Analysis of different sampling procedures in Fourier-transform spectroscopy

An analysis of spectral errors induced by the sampling method used for the interferogram acquisition in Fourier-transform spectroscopy is given. A model is presented that can be used for a rigorous determination of the expected spectral noise in the case of different sampling methods as a function of the quality of the implemented instrumental devices. Using this model numerical evaluations are made in the case of the REFIR (radiation explorer in the far infrared) instrument developed for the measurement of the long wavelength Earth's emission from satellite platforms. The different sampling techniques are considered and evaluated for the selection of the most suitable one for this application. The equal time sampling followed by a numerical filter and a re-sampling has shown the capability of best correcting for sampling errors in the case of this instrument. Furthermore, from the general model an approximate expression is derived that can be used for a preliminary estimate with simple analytical calculations of the spectral noise for different sampling methods. In the specific case of REFIR, a comparison between the numerical modeling and the approximate expression has confirmed that the latter gives a good estimation and can be very useful for the assessment of the relative relevance of the different components of the spectral noise induced by sampling errors.