Simultaneous precise measurements of multiple surfaces in wavelength-tuning interferometry via parameter estimation

Abstract

Multiple-surface interferometry with nanoscale accuracy is important in the precise manufacturing of optically transparent parallel plates. To measure the surface profile and thickness variation of the plates simultaneously, the frequencies of the interferometric signal must be estimated from overlaid interferograms. Traditional algorithms typically suffer from issues such as spectrum leakage, reliance on initial iterative values, and the need for prior knowledge. In this study, the time-domain estimation algorithm for multiple-surface interferometry (MSI-TDe) is introduced based on a difference model to improve the accuracy of frequency estimation. The MSI-TDe algorithm is based on a normal equation that is insensitive to environmental noise. Using the algorithm, the frequencies of an interferometric signal can be estimated without prior knowledge and employed for wavefront reconstruction in multi-surface interferometry. Numerical simulation results indicate that the MSI-TDe algorithm has better frequency estimation performance than the discrete Fourier transform (DFT) algorithm. The relative error of the frequency estimation is on the order of 10^–4. Three-surface interferometry was first performed. The root-mean square repeatability standard deviations of 0.07, 0.12 and 0.11 nm for the thickness variation, front surface profile, and rear surface profile, respectively, indicate the stability of the MSI-TDe algorithm. Four-surface interferometry with six frequency components was then performed. The adaptability of the MSI-TDe algorithm is validated by the measurement results.