Recent articles have claimed a significant S/N advantage of Hadamard transform spectroscopy over Fourier transform spectroscopy. The scanty published data does not support this assertion, and the possibility that the claim is valid in theory is examined. Existing theory, as reported in the literature, is not consistent with the claims made for the technique. The advantages and drawbacks of Hadamard transform spectroscopy are examined in detail.
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It is widely assumed that the resolution of a Fourier transform spectrometer is given by its retardation, giving 4.0 cm−1 for the FTS-12. However, this involves a resolution defined by the distance between zeroes in the slit function. If, instead, one uses the classical Rayleigh criterion by which the resolutions of grating spectrometers and, by extension, HTS systems are defined, the resolution is 2.83 cm−1.
Based on the published descrition13 of the HTS-255-15.
At the edges of the F.O.V., the modulation efficiency of a Michelson interferometer drops, giving an integral average 75% modulation efficiency over the entire spectrum.
The square-wave modulation employed in Hadamard transform spectroscopy puts 1-1/√2 of the signal energy into the higher harmonics of the modulation frequency. To accept this energy the amplification electronics must have a bandpass several times higher. This would entail more than √2 noise increase, to increase the signal by at most a factor of 2. The electronics of the HTS-255-15 are not described accurately in the literature; on the reasonable assumption that their design gives the highest possible S/N the modulation efficiency is 1/√2.
Derived geometrically for its 28.5-mm × 2.2-mm slit, 64-mm × 64-mm grating, 500-mm focal length, and f/6.9 illumination and assuming the over-and-under entrance and exit beams to have no clearance (optimum possible case).