Carrier squeezing interferometry with π/2 phase shift at the synthetic wavelength: Phase extraction in simultaneous dual-wavelength interferometry

Abstract

Dual-wavelength interferometry (DWI) could extend the measured range of each single-wavelength interferometry. The synchronization of the two working wavelengths in DWI is of high efficient, and the generated moiré fringe indirectly represents the information of the measured long synthetic-wavelength (λS) phase. However, the extraction of the measured synthetic-wavelength phase is rather arduous from the moiré fringe. To retrieve the synthetic-wavelength phase from the moiré fringe patterns, we present a carrier squeezing dual-wavelength interferometry method (CSDI) in simultaneous DWI (SDWI). After the mathematical square of the moiré fringe patterns, the multiplicative moiré phase-shift fringe patterns with π/2 phase shift at λS are combined into a single spatial-temporal fringe (STF). By converting the temporal phase shift into spatial carrier and the introduction of the carrier, the measured synthetic wavelength phase is retrieved by the filter and inverse Fourier transform of the STF spectrum. Compared with other methods, CSDI method could suppress the influence of the phase-shift error and only requires 4 frame phase-shift interferograms. Numerical simulations are executed to demonstrate the performance of the CSDI method in SDWI with the peak-to-valley (PV) value of 1.46 nm and the root mean square (RMS) values of 0.23 nm for the demodulated error. And the precision is better than PV of 20 nm (0.0059λs) and RMS of 6 nm (0.0017λs) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λS. Finally, our experimental results indicate that the measurement accuracy is better than 1.3% for a step with the height of 7.8 µm, and 0.5% for the step height of 6.233 µm for a Fresnel lens.