Abstract

It is shown that the Strehl ratio can always be written as an integral over an apodization-weighted phase histogram. The corresponding mathematical formalism, based on Federer’s co-area formula, is enumerated, and a practical numerical method to quickly and accurately calculate apodization-weighted phase histograms is detailed and compared with similar methods. Conditions for expressing the Strehl ratio as a product $S = {S_1}{S_2}$ are investigated.

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