Principal component analysis based simultaneous dual-wavelength phase-shifting interferometry

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

“…Their approach [17] worked well for the example provided but we think their method could easily cross-talk between fitted polynomials for complicated modulating phases [17]. Yet another approach by Zhang et al was published [18][19]. Zhang used a simultaneous two-steps [18], and principal component interferometry [19] to solve the dual-wavelength phase-shifting measurement.…”

“…Yet another approach by Zhang et al was published [18][19]. Zhang used a simultaneous two-steps [18], and principal component interferometry [19] to solve the dual-wavelength phase-shifting measurement. Zhang et al used 32 randomly phase-shifted interferograms [19].…”

“…Zhang used a simultaneous two-steps [18], and principal component interferometry [19] to solve the dual-wavelength phase-shifting measurement. Zhang et al used 32 randomly phase-shifted interferograms [19]. Even though Zhang [19] could demodulate the two phases, they used 32 phase-shifted temporal interferograms.…”

“…Zhang et al used 32 randomly phase-shifted interferograms [19]. Even though Zhang [19] could demodulate the two phases, they used 32 phase-shifted temporal interferograms. All these works on temporal DW-PSA [2][3][4][5][14][15][16][17][18][19] have given just specific DW-PSAs without explicit formulae for their spectra, signal-to-noise, detuning and harmonic robustness.…”

“…In contrast to previous ad-hoc temporal DW-PSA formulas, here we give a general theory for synthesizing DW-PSAs formalizing their spectrum, their signal-to-noise, and their detuning-harmonic robustness. At the risk of being repetitive, we emphasize that we are not just giving particular DW-PSAs formulas as previously done [2][3][4][5][14][15][16][17][18][19]. Here we are giving a general FTF-theory for synthesizing DW-PSA giving with explicit formulae for the most important characteristics of any PSA: spectra, signal-to-noise, detuning and harmonic robustness.…”