Interferometric measurement of a multiparallel-surface transparent object by a new class of wavelength tuning algorithms

Wavelength scanned interferometry can distinguish in frequency space interference signals from different surfaces , and therefore allows the measurement of optical thickness variation between several quasi-parallel surfaces of a composite transparent object. Discrete Fourier analysis of the signal spectrum with a suitable sampling window can then detect the phase of the individual signals. The actual frequencies of the various signals can deviate from their nominal detection frequencies because of refractive index dispersion of the material and/or nonlinearities in the wavelength scanning. This creates problems for conventional sampling window functions, such as the von Hann window, because they are sensitive to detuning of the signal frequency. Therefore we have derived an error-compensating algorithm (with 2N-1 samples and individual phase steps of 2p/N) with a modified triangular window that allows some frequency detuning and can determine the phase of any specific harmonic order within the frequency range of the detected signal. A composite object consisting of four reflecting surfaces was measured using the new algorithm in a Fizeau interferometer. Experimental results show that the new algorithm measured the front surface and the optical thickness variations in a glass-air-glass cavity with an error of 10 nm rms over a 90 mm diameter aperture.