Abstract
To accurately obtain the phase distribution of an optical surface under test, the accurate phase extraction algorithm is essential. To overcome the phase shift error, a random two-step phase shifting algorithm, which can be used in the fluctuating and non-uniform background intensity and modulation amplitude, Lissajous ellipse fitting, and least squares iterative phase shifting algorithm (LEF&LSI PSA), is proposed; pre-filtering interferograms are not necessary, but they can get relatively accurate phase distribution and unknown phase shift value. The simulation and experiment verify the correctness and feasibility of the LEF & LSI PSA.
Highlights
Interferometry is the industry standard for optical measurement [1]
Based on the principles of LEF-phase-shifting algorithm (PSA) and least squares algorithm (LSA), we propose a novel PSA, namely Lissajous ellipse fitting and least squares iterative phase shifting algorithm (LEF & LSI-PSA), which uses only two phase-shifted interferograms without other information
Based on the above different simulations, the advantages of proposed LEF & LSI PSA can be summarized as: 1) It has a higher accuracy than LEF PSA; 2) it is less sensitive to the phase shift value; 3) it is almost insensitive to the fluctuations of the background intensity and modulation amplitude; and 4) it can partially suppress the effect introduced by the nonuniform of the background intensity and modulation amplitude distribution
Summary
Interferometry is the industry standard for optical measurement [1]. The phase-shifting interferometer (PSI) was introduced by Brunning [2] to achieve accurate optical metrology in 1974, PSI and its variations have been widely used [1,3,4]. We proposed a method which can correct fringe-print-through (FPT) error in snapshot phase-shifting interference microscope based on the 4-step PSA and Lissajous ellipse fitting [27], this algorithm uses all four phase-shifted interferograms and can be applied in the different intensity distribution conditions, even the intensity distribution is nonuniform, it can correct the FPT error by only one measurement. It is only suitable for the 4-step PSA, and the phase shift should be a constant (π/2).
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