Variable gap Fabry Perot(F-P)interferometric spectrometer imaging system has become a research hotspot becauseofitssmallsize, largeluminousflux, highspatialresolution, highspectralresolutionandmanyotheradvantages. Because the interference fringes are not sinusoidal, the exact spectral curves cannot be obtained directly by fast Fourier transform. In this paper, the multi beam interference principle and spectral recovery principle of variable gap Fabry Perot(F-P)interferometer are derived in detail, and the mathematical relationship between interference fringes and spectral curvesisobtained. Then, thefeasibilityandnecessaryconditionsofthespectralrecoverymethod areprovedtheoretically, andthetheoreticalerrorisgiven.Inaddition, thespectralimagingsystembasedonMATLABissimulated, andthephysical experiments are carried out to verify the correctness of the theoretical analysis. It provides theoretical basis for the engineering of Fabry Perot(F-P)interference spectrometer imaging system, and has positive guiding significance for the determinationofparametersinsystemdesign.