Integrating bias and gain invariance with the generalized Anscombe transform for wavefront sensing

Abstract

In image-based wavefront sensing by phase retrieval, the sum-squared difference (SSD) of simulated and measured PSF intensities, i.e., the intensity error metric (IEM), suffers from noise model mismatch. The IEM assumes additive Gaussian noise, but the true noise model is mixed Poisson-Gaussian (PG). The generalized Anscombe transform (GAT) addresses this issue by transforming the noise model from mixed PG to approximately additive Gaussian. We developed a method that uses the bias and gain terms derived for the bias-and-gain-invariant (BGI) IEM to create a BGI GAT error metric (GEM) and a BGI SSD of field amplitudes, i.e., amplitude error metric (AEM). We performed simulations comparing the retrieval accuracy of the three BGI metrics for various amounts of mixed PG noise. We found that the BGI GEM performs comparable or better than the BGI IEM and AEM for all amounts of mixed PG noise. Therefore, the BGI GEM is a good general-use error metric that works well for any mixed PG noise.