Information in Spectra of Collision-Broadened Absorption Lines

A mathematical model is introduced for experiments which yield spectra of isolated, collision-broadened absorption lines. A nonlinear design analysis is then performed on the model to identify the optimum experimental conditions. The information in the spectra is split into components associated with each of the unknown parameters to be estimated from the spectra. By exploring the variation of these components it is shown that spectra with line center transmittances of 0.25 are nearly optimum for measuring the line position, the Lorentz width α, the instrument resolution H, and the product of line intensity and absorber amount. The trade off between signal/noise ratio and resolution is investigated for several different resolution-dependent noise levels. The analysis shows that when signal/noise ratio is proportional to the square root of the ratio of resolution and Lorentz width, a single optimum resolution and line center transmittance combination of H/α ≅ 1.5 and 0.28, respectively, exists.