Wavelength-tuning phase-shifting interferometry is a modern optical measurement method based on the propagation characteristics of light, which can determine sample topography by wavelength-level non-contact method with high-precision. The accuracy of this method can be up to nanometer and sub-nanometer precision. The measurement of transparent parallel plates is important and significant in optical measurement. Based on the design of window and sampling functions, the introduced 36 steps phase-shifting algorithm can effectively extract the target information. The influences of constant and first-order phase-shifting errors are analyzed. The least square separation method based on 19 steps iteration can determine the surface phase information accurately and separate surfaces including front, rear, thickness information, even the parasitic term. The influence of different iteration steps for the PV and RMS values is considered, which provides the basis and reference for the design of the separation algorithm.
Two methods that used to measure the thickness of transparent plate were introduced in this paper. In conventional interferometry, multiple-surface interference fringes and the nonzero incidence angle complicated the calculation. In this study, the absolute thickness was obtained from the interferogram generated by two beams of coherent light reflected from the front surface and the rear surface of the transparent plate without reference surface. The thickness was obtained by analyzing light intensity of each point in the interferogram which varies sinusoidally with the wavelength in period method. While slope method figured out the mean thickness of whole surface with phase-shifting algorithm and least-square fitting algorithm. When the beam was perpendicular to the surface, the absolute thickness can be figured out with the refractive index n and λ1, λ2 in first technique. The results of simulation experiments indicated that the error in first technique was with sub micrometer, however the error of slope method was only a few nanometers.
The information about the profiles of both surfaces of the transparent plate are contained in an interferogram. This information can be extracted by processing fringe patterns measured at different wavelengths. The conventional Fourier analysis applied to solve such problems with a set of a restricted number of the fringe patterns, otherwise this analysis is quite sensitive to the error of frequency drift and suffers from fringe patterns interference noise. This study proposes a method of frequency estimation to obtain profiles of surfaces of transparent plate. A series of fringe patterns obtained at different phase shift caused by wavelength changing are regarded as a set of overlapped sinusoidal signal. Using Total Least Squares method to find the frequency of different signal to attain the separation of interferogram. The simulation shows that the proposed method has the immunity from noise interference.
The multi-grid method is a common method for solving the transport of intensity equation (TIE). Transport of intensity equation can retrieve phase information from the directly measured intensity image. When using multi-grid method to solve the TIE, firstly, the phase distribution is directly solved on the coarsest layer. The solved phase distribution is regard as the initial value on the finest grid layer to increase the convergence speed of the algorithm. Residual error on the finest grid can be obtained, then, using the restrict operators transfer the residual error from finer grid to coarser grid, until the solution on the coarsest grid is obtained. the solution on coarser grid transfer to finer grid by using prolongation operator, until the accurate phase distribution solution obtained on the finest grid. The Simulation experiments show that this method has a better convergence rate and retrieves complicated phase with higher accuracy.