An introduction to Hadamard spectrometry and the multiplex advantage

The authors consider a special class of problems in which the dominant noise source in the spectrum measurements is the noise generated in the detector itself. In this case, the signal-to-noise ratio of the spectrum estimates can be improved by a multiplexing technique known as Hadamard spectrometry. Specifically, if the MSE (mean-square error) of a single-slit spectrometer is σ², the MSE of a Hadamard system will be approximately 4/σ²/N. In this expression, N is the number of spectral components to be estimated and the number of measurements to be taken