Hyun Surk Ryu

Least-squares fitting of the phase map obtained in phase-shifting electronic speckle pattern interferometry.

A new method has been developed to remove noise from the deformation phase map obtained by a phase-shifting electronic speckle pattern interferometry. Unlike usual methods, it estimates almost noise-free phase values directly from the distributions of the intensity differences of four interference patterns by a least-squares fit. The fluctuations of uniform deformation phases are reduced to less than 0.05 rad with a 5 x 5 pixel fitting window. The so-called sawtooth phase jumps that are due to the use of arctangent functions are retained sharply in this method.

MAXIMUM-LIKELIHOOD PHASE ESTIMATION IN PHASE-SHIFTING ELECTRONIC SPECKLE PATTERN INTERFEROMETRY AND ITS COMPARISON WITH LEAST-SQUARES ESTIMATION

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 , 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 Cramer–Rao lower bound. The limitations of the two methods subject to the phase variation within a fitting window are also studied.