Phase retrieval and design with automatic differentiation: tutorial

The principal limitation in many areas of astronomy, especially for directly imaging exoplanets, arises from instability the point spread function (PSF) delivered by telescope and instrument. To understand transfer function, it is often necessary to infer a set optical aberrations given only intensity distribution on sensor - problem phase retrieval. This can be important post-processing existing data, or design masks engineer PSFs optimized achieve high contrast, angular resolution, astrometric stability. By exploiting newly efficient flexible technology automatic differentiation, which recent years has undergone rapid development driven machine learning, we perform both retrieval way that systematic, user-friendly, fast, effective. using modern gradient descent techniques, this converges efficiently easily extended incorporate constraints regularization. We illustrate wide-ranging potential approach our new package, Morphine. Challenging applications performed with code include precise discrete continuous distributions, even where information been censored such as heavily-saturated data. also show same algorithms optimize binary are competitive best solutions two example problems: an Apodizing Phase Plate (APP) coronagraph exoplanet direct imaging, diffractive pupil narrow-angle astrometry. Morphine source examples available open-source, similar interface popular physical optics package Poppy.