Journal ArticleDOI
On the Mean-Square Error of Various Spectrum-Recovery Techniques in Hadamard Transform Spectrometry
TLDR
In this article, three spectrum-recovery techniques for an HT spectrometer having a nonideal electro-optic mask are considered in terms of the mean-square error (MSE) associated with a given estimate.Abstract:
The multiplexing inherent in the Hadamard transform (HT) spectrometer can result in an improved spectrum-estimate when the detector is the major source of noise. A spectrum-estimate may be further improved by taking into account any nonidealities in the system. In this paper, observations concerning the errors associated with such estimates are presented, with the use of results obtained from computer simulations. Three spectrum-recovery techniques for an HT spectrometer having a nonideal electro-optic mask are considered in terms of the mean-square error (MSE) associated with a given estimate. The discussion of the MSE is with respect to the input spectrum to be estimated, the detector noise, the transmittances of the nonideal mask, and the use of coaddition. Included is a review of the computational efficiency and the statistical bias of each method. The relative performances of the spectrum-recovery methods are presented with examples to help identify the sources of error for each of the techniques.read more
Citations
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Journal ArticleDOI
Hadamard transform Raman microscopy of laser-modified graphite electrodes
TL;DR: In this article, the authors describe the application of Hadamard transform Raman microscopy to the imaging of edge plane microstructures in laser-modified highly ordered pyrolitic graphite (HOPG) electrodes.
Journal ArticleDOI
Chemical Mapping in the Mid- and Near-IR Spectral Regions by Hadamard Transform/FT-IR Spectrometry
TL;DR: In this paper, a movable 2D Hadamard encoding mask is obtained and combined with conventional FT-IR spectrometers for use in both the mid and near-infrared spectral regions.
Journal ArticleDOI
Instrument for Hadamard transform three-dimensional fluorescence microscope image analysis
TL;DR: In this article, an instrument combining fluorescence microscopy with Hadamard transform multiplexed imaging was designed by which a three-dimensional HadAMT fluorescence microscopic cell image was obtained.
Journal ArticleDOI
Hadamard transform spectrometry
TL;DR: Hadamard transform spectrometry (HTS) provides a means of obtaining a multiplex advantage with a dispersive spectrometric technique Two recent advances, stationary electro-optic encoding masks and efficient spectrum-recovery techniques to compensate for nonidealities in the masks, have combined to revive interest in HTS as mentioned in this paper.
Journal ArticleDOI
Temporal systematic errors using stationary Hadamard encoding masks
TL;DR: In this article, the temporal systematic errors due to the use of a stationary Hadamard encoding mask in a hadamard transform spectrometer when the time between encodements is made too short relative to the mask response time are characterized and an empirical method has been developed to correct the resulting artifacts appearing in the spectra.
References
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Journal ArticleDOI
A Visible Near-Infrared Hadamard Transform Spectrometer Based on a Liquid Crystal Spatial Light Modulator Array: A New Approach in Spectrometry
TL;DR: In this paper, a stationary Hadamard encodement mask was designed from a liquid crystal display, which can be installed and positioned in a dispersive instrument, allowing the selected Hadamards encoded spectral elements to be focused on a single detector.
Journal ArticleDOI
A Fast Spectrum-Recovery Method for Hadamard Transform Spectrometers Having Nonideal Masks
TL;DR: In this article, a computationally inexpensive method for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks is presented, requiring only O(N[log 2N + 2] arithmetic operations.
Journal ArticleDOI
An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks
TL;DR: A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks.