- The transmittance is given by
where K(s, T, P) is the absorption coefficient depending on the wavenumber, temperature, and pressure. This coefficient may be written as
where S(T) is the line strength and f (s - so , T, P) is the line profile. For this last one, we use the Whiting expression
modified by Oliveiro and Longbothum. [Ref.: J-J. Olivero and R.L. Longbothum, J.Q.S.R.T 17, 233 (1978)]
- The following step is to convolute the transmittance with the apparatus function. This convolution may obviously been applied to
any experimental set-up.
For a FT spectrometer, the apparatus function is first of all due to the maximum path difference which is limited; this function
could be written as
where L is the maximum path difference. Various numerical apodization could be used as for example
- The next step is to convolve this function with a second one, due to the entrance diaphragm
This leads to a shift in frequency
proportional to the wavenumber and the square of the radius r of entrance diaphragm.
f being the entrance focal of the apparatus.
Then the entire apparatus function is
where j is a parameter which describes the asymmetry of the line.