Asymmetrical interferogram

However, for illustration, only one side of the interferogram and its spectrum will be shown, usually the function of the positive spatial and spectral variable. In other operating modes of the interferometer, asymmetric interferograms are produced that have a complex Fourier transform. Asymmetric interferograms will not be treated in this work. For a more complete discussion of Fourier transform spectroscopy, the reader should consult Bell (1972), Vanasse and Strong (1958), Vanasse and Sakai (1967), Steel (1967), Mertz (1965), the Aspen International Conference on Fourier Spectroscopy (Vanasse et al., 1971), and the two volumes of Spectrometric Techniques (Vanasse, 1977, 1981). A review of early work, which includes several major contributions of his own, is given by Connes (1969). Another interesting paper on the earlier historical development of Fourier transform spectroscopy is that by Loewenstein (1966). 

In practice, the interferogram measured is not mirror symmetrical about the point d = 0. Call up the interferogram of the file MIR GLYCIN or ACQUIS in order to verify that. This asymmetry originates from experimental errors, e.g., wavenumber-dependent phase delays of the optics, the detector/ amplifier unit, or the electronic filters. The Fourier transformation of such an asymmetrical interferogram generally yields a complex spectrum C(v) rather than a real spectrum S(r) as known from spectrometers based on the dispersive technique. That is why phase correction is necessary. 

THE USE OF ASYMMETRIC INTERFEROGRAMS IN TRANSMITTANCE MEASUREMENTS. FROM COLLOQUE SUR LES METHODES NOUVELLES DE SPECTROSCOPIEINSTRUMENTALE, 2ND,... 

The cosine Fourier transform given by Eq. (2) is only applicable if the interferogram is perfectly symmetrical about <5 = 0. In practice additional wavenumber-dependent phase shifts are present, owing to beamsplitter characteristics or refraction effects, and cause the interferogram to appear partially asymmetric. The modulated part of Eq. (1) then becomes... 

Fig. 33. Transmission (a) and reflection measurements (b) by means of asymmetric Fourier transform spectroscopy. The samples are polyethylene (PET) and mylar (transmission), and KBr (reflection). The difierent curves show background and sample interferograms as well as power transmittance (reflectance) and phase angle spectra. Data taken from Ref. 59)...

When the Michelson interferometer with finite aperture is not properly adjusted nonlinear phase errors arise These phase errors are no longer linearly dependent on the wave number v, and they cause an asymmetric distortion of the interferogram (Figs, 40b and 41). It should be noted that all illustrations in connection with errors (Figs. 39, 40 and 41) have been produced by computer simulation (cf. Appendix 1). In order to make the essential features as clear as possible the effects of finite resolution etc. are left out where they have not necessarily to be included. In these cases, the resolution width /d is given in the figure (Figs. 39a—c). In Fig. 41, the error correction is demonstrated with finite... 

In fact, it is this phase shift (p(i>) which causes the asymmetric distortion of the interferogram. For linear or nonlinear function of wave number P, the assumption generally holds that it is a smooth and slowly varying function of P. 

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