REDUCING BACKGROUND EFFECTS IN NONLINEAR LEAST-SQUARES LINE INTENSITY ESTIMATES

$^{1}$ A.H. Lipkus, Appl. Spectrosc. 42 395 (1988). $^{2}$ P.J. Statham. Anal. Chem. 49, 2149 (1977). $^{3}$ A. K. Atakan, W.E. Blass and D. E. Jennings. Appl. Spectros. 34, 369Author Institution: Infrared Physics Branch, Optical Physics Division, Air Force Geophysics Laboratory.This paper proposes a method for reducing the effects of background (100\% transmittance level) variations on line intensities measured by nonlinear least-squares fitting of transmittance spectra, without modelling the background. Let f be a low-pass filter function, much wider than the lines in the spectrum. The spectrum is BT. where B is a slowly varying background and T the transmittance. The convolution $f^{\ast}(BT)$ is then a lower-resolution version of the spectrum, with essentially the same background. The ratio $BT/(f^{\ast}(BT))$ is a distorted version of T with the background cancelled out. If T' is a calculated transmittance, then $T'/(f^{\ast}T')$ can be fit to the distorted spectrum, obtaining line intensities without modelling B. This method reduces peak (observed-calculated) errors due to an unmodelled background by more than a factor of 10. Careful selection of the filter function ? can yield error spectra which have almost zero correlation with the true spectrum, and therefore cause reduced errors in the retrieved intensities. Lipkus1 used this ratio, but with f a Legendre filter, to permit comparison between a sample spectrum containing a background and a background-free standard spectrum. Statham2 and Atakan et. al.3 used a similar method based on direct high-pass filtering of the spectrum. However, their filters produce error spectra which are highly correlated with the spectrum being fit