Wavelength-shifting interferometry using the frequency-modulated Chirp-Z transform and effective multi-harmonic sampling. (April 2023) - Chang, Lin; Li, Bing; Wei, Yulan; Yu, Yingjie
Highlights: The proposed MWI-CZT algorithm enables multi-surface wavelength-shifting interferometry with free measurement distances, and the profiles of the front surface, rear surface, and thickness variation of the measured transparent flat can be reconstructed simultaneously. Harmonic frequencies are more easily identified through the spectrum densification technique (CZT) method. Light intensity sequences of some pixels are selected for harmonic frequency solving, efficient phase demodulation is achieved, and pixel-by-pixel calculations are avoided. The proposed algorithm provides suppression capability for the phase-shifting error and the background noise, which is better than the classical FFT method. The algorithm performance is fully verified by sufficient experiments and multi-perspective simulation analysis, then visual displays of the solution results are shown in the manuscript. 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.