  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.
