Impact of the Sinusoidal Drive on the Instrumental Line Shape Function of a Michelson Interferometer with Rotating Retroreflector

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Abstract
In Fourier spectrometers using the classical Michelson setup, conventionally a plane mirror travels with constant speed to generate an optical pathlength alteration. Recently, different types of Michelson interferometers have been developed that use one or more rotating retroreflectors for pathlength variation. They all exhibit a sinusoidal dependence of the pathlength on time. This paper discusses the effects of the nonlinear mirror motion on the interferogram and the calculated spectrum. The requirements necessary for the acquisition system are deduced, and distortions due to nonideal analog electronics are calculated quantitatively. The investigations concentrate on the influence of a nonconstant electronic transfer function and differences in the delay times of the measurement channel and the reference channel, which generates the sampling pulses. The results are applied to the laboratory model of a Michelson interferometer with rotating reflector (spectral resolution ≈0.5 cm−1). It is proved by measuring the instrumental line shape function (ILS) that there can be compensations for the effects mentioned above, with a residual error of less then 1% in comparison to the results for the ideal ILS.