Direct Determination of Line Shapes of Rotational Spectra from Interferometric Measurements*

Abstract

It is shown that all the structure present in the interferogram of an “ideal” rotational spectrum consisting of many equally-spaced, identical lines is contained in a sequence of “signatures” at path differences of 0, 1/(2B), 2/(2B),…, where B is the reciprocal of inertia. For a symmetric line shape the signatures are all symmetric and homologous, the central one being upright and all successive ones inverted; but asymmetry in the line shape introduces increasing asymmetry in the successive signatures. This agrees with experience. Further, by measuring two vertical distances on each signature one may determine as many harmonics of the line shape as there are signatures. As an example, a typical run of the large interferometric modulator at The Johns Hopkins University is so analyzed.