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

摘要

Synthesis of single-wavelength temporal phase-shifting algorithms (PSA) forinterferometry is well-known and firmly based on the frequency transferfunction (FTF) paradigm. Here we extend the single-wavelength FTF-theory todual and multi-wavelength PSA-synthesis when several simultaneous laser-colorsare present. The FTF-based synthesis for dual-wavelength PSA (DW-PSA) isoptimized for high signal-to-noise ratio and minimum number of temporalphase-shifted interferograms. The DW-PSA synthesis herein presented may be usedfor interferometric contouring of discontinuous industrial objects. Also DW-PSAmay 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 formulaeoptimized for high signal-to-noise and high detuning robustness. To this date,no general synthesis and analysis for temporal DW-PSAs has been given; onlyhad-hoc DW-PSAs formulas have been reported. Consequently, no explicit formulaefor their spectra, their signal-to-noise, their detuning and harmonicrobustness has been given. Here for the first time a fully general procedurefor designing DW-PSAs (or triple-wavelengths PSAs) with desire spectrum,signal-to-noise ratio and detuning robustness is given. We finally generalizeDW-PSA to higher number of wavelength temporal PSAs.