A method for the spectroscopic investigation of electromagnetic radiation in the infrared spectrum by means of a Fourier spectrometer, whereby an interferogram is measured as the output signal of a detector comprising a sensor that is sensitive to the radiation to be detected, and amplifier electronics tuned thereto, in such a way that, through correction of a measured output signal I.sub.m, which is distorted due to detector non-linearities, a distortion-free interferogram is approximated by synthesizing a signal I.sub.s that is proportional to the required distortion-free interferogram of the detector from a finite mathematical series of orthogonal functions in such a way that the function terms of said mathematical series are based on the distorted measured output signal I.sub.m of the detector in the form I.sub.s =f(I.sub.m),
- characterized in that the determination of unknown coefficients a.sub.i takes place after Fourier transformation of the finite function series f(I.sub.m) in the spectral range in such a way that the resulting spectrum S.sub.s, which represents the Fourier transform of the signal I.sub.s that is proportional to the required distortion-free interferogram of the detector, possesses, in the spectral ranges in which the radiation detector has no or only a negligible optical sensitivity, spectral values that are as close to the ideal value zero as possible.