Maximum-likelihood phase estimation in phase-shifting electronic speckle pattern interferometry and its comparison with least-squares estimation

Abstract

The least-squares phase-fitting method, developed recently without any statistical justification, extracts an almost noiseless phase directly from the distribution of the intensities of phase-shifted speckle interference patterns [C. K. Hong et al., Opt. Lett. 20, 931 (1995)]. We present another method that can do the same by using the statistically well-established maximum-likelihood algorithm. Numerical simulations show that the precision of the maximum-likelihood estimate is better than that of the least-squares method by 19% and that its precision essentially achieves the one given by the Cramér–Rao lower bound. The limitations of the two methods subject to the phase variation within a fitting window are also studied.