# Filtering to Measure Gas Concentrations from Spectral Features

## U. S. Patent 6,615,142, issued September 2, 2003

The infrared spectra of many gases consist of discrete spectral lines. Gas concentrations can be determined by measuring the amplitude of one or more spectral lines. Extracting the concentration from the spectrum can require nonlinear least squares fitting algorithms because the spectrum is not a linear function of gas concentration. The shape of an individual spectral line depends on temperature, pressure and composition; the laser wavelength can drift, making the exact position of a spectral line uncertain; the relative amplitudes of a pair of lines depends on temperature. Nonlinear least square algorithms generally require good initial guesses and many iterations to converge on an answer.

In this invention, the nonlinear fit is linearized by including in the fit derivatives of the spectrum taken at reference conditions similar to those at which the spectrometer will operate. The figure shows a fit that includes a quadratic background, the fit vectors and the derivative of the spectral line with respect to wavelength. The fitted values of these derivatives can then be used to correct the results of the fitted concentration. The derivatives can also be used to measure important quantities from the spectrum. For instance, the derivative with respect to wavelength can be used to lock the laser wavelength with appropriate feedback, while the derivative with respect to temperature or pressure can be used to estimate the temperature or pressure. Because the fitting algorithm is linear, it is very fast, requiring a single step. By storing an inverted matrix, the algorithm can be recast as a filtering step that extracts a gas concentration from the spectrum using only matrix multiplication and a polynomial correction.

## Contact Information

**Southwest Sciences, Inc.**1570 Pacheco St., Suite E-11, Santa Fe, NM 87505 tel. (505) 984-1322/ fax (505) 988-9230

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