The problem of nonlinear phase errors introduced by misalignment of a Michelson interferometer

Abstract

In Fourier transform spectroscopy, a slight angular misalignment or canting of one of the mirrors in the Michelson interferometer causes not only a reduction of the oscillatory part of the interferogram but may also lead to an asymmetry. In order to elucidate the reasons for this effect, we performed calculations for a Michelson interferometer including the effects originating from a source of finite area and from a finite aperture. Our treatment also takes into account the effect of a thin film beam-splitter in the parallel beam with a relatively large angle of incidence. The beam-splitter may be considered a dispersive medium in the sense that its efficiency varies strongly with frequency. The essential results of our calculations are that nonlinear phase errors arise under the considered conditions depending on the product of the angle of mirror misalignment and the solid angle subtended by the source from the collimator mirror. Experimentally, we studied the occurrence of asymmetric interferograms and nonlinear phase errors due to misalignment for three different types of interferometers. In the case of lamellar grating interferometer, a misalignment of one of the cam systems caused only a symmetric reduction of the oscillatory part of the interferogram. A similar symmetric reduction with no asymmetry was observed for a two-beam interferometer with the beam-splitter placed at a focus. For a Michelson interferometer with a thin film beam-splitter in the parallel beam (Polytec FIR 30), however, a mirror misalignment of a few hundredths of a degree caused asymmetries in the interferogram of as much as 30%, in satisfactory quantitative agreement with our theoretical approach.