Comparing optical to digital metrics: What is the optimal defocus in a rotationally symmetric system?

We address the problem of finding the optimal focus of an optical system with spherical aberration, under three optimization criteria: the classical optical root-mean-square second order moment minimization, the expected mean square error on the sensor, and the expected mean square error at the output of a Wiener restoration filter. We observe that these three criteria may behave very differently, and, particularly, the classical optical criterion typically provides very poor results in comparison. This has a direct impact on the design of new hybrid optical-digital imaging systems, which account for the image quality after an optics-aware embedded digital restoration stage. We present some very encouraging results for simulations under different noise and aberration levels.