An improved 2+1 phase-shifting algorithm

• Published in: Optics communications Vol. 444; pp. 165 - 171
• Main Authors: Li, Donglin, Cao, Yiping, Fu, Guangkai, Li, Chengmeng, Wan, Yingying
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2019
• Subjects: 3D shape measurement; Calibration; Flat image; Least squares fit; Phase measuring profilometry; Flat image; Calibration; Phase measuring profilometry; Least squares fit; 3D shape measurement
• ISSN: 0030-4018; 1873-0310
• DOI: 10.1016/j.optcom.2019.03.081

An improved 2+1 phase-shifting algorithm based on the flat image fitting calibration is proposed. The 2+1 phase-shifting algorithm proposed by Zhang uses one uniform gray image whose gray is the same as the mean gray of the phase-shifting sinusoidal grating patterns instead of one of these grating patterns in traditional three-step phase measuring profilometry to reduce measuring error caused by motion. It maintains that the light intensity distribution of captured flat image is equal to the dc component of the captured phase-shifting deformed patterns. But extensive experimental results show that there is a certain inconsistency between the light intensity distribution of the captured flat image and the dc component of the deformed patterns. It will bring some nonnegligible errors. So a calibration procedure is introduced before measuring to obtain a calibration coefficient between the captured flat image and the dc component of the captured fringe pattern by the least squares fit. While measuring, the veritable dc component of the captured deformed pattern is extracted by just multiplying the calibration coefficient with captured flat image. Thus, the above nonnegligible errors can be effectively improved. Furthermore, the proposed algorithm is more flexible because its shifting-phase is no longer fixed to be π/2 but optional. The experimental results show the effectiveness and practicability of the improved 2+1 phase-shifting algorithm.