Sequency encoding single pixel spectroscopy based on Hadamard transform

Single pixel spectroscopy based on Hadamard transform (SPS-HT) has been applied widely because of its capability of wavelength multiplexing and associated advantage in signal-to-noise ratio. In this paper, we propose a sequency encoding single pixel spectroscopy (SESPS) based on two-dimensional (2D) masks for concurrent coding of all Hadamard coefficients instead of one-dimensional (1D) Hadamard masks (only coding one coefficient at a time) widely used in the traditional SPS-HT. Moreover, each Hadamard coefficient is coded along the time dimension with a different sequency value such that the alternating current (AC) measurements of the time-domain signal can be used to reconstruct all Hadamard coefficients simultaneously, which reduces the influence of noise and dramatically speeds up data acquisition. We demonstrate that the SESPS with 32 spectral channels can accelerate spectral measurements from white light sources and fluorescence particles by around 14 times and 70 times, respectively, compared to measurements using a commercial spectrometer when the relative root mean square error (RMSE) is around 3% or smaller. The acceleration factors can be boosted by an extra 4 times when only eight spectral channels are used to achieve a compression ratio of 4:1, in which the relative RMSEs change only marginally. Compared to our previous SPS-HT, this new scheme can increase the speed by three orders of magnitude. This technique is expected to be useful in applications requiring high-speed spectral measurements such as the spectral flow cytometry and on-site medical diagnosis using fluorescence or Raman spectroscopy.