Optimal parameter selection in the phase differencing algorithm for 2-D phase estimation

A parametric model and a corresponding algorithm for estimating two-dimensional (2-D) phase functions were presented in a previous paper. The performance of the phase estimation algorithm and, hence, the performance of any algorithm that employs it, strongly depends on the choice of the two free parameters of the algorithm. In this correspondence, we systematically analyze the performance of the phase estimation algorithm and derive rules for selecting the algorithm parameters such that the mean squared error in estimating the signal phase is minimized. It is shown analytically and verified using Monte-Carlo simulations that this choice of parameters results in unbiased estimates of the phase and spatial frequency functions. The variances of both the estimated phase and frequency functions are very close to the corresponding Cramer-Rao lower bounds