The Strehl ratio for imaging systems with circular and annular pupils aberrated by primary aberrations is considered in terms of the variance σΦ2 of the phase aberration across the pupil. Classical as well as balanced (Zernike) aberrations are considered. By comparing the actual numerical results with the approximate ones, we find that exp(−σΦ2) gives a better approximation for the Strehl ratio than does the Maréchal formula. Whereas the Maréchal formula underestimates the Strehl ratio, exp(−σΦ2) generally overestimates it, especially for annular pupils with a large obscuration.
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