Cramer-Rao bound and phase-diversity blind deconvolution performance versus diversity polynomials

Information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions are presented. We show that, in certain cases, defocus diversity may yield a higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Using simulated images to evaluate the performance of the phase-diversity algorithm, we find that, for an extended scene and defocus diversity, the phase-diversity algorithm achieves the CRLB for known objects. Furthermore, the phase-diversity algorithm achieves the CRLB by a factor of ~ 2 for unknown objects.