Machine learning approach to estimating optical-phase discontinuities using single-aperture irradiance patterns

This paper explores the efficacy of employing a machine learning approach, specifically an encoder-style, convolutional neural network (CNN), to estimate the magnitude of an optical-phase discontinuity (<i>Δ</i><i>ϕ</i>) that results in an aberrated, far-field irradiance pattern. The model receives a single, 32×32 normalized far-field irradiance pattern and returns the estimated <i>Δ</i><i>ϕ</i>. The model was trained and validated using simulated data with varying values of <i>Δ</i><i>ϕ</i> (from 0 to 2<i>π</i> radians), discontinuity locations within the aperture of the simulated system, and strengths of additive background noise. The model's robustness was evaluated by testing on irradiance patterns with varying spatial resolution. This was simulated by changing the physical size of each irradiance pattern while keeping pixel size (sampling spacing) constant. It was found that when various irradiance pattern sizes were included in the training procedure, the model accurately estimated the aberration-inducing <i>Δ</i><i>ϕ</i> down to an irradiance pattern width of roughly 2 pixels across. Finally, the model was tested on experimentally collected Shack-Hartmann wavefront sensor (SHWFS) data taken in the presence of an optical-phase discontinuity imposed by a spatial light modulator. Through testing, it was found that the proposed CNN model can be applied to experimentally collected SHWFS data, providing accurate estimates of <i>Δ</i><i>ϕ</i>. This research supports the development of a shock-wave-tolerant phase reconstruction algorithm for the SHWFS. Overall, robust shock-wave-tolerant phase reconstruction algorithms will improve wavefront sensing efforts where shock waves are present.