Phase retrieval with a three-frame phase-shifting algorithm with an unknown phase shift

A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry. For a fringe pattern with slow-varying background intensity, the background removal is achieved in the frequency domain. For a speckle pattern, a background removal technique is integrated with the three-frame algorithm. In this process, manual intervention is minimal, and high computational speed is achieved. In addition, high-frequency phase signals would not be removed in the noise-reduction process as is the case in the bandpass-filtering technique. Accuracy of the method is discussed.