Analysis on the Lower Limit of Measurable Cavity Thickness Using Fourier-Transform Phase-Shifting Interferometry

Abstract

Fourier-transform phase-shifting interferometry is capable of measuring surface error and cavity thickness (e.g. the thickness of a glass plate) at the same time with high precision. The limit of measurable cavity thickness is related to the range of wavelength tuning, which means the wider range the interferometer could have, the thinner cavity could be measured. In this paper, the lower limit of optical cavity thickness is determined for a given range Δν of wavelength tuning. The theoretical limit is 2c/Δν based on the theory of Fourier-transform phase-shifting interferometry where c is the light speed. We show this limit can be even lower down to 0.7*c/Δν, and the measurements are still reliable which are verified through simulations. For those cavities thinner than the limit, the interferometer may also give good measurements at a certain probability level. Finally a cross test is presented for a glass plate whose physical thickness is about 0.7 mm. The measurement of Fourier-transform interferometry is consistent with that of conventional transmitted wavefront interferometry.