# Deep Learning Estimation of Modified Zernike Coefficients and Recovery of Point Spread Functions in Turbulence

arXiv: https://arxiv.org/abs/2304.02576 · HTML: https://mlsanity.com/paper/2304.02576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Direct Zernike Coefficient Prediction from Point Spread Functions and Extended Images using Deep Learning](https://mlsanity.com/paper/2404.15231/) (2024)

## Abstract (arXiv)

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.