We present a general mathematical framework within which the relative performance of singly multiplexed Hadamard transform spectrometers (HTS) and conventional scanning spectrometers (SS) may be compared. The theoretical multiplex advantage (Fellgett advantage) is calculated for spectrometers operating in two spectral regions. For the low energy region, i.e., infrared, the determined multiplex advantage F is (N/2)½ (N is tle number of slots), in accordance with predictions given by Fellgett. For the high spectral energy region, i.e., uv-vis, F = (x/2x¯)½, where x is the intensity of the spectal element sought and x¯ is the average intensity produced across the whole spectrum. Our predictions are verified by computer simulation of various characteristic spectra. Based on these results, we arrive at some conclusions concerning the practical application of HTS systems.
N. M. Larson, R. Crosmun, and Y. Talmi, "Theoretical Comparison of Singly Multiplexed Hadamard Transform Spectrometers and Scanning Spectrometers," Appl. Opt. 13, 2662-2668 (1974)