Abstract
To overcome the phase shift error in phase shifting interferometry, a two-step random phase retrieval approach based on Gram-Schmidt (GS) orthonormalization and Lissajous ellipse fitting (LEF) method (GS&LEF) is proposed. It doesn't need pre-filtering, and can obtain relatively accurate phase distribution with only two phase shifted interferograms and less computational time. It is suitable for different background intensity, modulation amplitude distributions and noises. Last but not least, this method is effective for circular, straight or complex fringes. The simulations and experiments verify the correctness and feasibility of GS&LEF.
Highlights
Phase-shifting interferometry (PSI) has been widely used in the high precision phase measurement, such as optical surface testing, deformation measurement [1,2,3]
The algorithm provides stable convergence and accurate phase extraction with as few as three interferograms, even when the phase shifts are completely random. This approach consumes a lot of computational time [19,20,21,22,23,24,25]. proposed a series of phase-shifting algorithm (PSA) based on principal component analysis (PCA), which can fast and extract the phase distribution from randomly phase shifted interferograms
We begin to discuss the effect of noise, we only add the noise to the interferograms, and the background intensity and modulation amplitude are perfect, but we found that the phase error is increasing for both methods, especially for GS&Lissajous ellipse fitting (LEF), the RMS phase error which is 0.1281 rad is more than 10 times of the third simulation, that is to say, LEF process only can correct the piston, it cannot correct the noise, and the RMS phase error of GS (0.1701 rad) is a little bigger than that of the third simulation, but the effect of the filtering error is largest
Summary
Phase-shifting interferometry (PSI) has been widely used in the high precision phase measurement, such as optical surface testing, deformation measurement [1,2,3]. The first type is multi-step random PSA, where the number of the phase shifted interferograms is greater than or equal to 3 While it can obtain the tested phase more the phase error may be introduced due to the multiinterferograms, and it spends more time on the measurement and calculation [18]. We proposed a random two-step PSA based on Lissajous ellipse fitting and least squares technologies [16], this algorithm uses only two interferograms to extract the relatively accurate tested phase distribution and unknown phase shift without pre-filtering, the least squares technologies are time consuming. For two-step random PSAs, it is difficult to obtain the high-precision phase distribution with less time because of the pre-filtering or the DC term subtraction.
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