Algorithm for surfaces profiles and thickness variation measurement of a transparent plate using a fizeau interferometer with wavelength tuning

Abstract

An interferogram obtained from a transparent plate contains information on the profiles of both surfaces and on the thickness variation. The present work is devoted to the processing of interferograms of this type. The processing technique is based on a 36-step algorithm developed by the authors for characterization of transparent plates having approximately equal reflections from both sides. The algorithm utilizes weighted multi-step phase shifting that enables one not only separately to extract the front and rear surface profiles together with the thickness variation of the tested plate but also to suppress the coupling errors between the higher harmonics and phase-shift deviation. The proposed measuring method was studied on a wavelength tunable Fizeau interferometer. The tested sample had an optical thickness and surface profile deviations equal to 0.51 µm, 1.38 µm and 0.89 µm, respectively. According to the results obtained using 10 repeated measurements, the root mean square (RMS) errors for determining both surface profiles did not exceed 1.5 nm. Experimental results show that the setup and presented 36-step algorithm are suitable for the measurement of a transparent plate of arbitrary thickness.