The Maréchal evaluation of the Strehl definition is reexamined for a Gaussian aperture where we have included the primary aberrations and all orders of spherical aberration. The result is particularly useful for evaluating the far-field peak intensity degradation, due to aberrations, for a well-corrected optical system when the wavefront distortion at the exit pupil is known. Further, the resulting equations have the same form as Maréchal’s equations for a uniform beam with the exception of additional factors that are the consequence of the Gaussian beam. These factors approach unity as the Gaussian beam approaches a uniform beam. As a consequence, the effects of the Gaussian illumination are readily identified. It is also shown how various aberrations may be balanced against one another in order to obtain the best peak intensity in the presence of a truncated Gaussian beam.
D. D. Lowenthal, "Maréchal Intensity Criteria Modified for Gaussian Beams," Appl. Opt. 13, 2126-2133 (1974)