Maréchal’s treatment of tolerance theory shows that, in designing high-quality optical systems, we should aim at minimizing the variance <i>E</i> of the wave aberration. This suggests that the value of E may serve as a diffraction-based criterion of image quality in the fine-correction stage of automatic optical design. For this purpose, it would be desirable to know the range of states of poorer correction over which <i>E</i> may still be regarded as a useful criterion. In the present investigation, it is found that a necessary condition to be satisfied is that the Strehl ratio of the system should exceed 0.5.
W. B. KING, "Dependence of the Strehl Ratio on the Magnitude of the Variance of the Wave Aberration," J. Opt. Soc. Am. 58, 655-661 (1968)