Synthesis of multi-wavelength temporal phase-shifting algorithms optimized for high signal-to-noise ratio and high detuning robustness using the frequency transfer function

TL;DR

This paper extends the frequency transfer function approach to synthesize multi-wavelength temporal phase-shifting algorithms, optimizing for high signal-to-noise ratio and robustness, with explicit formulas and generalization to multiple wavelengths.

Contribution

It introduces a general FTF-based synthesis method for dual and multi-wavelength PSAs, providing explicit formulas and extending to multiple wavelengths for the first time.

Findings

Optimized dual-wavelength PSA formulas for high SNR and robustness

Explicit spectral and robustness analysis of DW-PSAs

Generalization of DW-PSA synthesis to multiple wavelengths

Abstract

Synthesis of single-wavelength temporal phase-shifting algorithms (PSA) for interferometry is well-known and firmly based on the frequency transfer function (FTF) paradigm. Here we extend the single-wavelength FTF-theory to dual and multi-wavelength PSA-synthesis when several simultaneous laser-colors are present. The FTF-based synthesis for dual-wavelength PSA (DW-PSA) is optimized for high signal-to-noise ratio and minimum number of temporal phase-shifted interferograms. The DW-PSA synthesis herein presented may be used for interferometric contouring of discontinuous industrial objects. Also DW-PSA may be useful for DW shop-testing of deep free-form aspheres. As shown here, using the FTF-based synthesis one may easily find explicit DW-PSA formulae optimized for high signal-to-noise and high detuning robustness. To this date, no general synthesis and analysis for temporal DW-PSAs has been given; only had-hoc DW-PSAs formulas have been reported. Consequently, no explicit formulae for their spectra, their signal-to-noise, their detuning and harmonic robustness has been given. Here for the first time a fully general procedure for designing DW-PSAs (or triple-wavelengths PSAs) with desire spectrum, signal-to-noise ratio and detuning robustness is given. We finally generalize DW-PSA to higher number of wavelength temporal PSAs.