The Strehl ratio for imaging systems with circular and annular pupils aberrated by primary aberrations is considered in terms of the variance σΦ<sup>2</sup>, 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(-σΦ<sup>2</sup>) gives a better approximation for the Strehl ratio than does the Maréchal formula. Whereas the Maréchal formula underestimates the Strehl ratio, exp(-σΦ<sup>2</sup>) generally overestimates it, especially for annular pupils with a large obscuration.
© 1983 Optical Society of AmericaPDF Article