Abstract

A computationally inexpensive method is presented for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks. Normally, <i>N</i> measurements are required in order to recover an <i>N</i>-point spectrum; this method requires <i>N</i> + <i>N</i>₀ measurements to be taken, where, typically, <i>N</i>₀ ≤ 10. Once the additional measurements have been taken, only <i>O(N</i>[log₂<i>N</i> + 2]) arithmetic operations—mostly additions or subtractions—are needed in order to recover the spectrum; a conventional procedure requires <i>O</i>(2<i>N</i>²) operations. Preliminary work for this method is minimal, requiring <i>O(N</i>) operations as opposed to <i>O(N</i>³) for a conventional procedure; this work needs to be done only once for a given spectrometer. The spectrum-estimate obtained is unbiased.

Practical multi-spectrum Hadamard transform spectrometer

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Fast delta Hadamard transform

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Multiplex advantage in Hadamard transform spectrometry utilizing solid-state encoding masks with uniform, bistable optical transmission defects

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Appl. Opt. 26(19) 4285-4292 (1987)

Theoretical Comparison of Singly Multiplexed Hadamard Transform Spectrometers and Scanning Spectrometers

N. M. Larson, R. Crosmun, and Y. Talmi
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High Resolution Hadamard Transform Spectrometer

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