Correction of non-linearities in detectors in fourier transform spectroscopy

TLDR: In this article, two correction factors are calculated from this Fourier transform and these correction factors were then used to calculate a corrected interferogram, and these two corrections factors are then used in calculating a second order approximation to a corrected Interferogram.

Abstract: An interferogram is formed as in the prior art by dividing a beam of radiation from the source into two beams and interfering these beams so as to form an interferogram on the detector. A Fourier transform is then made of this interferogram. This transform has a signal spectrum above the cutoff frequency of the detector; and because of non-linearities in the detector and in the electronic signal processing circuitry, this transform also has a spectrum below the cutoff frequency of the detector. In accordance with the invention, two correction factors are calculated from this Fourier transform and these correction factors are then used to calculate a corrected interferogram. The first correction factor is evaluated by determining from the portion of the spectrum below the cutoff frequency a valve for the spectral signal at zero frequency. In addition, the integral of the square of the spectrum signal above the cutoff frequency is determined and the correction factor is found by dividing the signal at zero frequency by the integral of the square of the spectrum above the cutoff. The second correction factor is a function of the first correction factor and the integral of the spectrum signal above cutoff. These two corrections factors are then used in calculating a second order approximation to a corrected interferogram. Finally to produce the corrected Fourier transform, a Fourier transformation is made.