Abstract

The utility of various mathematical techniques in assessing and predicting the performance of guide star wavefront compensation experiments is addressed. The techniques discussed include optimal estimation theory, matrix reconstruction, rapid evaluation of guide star performance using Gegenbauer polynomials and Mellin transforms, noise theory, and techniques for wave optics simulation of guide star experimental performance. After a brief introduction to the theory a comparison of the analytical predictions are made with the results of experiments. The H-matrix wavefront reconstruction technique used in the first guide star experiment is discussed. This technique is of note because it was the first time that an optimal estimator was used that took the statistics of turbulence and noise into consideration. In addition, the design of the reconstructor was such that an assessment of r₀ and the subaperture tilt measurement noise was also reported. Because of these factors an accurate comparison between the experimental results and theory could be made; the degree of agreement was excellent.

© 1991 Optical Society of America