Symmetries and Periodicities of the Strehl Ratio

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Abstract
McCutchen's theorem relates the complex amplitude u(z) along the optical axis to the complex amplitude ᵱ(ν,μ) in the exit pupil. This relation is a Fourier transform. The assumptions made are that ᵱ is rotationally symmetric and that the paraxial approximation applies. The normalized quantity |u(z)/u(0)|2=S(z) is called the Strehl ratio. By using McCutchen's theorem we derive the necessary and sufficient conditions for axial symmetry: that S(z) = S(-z), where z=0 refers to the focal plane. We also discuss the periodicities of the Strehl ratio. There are similar symmetry and periodicity relationships for partial coherence. Our investigation might be useful since the Strehl ratio may serve as a focus criterion.

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