Correction and analysis of noise in Hadamard transform spectrometer with digital micro-mirror device and double sub-gratings

In order to correct spectra anomaly in Hadamard transform (HT) spectrometer with digital micro-mirror device (DMD) and double sub-gratings (DSG) which was proposed by our research team, the analysis of noise is carried out from two aspects, one noise is the intensity noise caused by the instability of light source, detector, substance concentration, electrical system, etc. The other noise is the spectral response noise caused by the diffraction efficiency of DMD and DSG. Consequently, the effects of these noises on Hadamard transform encoding matrix equation are determined and the decoding matrix equations are derived. As a result, the method of inserting testing masks is proposed to correct the intensity noise and the method of correcting spectra by spectral response function is presented to correct the spectral response noise. The simulation results show that the Pearson correlation coefficient (PCC) between detected spectra and original spectra is enhanced gradually from 0.9108 to 0.9997 and the experimental results also demonstrate those two methods are valid, concise and significant.