Zero retardation

Equation 5.24 will be at a maximum, at zero retardation and reach its maximum again when the waves are in phase when vAt—vBt is unity or... 

Interferogram and transformed spectra for acetylene in the 670 to 800 cm V5 bending region. The transformed spectra show the effect of retardation distance on the spectral resolution the 1-cm case corresponds to a total mirror travel of 0.5 cm. The vertical scale of the interferogram is greatly expanded the peak-to-peak voltage at zero retardation is 4 V. 

Figure 5.2.4.2. Ion current against retarding potential for ions from GO (after Hagstrumt Sj. The zero retarding potential scale is taken from CO+. The curves were taken for an electron energy of 100 V.

The interferogram of a polychromatic source exhibits a maximum at <5 = 0, which is called a centerburst (Fig. 2b). At zero retardation both parts of the beam have equal optical path and consequently neither constructive nor destructive interference is produced all frequencies pass the beam splitter undisturbed and the intensity reaches a maximum. 

At the analyzer these vectors Ez and Ey are combined to form a beam of light polarized 90° to the incident beam. It should be clear that the intensity of this final light will depend on the phase angle 8 which in turn depends on the retardation. As 8 increases from zero (retardation increases) the light transmitted will periodically vary from zero to a maximum and decrease to zero again. Theoretically one can show that this dependence of transmitted intensity, It, depends on the retardation as follows... 

The optical path difference (OPD) between the beams that travel to the fixed and movable mirror and back to the beamsplitter is called retardation, 8. When the path length on both arms of the interferometer are equal, the position of the moving mirrors is referred to as the position of zero retardation or zero path difference (ZPD). The two beams are perfectly in phase on recombination at the beamsplitter, where the beams interfere constructively and the intensity of the beam passing to the detector is the sum of the intensities of the beams passing to the fixed and movable mirrors. Therefore, all the light from the source reaches the detector at this point and none returns to the source. To understand why no radiation returns to the source at ZPD one has to consider the phases on the beam splitter. 

Two additional features of the mirror system are necessary for successful operation. The first is a means of sampling the interferogram at precisely spaced retardation intervals. The second is a method for determining exactly the zero retardation point to permit signal averaging. If this point is not known precisely. 

In photoacoustic spectroscopy, signal amplitude increases only when absorption occurs. Thus, photoacoustic spectra will be absorption spectra as opposed to FTIR spectra which are transmission spectra. FTPAS interferograms should then show modulation at high values of retardation as well as near zero retardation. This comes about as a consequence of the properties of Fourier transforms which cause very broad general feature information to be collected at low retardation, with narrow and sharp features ("high frequency") to be collected at higher retardation. 

If we make use of the fact that the interferogram as represented in Eq. 2.12 is symmetrical about 8 = 0 but the first data point is actually sampled before the zero retardation point, at 8 = —e the interferogram takes the form... 

Let us now consider the classical Fourier transform from a more mathematical basis by considering the case of a symmetrical interferogram that has been measured from the zero retardation point [1]. The integral... 

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