Abstract

This paper examines the problem of linear least-mean-squares reconstruction of a wave front distorted by turbulence described by the Kolmogorov 5/3 law. The wave-front sensors are assumed to be of the Hartmann imaging type, with circular apertures of arbitrary size and location relative to the beam to be reconstructed and having a four-quadrant photodiode detector in the focal plane. The weighting function for x₁ and x₂ slopes across the sensor aperture is determined, and the sensor signal-to-noise ratio, modulation transfer function, and cross-correlation matrix are calculated. Some examples involving various sensor configurations and the interpolation functions for their outputs are presented as well as the least-squares estimation of a low-order Zernike coefficient.

© 1986 Optical Society of America

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