A great deal of theoretical research and experimental verification has been done on the DMD spatial light modulated Hadamard transform spectrometer, but the research on this technology was still immature, many problems need to be further studied. The spatial distribution of the dispersion spectrum on the DMD was different because of the different spatial positions of the pixels on the image which resulted in the different encoding matrices of the dispersion spectrum of each pixel. An identification method of spectral recovery matrix was proposed by comparing the gray values of laser-coded images and combining with the changing rules of S-matrix elements. Taking the 7-order left-shift cyclic S-matrix as an example, the results of spectral recovery were verified by two imaging experiments. In the first experiment, a laser beam of 632.8 nm was directed into the spectrometer, the spectral response range of the spectrometer was 550-680 nm, and 632.8 nm within the fifth band range from 626 nm to 644 nm. Theoretically, only the fifth spectral images with a bond range of 626-644 nm was bright, and the rest of the images have no energy distribution. The actual experimental results are in agreement with the theoretical analysis. In the second experiment, the spectrometer was used to image a color butterfly model. The spectral curves of two test points were extracted from the recovered spectral images, and compared with the spectral characteristic curves obtained by radiometer. The experimental results show that the spectral curves obtained from the recovered spectral images are basically the same as the spectral characteristics curves extracted by radiometer. Two groups of spectral recovery experimental results verify the effectiveness of the proposed identification method for spectral recovery matrix.