Phase-shifting algorithms for electronic speckle pattern interferometry.

A set of innovative phase-shifting algorithms developed to facilitate metrology based on electronic speckle pattern interferometry (ESPI) are presented. The theory of a phase-shifting algorithm, called a (5,1) algorithm, that takes five phase-shifted intensity maps before a specimen is deformed and one intensity map after a specimen is deformed is presented first. Because a high-speed camera can be used to record the dynamic image of the specimen, this newly developed algorithm has the potential to retain the phase-shifting capability for ESPI in dynamic measurements. Also shown is an algorithm called a (1,5) algorithm that takes five phase-shifted intensity maps after the specimen is deformed. In addition, a direct-correlation algorithm was integrated with these newly developed (5,1) or (1,5) algorithms to form DC-(5,1) and DC-(1,5) algorithms, which are shown to improve significantly the quality of the phase maps. The theoretical and experimental aspects of these two newly developed techniques, which can extend ESPI to areas such as high-speed dynamic measurements, are examined in detail.