Two-wavelength interferometry: extended range and accurate optical path difference analytical estimator.

Two-wavelength interferometry combines measurement at two wavelengths lambda(1) and lambda(2) in order to increase the unambiguous range (UR) for the measurement of an optical path difference. With the usual algorithm, the UR is equal to the synthetic wavelength Lambda=lambda(1)lambda(2)/|lambda(1)-lambda(2)|, and the accuracy is a fraction of Lambda. We propose here a new analytical algorithm based on arithmetic properties, allowing estimation of the absolute fringe order of interference in a noniterative way. This algorithm has nice properties compared with the usual algorithm: it is at least as accurate as the most accurate measurement at one wavelength, whereas the UR is extended to several times the synthetic wavelength. The analysis presented shows how the actual UR depends on the wavelengths and different sources of error. The simulations presented are confirmed by experimental results, showing that the new algorithm has enabled us to reach an UR of 17.3 microm, much larger than the synthetic wavelength, which is only Lambda=2.2 microm. Applications to metrology and fringe tracking are discussed.