Wavelength-shifting interferometry using the frequency-modulated Chirp-Z transform and effective multi-harmonic sampling

Abstract

In wavelength-shifting measurements of the transparent flat, multi-surface harmonics of the measured surfaces with different frequencies provide the corresponding intensity information in the captured interferograms. The limitations of such measurements arise from the limited measurement distance and unsatisfactory frequency detection accuracy. Therefore, a local spectral intensifying method using the Chirp-Z transform is introduced. Based on the distribution characteristics of the phase-shifts within each harmonic period, the calculation method of the measurement distance and the available sampling frequency that can avoid under-sampling is proposed. Based on the above methods, efficient multi-surface phase demodulation can be implemented. Using the Zernike polynomials, the robustness of the proposed algorithm to some common measurement errors is analyzed and demonstrated. In experiments, two transparent plates with thicknesses of 6.35 mm and 15 mm were measured using a wavelength-shifting interferometer. The RMS errors of three repeatability measurements in the experiments are 5.71 nm and 0.64 nm, respectively. Both the simulation analysis and the experiments verify the effectiveness of the proposed method.