Prediction of Wavefront Sensor Slope Measurements Using Artificial Neural Networks

Abstract

The resolution of ground based telescopes is limited by the random wavefront abberations caused by atmospheric turbulence. Adaptive optics systems, which compensate for atmospheric effects, have been shown to improve the resolution of these telescopes. The purpose of an adaptive optics system is to remove the atmospheric induced aberrations from an incident optical wavefront. This is accomplished by measuring the incident aberrations and removing them using a deformable mirror. Correction with a deformable mirror must take into account the effects of additive noise in the wavefront sensor, system time delays, and the possibility of a spatial separation between the object of interest and the beacon used to measure the incident wavefront. While an optimal wavefront reconstruction algorithm, such as the minimum variance reconstructor, can be derived based on statistical knowledge of the atmosphere, noise and other random effects in the adaptive optics system, the actual performance of this reconstructor may be limited by imperfect knowledge of several key parameters [1, 2, 3]. These parameters include both atmospheric and system parameters. The key atmospheric parameters include the Fried coherence length [4], r0, the C N 2 profile, and the wind speed profile. The key system parameter is the wavefront sensor (WFS) mean square slope measurement error. One source of wavefront reconstruction error is the system time delay. While it would be impossible to build an adaptive optical system without delay, it may be possible to predict the wavefront at the time of reconstruction based on the measured slopes. A statistical technique exists for slope measurement prediction which relies on prior knowledge of the key atmospheric and system parameters. This technique is based on knowing the covariance of the measured WFS data. Artificial neural networks, which do not require knowledge of the key parameters or the covariance statistics of the data, are compared to the statistical techniques to see if a single neural network offers the adaptability to perform well over a broad range of parameter values, without prior knowledge of the statistical parameters.