Absorption Spectrometry by Narrowband Light in Optically Saturated and Optically Pumped Collision and Doppler Broadened Gaseous Media under Arbitrary Optical Thickness Conditions

This work examines absorption spectrometry by narrowband light in gaseous media with arbitrary optical thickness when the light induces optical saturation or optical pumping. Two quantities are defined: the observed absorbance, Aobs, and the true absorbance, Atrue. The former is the absorbance that is measured under the existing conditions, whereas the latter represents the absorbance one would measure if the light acted solely as a probe of the populations of the various levels, and it is therefore directly proportional to the concentration or density of absorbers. A general integral equation for the propagation of light in media of arbitrary optical thickness in which the light influences the populations of the levels involved is derived. This expression is transcendental in the observed absorbance and cannot be solved analytically. It is shown that an analytical expression can be derived by investigating the inverse relationship, i.e., Atrue = f (Aobs). Inasmuch as collision and Doppler broadened media react differently to optical saturation, they are considered separately. It is shown that a nonlinear response results if the medium is optically saturated (or pumped) and not optically thin. Expressions for the error introduced if the technique of standard additions is uncritically applied to such a system are derived.