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

•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.