A method to calculate the spectrum of the light incident on a cascaded Fabry-Perot interferometric spectrometer from the detector signal versus the scanning mirror position is presented. The method is based on modifying the Fabry-Perot integral equation to reduce possible spectrum reconstruction errors that arise due to inaccurate determination of the optical path difference reference position and the dependence on the dispersion of the cavity material. A transformation algorithm that employs the suggested kernel modification is derived and tested. The presented algorithm is then compared to the conventional kernel, showing spectral error reductions by larger than 20 dB.
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