Denoising analysis of spatial pixel multiplex coded spectrometer with Hadamard H-matrix

We present a multiplex coded Hadamard transform spectrometer with which Hadamard H-matrix is employed to encode the entrance pixels. Specifically, the Hadamard H-matrix is divided into two coding matrices, H+ and H−; here H−=H−J∕2 and H+=H+J∕2, where each element of J equals 1. We analyzed its denoising capability and compared with the ordinary Hadamard spectrometer with cyclic-S matrix coded and slit spectrometers. The simulation and experiment show that the proposed Hadamard spectrometer with H-matrix outperforms Hadamard transform spectrometer with cyclic-S matrix, gaining about 2 dB of the signal-to-noise ratio.