The problem of reconstructing the spectrum from the multiple-beam interferogram given by the Fabry-Perot interferometer or from the intensity distribution by a diffraction grat ing is reduced to solving Fredholm's integral equation of the first kind. This equation being solved by the method of Hilbert and Schmidt, the following conclusions are obtained.
1) In Fourier spectroscopy the resolution is one half of the reciprocal of the maximum optical path difference.
2) The resolution of the Fabry-Perot interferometer is infinite because the maxmum optical path difference is infinite.
3) The diffraction grating is, with respect to resolution, similar to the Fabry-Perotinterferometer giving finite number of beams. This number is equal to 2
Ns-1, where
Ns is the number of slits, and accordingly the resolution is finite.
4) Fourier spectroscopy is equivalent to the grating spectpscopy when
Ns=1.
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