Deep learning estimation of modified Zernike coefficients and recovery of point spread functions in turbulence

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to predict a modified set of Zernike polynomial coefficients corresponding to wavefront aberrations in the pupil due to turbulence. The modified set assigns an absolute value to coefficients of even radial orders due to a sign ambiguity associated with this problem and is shown to be sufficient for specifying the intensity point spread function. Simulated image data of a point object and simple extended objects over a range of turbulence and detection noise levels are created for the learning model. The MSE results for the learning model show that the best prediction is found when observing a point object, but it is possible to recover a useful set of modified Zernike coefficients from an extended object image that is subject to detection noise and turbulence.