Abstract
Atmospheric wavefront residual errors for Zernike compensation are calculated using both the spatial domain approach and the frequency domain approach. It is found that the approaches give identical results. The results are used to examine numerical solutions of atmospheric Karhunen-Loeve functions through the spatial domain approach (solving an integral equation) and the frequency domain approach (diagonalization of the Noll matrix). The obtained Karhunen- Loeve eigenvalues and eigenfunctions are used to simulate atmospheric wavefronts from different methods is discussed. We find that from a statistical point of view, the method described here is the best one for atmospheric wavefront simulation. The structure functions calculated from simulated wavefronts are used to obtain the Strehl ratio for partial correction so that a validity range can be inferred for the Marechal approximation.
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