Study of the performance of 84 phase-shifting algorithms for interferometry

Abstract

When performing phase-shifting, phase differences in a periodic intensity profile are changed, and the resulting irradiance distributions are recorded at each step. The wanted phase can be obtained from the arctangent of the ratio between two combinations of the observed irradiances, according to the phase-shifting algorithm (psa) used. There are many such combinations and thus different psas, each with specific performance and properties. We briefly discuss some error sources which might influence the performance and quality of interferometry measurements. The robustness against these error sources is strongly dependent on the psa used. Several computer simulations on all of the 84 psas were carried out to confirm which algorithms perform best in the presence of some straightforward error sources.

Practical eight-frame algorithms for fringe projection profilometry

“…On the other hand, having a good algorithm and considering the particular experimental conditions, more economic equipment will be enough to cover the needs of precision and accuracy of the experiment. Most eight step algorithms are centered at π/2 [22]; however, as the error distribution is greater for each step, a filter centered in a further step (π/4 in this case) and immune to detuning (given the dispersion of the phase steps in Fig. 8) is needed to compensate experimental errors.…”

Quadrature wavelength scanning interferometry

“…In phase shifting interferometry (PSI) fringe data is obtained by modulating the optical path difference between the measurement and the reference arm by a known amount and recording the intensity values [6,7]. The modulation is typically achieved by mechanically scanning the reference mirror (or sample), and it requires a highly stable system with precision motion control.…”

Heterodyne moiré surface profilometry

“…In moiré surface profilometry, the information related to the tested surface profile can be recorded in the moiré fringes; thus, the capability of the moiré fringe analysis technique strongly affects the precision and resolution of the measurement, and whether the relevant information involved in the moiré fringes can be completely extracted. Moiré fringe analysis techniques, like the interferometric fringe analysis of the optical interferometer, can be divided into two primary groups, the Fourier transform methods [10,11] and phase-shift methods [12][13][14][15][16][17][18]. However, the harmonic noise which results from the grating lines spreads throughout the whole moiré fringes, and eliminating this noise is a critical concern when conducting moiré fringe analysis.…”

“…Because this procedure is an approximate approach, the resulting information regarding the surface profile may lack detail. Choi et al [14] and Buytaert et al [15][16][17] used an optical compensation technique in phase-shift method to filter out the grating noise, and the use of DFT to extract the moiré phase is further explained by Buytaert et al [18]. This technique synchronously moved two gratings, displacing one grating pitch per phase-shift step and setting the moving time as the exposure time of the camera; repeating this at every phase-shift step removed the harmonic noise.…”