Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry

Abstract

A phase shifting interferometer using a tunable laser as a light source is proposed for measuring shapes of both surfaces of a glass plate and the distribution of refractive index. To separate the superimposed interferograms generated with many wavefronts reflected from the plate, the phase shift associated with the wavelength shift is applied in the phase shifting interferometer with unequal optical paths in testing and reference beams. A laser diode is used for the tunable light source, and the data processing for obtaining phase distribution is based on the least-squares fitting in interferograms. The rms errors of the measurements are <1/50 wavelength for the surface shape, and 10(-5) of the refractive index for a 5-mm thick optical glass plate.

Analyses of multiple surfaces transform interferometry in parallel plate measurement

“…We assume that the normal values for the plate thickness and the refractive index are 10 mm and . The index inhomogeneity of the testing plate is assumed to be a parabolic dish with PV value of 6 7.83 10 − × . As shown in the Fig.…”

“…Okada et al propose a new approach by extracting the useful information from the multi-beam interference pattern rather than suppressing the unwanted interference [6] . Later Deck et al present a much more flexible approach using a Fourier based analysis method combined with phase-shifting interferometer [7,8] .…”

Alternative phase-shifting technique for measuring full-field refractive index

“…Currently, some methods have been proposed to measure full-field refractive index, such as the interferometric methods, [1][2][3][4][5][6] digital holographic microscopy, 7 and ellipsometric methods. 8 In the interferometric methods, the phase difference is relative to the refractive index.…”

“…Generally, the phase-shifting methods introduce successive phase steps into interferometric signals with various phase-shifting strategies, such as piezoelectric transducer, 1,2 holographic grating, 3 and tunable wavelength. 4 Aforementioned methods could suffer from mechanical perturbations, and their costs are high. In addition, to reveal the phase distribution, techniques of three-step and four-step phase-shifting methods are commonly applied.…”

Exact measurements of surface profiles of a glass plate by a superluminescent diode interferometer

“…It has been reported that front and rear surface profiles and distribution of refractive index of a glass plate were measured by a wavelength-scanning interferometer. 5 In this case, phase-shifting interferometry was employed to detect the phase of the interference signal, and the root mean square ͑rms͒ error in the measurement of surface profiles was less than 15 nm.…”