Dependence of the Strehl Ratio on the Magnitude of the Variance of the Wave Aberration

Abstract

Maréchal’s treatment of tolerance theory shows that, in designing high-quality optical systems, we should aim at minimizing the variance E 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 E 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.