Direct Interpretation of Far-Infrared Interferograms with Application to Diatomic and Linear Molecules

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Abstract
Interferograms, the information directly available from lamellar grating and Michelson interferometertype spectrometers, are derived on the basis of an absorption spectrum whose lines are sharp, symmetrical, and reasonably well isolated from each other. The formulation shows that if the absorption spectrum is periodic in wavenumber, the interferogram will also have periodic structure characterized by features called signatures. The results are used to predict the interferogram for the pure rotational spectrum of a molecule whose rotational constants approximate those of carbon monoxide. It is found for an absorption spectrum consisting of equally spaced lines (rigid rotor model) that the shape of the individual signatures should be almost identical although damped out exponentially. However when centrifugal distortion is taken into account (nonrigid rotor model), which cause the absorption lines for a linear or diatomic molecule to converge slightly at higher wavenumbers, it is found to lead to a distortion of the signatures, the distortion becoming more pronounced toward large differences of optical path between the interfering beams.