Information theoretic bounds of phase diversity for diversity polynomials and noise statistics

Information theoretic bounds on the estimated Zernike coefficients for various diversity phase functions are analyzed in this paper. We will show that, in certain cases, defocus diversity may yield higher Cramer-Rao lower bound (CRLB) than some other diversity phase functions. Evaluating the performance of the phase diversity algorithm using simulated images, we find that for an extended scene and defocus diversity, the phase diversity algorithm achieves the CRLB for known objects and approaches the CRLB by about a factor of two for unknown objects.