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Fourier and Hadamard transform spectrometers: a limited comparison.

M H Tai, M Harwit

|February 19, 2010

Summary

Fourier transform spectrometers (FTS) show double the error of Hadamard transform spectrometers (HTS) due to modulation limitations. This study quanties the encoding figure of merit for these systems.

Area of Science:

Spectroscopy
Optical Engineering
Signal Processing

Background:

Fourier transform spectrometers (FTS) and Hadamard transform spectrometers (HTS) are key spectroscopic instruments.
Understanding their performance limitations, especially in detector-noise limited scenarios, is crucial for accurate spectral analysis.

Purpose of the Study:

To establish and compare an encoding figure of merit for detector-noise limited FTS and HTS.
To analyze the sources of error and performance differences between FTS and HTS systems.

Main Methods:

Development of an encoding figure of merit for detector-noise limited spectroscopy.
Comparative analysis of mean square errors for FTS and HTS systems with N spectral densities.
Evaluation of modulation characteristics and orthonormality of spectral functions in FTS.

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Main Results:

Detector-noise limited FTS exhibits mean square errors twice as large as analogous HTS systems for N measurements.
FTS limitations stem from cosine-squared modulation and non-orthonormal spectral functions.
Fellgett's advantage for Michelson interferometers is (N/8)(1/2), not (N/2)(1/2) as commonly cited.

Conclusions:

HTS offers superior performance over FTS in detector-noise limited conditions.
The theoretical performance limit for spectral analysis, while high, may be unachievable with current practical FTS instruments.