Multi-surface Phase-shifting Interferometry Using Harmonic Frequency Solution Based on the Total Least Squares

Abstract

Wavelength-tuning phase-shifting interferometry plays a significant role in the measurements of transparent parallel plates. The difficulty of multi-surface measurements is that the harmonics with different frequencies and phases make the captured interference signal mixed. In multi-surface measurements, the demodulation of phases builds on the determination of the frequency of each signal, which is traditionally estimated from the prior information including the cavity length and the optical thickness of the measured plate. However, the estimation accuracy of this method is not satisfactory. In order to accurately obtain the signal frequencies and demodulate the initial phases of the measured surfaces simultaneously, this paper proposes a total least squares wavelength-tuning phase-shifting algorithm (TLSWPA). The developed TLSWPA includes two steps: Firstly, considering the influence of the Gaussian noise on the captured interferograms, the signal frequencies are obtained based on the total least squares principle with high accuracy; Secondly, introducing the Householder transformation, the least squares error based on the 2-Norm is used to demodulate the initial phase distribution for each signal. Comparison of the obtained results of the frequency solution and the accuracy of wavefront reconstruction shows that the developed TLSWPA allows obtaining results with an accuracy 2 orders of magnitude higher than the algorithm based on the fast Fourier transform and 1 order of magnitude higher than the advanced iterative algorithm. Experimental study on a borosilicate crown glass using a Fizeau wavelength-tuning interferometer further verifies its effectiveness.