Apodization and Phase Correction

Abstract

Consider the Michelson Interferometer shown in Fig. 1 to be perfectly aligned. The intensity, I_o(x), of radiation that reaches the detector when the path-difference between the two arms of the interferometer is x is given by

$$I(x) = \int\limits_0^\infty {{I_o}(k) \cdot T(k) \cdot S(k)(1 + \cos 2\pi kx)dk;} $$

((1))

(1) k is the wavenumber of the radiation in the gas, or vacuum, which fills the dashed box in Fig. 1; I₀(k) is the intensity of radiation emitted by the source at wavenumber k; S(k) is the transmittance of the sample at wavenumber k; and T(k) is the part of the transmittance of the instrument that is independent of path difference. For many purposes, Eq. 1 can be abbreviated to

$$I(x) = \int\limits_0^\infty {A(k)(1 + \cos 2\pi kx)dk} $$

((2))

. (2)