Generating the Interferogram

By displacing the movable mirror one alters the retardation between the beams. If the mirror is displaced a distance X/4, the optical path difference between the beams on the beamsplitter is X jl and the beams interfere destructively as they are out of phase. In this situation, all the light returns to the source. Likewise, if the retardation is X (corresponding to a mirror displacement of X/2), the beams interfere constructively on the beam splitter, and ah the light travels to the detector. 

In the case of monochromatic light of wavelength ko (or wavenumber vo = 1 Ao), as shown in Fig. 2.2, the intensity of the beam at the detector measured as a function of retardation has a cosine shape, where the maximums correspond to retardation intervals multiple of ko. At other wavenumbers v, the intensity of the beam at the detector is 

As seen in Eq.2.4, for the particular case of the ZPD where 5 = 0, the intensity of the beam at the detector is 7 (5) = ARTIq v). Considering an ideal beam splitter (7 = r = 1/2) this equation becomes 

For a broadband source B(v), where radiation of more than one wavelength is emitted by the source, the measured interferogram is the result of the sum of the cosines contributions corresponding to each wavenumber, in other words, a measure of the interference of all the spectral components of B(v) as the retardation is varied. In this situation the measured interferogram is 

In theory, by scanning an infinite distance one could recover the spectrum at infinitely high resolution. In practice one selects a maximum optical path difference to be scanned, limiting the spectral resolution of the measurement. 

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