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.
A new error metric, known as the Parseval error metric, was developed for phase retrieval algorithms for wavefront sensing that use a cropped discrete Fourier transform to deal with local minima of the sum-squared error metric that have high-frequency phase artifacts that incorrectly place energy outside the crop window. This was done by defining an energy consistency error metric based on a modified version of Parseval’s theorem, and then adding it with a relative weighting factor to the sum-squared error metric to form the Parseval error metric. Simulations were performed to examine the effect of the Parseval error metric compared to the sum-squared error metric alone and to downsampling the data PSF instead of cropping. We found that the cropping methods had better wavefront fits compared to the downsampled method, and the Parseval error metric had better retrieval success rates over the other two methods, although with greater computational requirements.