Effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry

• Published in: Journal of modern optics Vol. 55; no. 8; pp. 1291 - 1304
• Main Authors: Xu, X.F., Cai, L.Z., Wang, Y.R., Meng, X.F., Zhang, H., Cheng, X.C., Dong, G.Y., Shen, X.X.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 10.05.2008; Taylor & Francis
• Subjects: Computers in experimental physics; digital image processing; Exact sciences and technology; Fundamental areas of phenomenology (including applications); holographic interferometry; Holographic interferometry; other holographic techniques; Holography; Image processing; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Interferometers; Optical instruments, equipment and techniques; Optics; phase measurement; phase shift interferometry; Physics; wave-front reconstruction; Phase measurement; Algorithms; Wave front; Image processing; Phase shifting interferometry; Random phase; Measuring methods; Optical method; Digital processing; Holographic interferometry; Square wave
• ISSN: 0950-0340; 1362-3044
• DOI: 10.1080/09500340701644383

We have investigated the effect of phase shift selection and phase shift errors on wave-front reconstruction errors in three-step generalized phase-shifting interferometry (GPSI) systematically. A general formula of the mean square wave reconstruction error for different phase shift selection and different phase shift errors is derived, and its specific expressions for the equal, linear, and random phase shift errors are deduced. The results reveal that there is a wide range for phase shift selection in GPSI, and the equal phase step algorithm is superior to the one of unequal step where the three kinds of phase shift errors are concerned. Specifically, the phase step leads to the minimum wave reconstruction error in the cases of equal and linear phase shift errors, while the phase step 1.91 rad yields the smallest wave reconstruction error for random phase shift errors. These results have been verified by a large number of computer simulations with over 100,000 samples.