In this paper, we present a convolution neural network based method to recover the light intensity distribution from the overlapped dispersive spectra instead of adding an extra light path to capture it directly for the first time. Then, we construct a single-path sub-Hadamard snapshot spectrometer based on our previous dual-path snapshot spectrometer. In the proposed single-path spectrometer, we use the reconstructed light intensity as the original light intensity and recover high signal-to-noise ratio spectra successfully. Compared with dual-path snapshot spectrometer, the network based single-path spectrometer has a more compact structure and maintains snapshot and high sensitivity. Abundant simulated and experimental results have demonstrated that the proposed method can obtain a better reconstructed signal-to-noise ratio spectrum than the dual-path sub-Hadamard spectrometer because of its higher light throughput.
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