Abstract
The Maréchal approximation for the Strehl ratio versus rms wavefront distortion is widely used in atmospheric scaling law codes, but a complete derivation is absent in the open literature. I present an updated derivation of the first term in Maréchal, then a complete derivation. The Strehl ratio is proportional to the square of the Fourier transform of the probability density function of the random phase noise. For Gaussian noise, the traditional Maréchal formulation is the result. The more general formulation suggests a method for characterization of random phase aberrations.
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