies have been performed with defocus as the diversity function. One may ask whether combining the defocus with another diversity function such as astigmatism could improve the performance. This paper will show that a phase diversity composed of an appropriate combination of defocus and astigmatism can result in performance superior to any one of the phase diversities considered separately.

Image based aberration retrieval using helical point spread functions

“…So far, numerical studies in this area assumed either solely additive Gaussian noise [33][34][35] (i.e., camera readout noise) or pure Poisson noise [34] (photon shot-noise). Furthermore, only idealized point sources or a single, dedicated object [33][34][35][36][37] were investigated. This stands in contrast to the PEPD approach presented in this paper, where the main motivation is to apply aberration retrieval in the context of imaging arbitrary extended objects.…”