Optimal filters for high-speed compressive detection in spectroscopy

Abstract

Recent advances allow for the construction of filters with precisely defined frequency response for use in Raman chemical spectroscopy. In this paper we give a probabilistic interpretation of the output of such filters and use this to give an algorithm to design optimal filters to minimize the mean squared error in the estimated photon emission rates for multiple spectra. Experiments using these filters demonstrate that detecting as few as ∼10 Raman scattered photons in as little time as ∼30 µs can be sufficient to positively distinguish chemical species. This speed should allow "chemical imaging" of samples.

Fluorescence modeling for optimized-binary compressive detection Raman spectroscopy

“…Thus, the presented OB-CD strategy is expected to be most useful in applications requiring fast analysis of liquid and solid samples whose fluorescence does not overwhelm the underlying Raman chemical fingerprints. This is consistent with previous results [10], which indicated that the trade-off between higher readnoise and higher spectral information content of full-spectral CCD measurements relative to the OB-CD detection strategy would indicate that OB-CD is most advantageous (relative to CCD measurements) in fast (low-signal) applications that unaccessible to CCD-based measurements. (e) Fig.…”

“…Previously [8][9][10], we demonstrated that the OB-CD strategy enabled high-speed chemical classification, quantitation, and imaging. Here we demonstrate an extension of the OB-CD method that facilitates Raman classification and quantitation in the presence of fluorescence background.…”

Compressive Detection of Highly Overlapped Spectra Using Walsh–Hadamard-Based Filter Functions

“…Wilcox et al and Buzzard and Lucier described an approach to create optimized filter functions using a Department of Chemistry and Biochemistry, California State Polytechnic University Pomona, Pomona, CA, USA nonlinear optimization to minimize the variance in their measurements. 3,4 They showed that such optimized filter functions were nearly binary, i.e., almost all of the elements consist of either zero or 1; they rounded the remaining non-integer values to make the entire function binary. In the low-signal photon counting regime, compressive detection offered an extra advantage; read noise was essentially eliminated.…”

“…In the low-signal photon counting regime, compressive detection offered an extra advantage; read noise was essentially eliminated. 4 Binary filters have distinct experimental advantages, as described below. Applied to multiple pairs of compounds with minimally, moderately, and highly overlapped Raman spectra, their optimized binary filters demonstrated excellent agreement between experimental and theoretical predictions of photon count rates, were capable of accurately distinguishing between species, and notably outperformed analog filter functions (the actual Raman spectra or linear combinations thereof).…”

Multiple-output multivariate optical computing for spectrum recognition

“…The task of analyzing a spectrum to determine what substance produced it is variously called molecular identification, chemical identification, or spectrum recognition. Multivariate optical computing, or MOC, is an established method whereby much of the computation of spectrum recognition is performed in the optical domain [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. MOC leads to faster processing, as well as a signal-to-noise ratio increase known as the Fellgett or multiplex advantage [18].…”