Imaging spectrometers usually use area array detectors as photoelectric conversion devices, but the inconsistencies of the spectral response among pixels can distort the collected target spectra. To improve the spectral radiometric accuracy of imaging spectrometers, calibrating and correcting the inconsistency of the spectral response among pixels is essential. The signal received by each pixel of area array detector of the indirect imaging spectrometer is usually the superposition of the target multi-spectral or full-spectral radiation signal. Therefore, its relative spectral radiometric calibration necessitates measuring the spectral response of each pixel across the array detector at different wavelengths. Under the ideal conditions, the response values of each pixel in the area array detector are different, so the indirect imaging spectrometer cannot simply calibrate the relative spectral response (RSR) function among pixels through the method of "monochromator + integrating sphere". In this work, we take the interferometric imaging spectrometer as an example, analyze the influence of the inconsistency of the RSR among pixels on the target spectral radiation measurement accuracy, propose a system-level RSR function measurement method for the indirect imaging spectrometer based on the Fourier transform modulation calibration source. In addition, we establish a mathematical model for the calibration of the RSR function，and provide guidelines for selecting calibration system parameters (light source、 spectral resolution and OPD sampling interval). The simulation results show that under the ideal noise-free condition, the 1% spectral response inconsistency among pixels results in a relative error of 1.02% to the recovered spectra. After RSR correction, the relative error of the recovered spectra of different rows decreases to 0.08%. Furthermore, this paper simulates and analyses the influence of spectral signal-to-noise ratio on the calibration accuracy of the RSR function, and points out that increasing the brightness of the calibration light source, extending exposure time, and combining multi-frame interferograms can enhance RSR function calibration accuracy in practical applications. The research result can provide a theoretical basis for the relative spectral radiometric calibration of indirect imaging spectrometer, which is of great significance in promoting quantitative spectral remote sensing.
