Reduction of Error in Spectrophotometry of Scattering Media Using Polarization Techniques

Abstract

Scattering can result in erroneous determination of the concentrations of constituent absorbers in spectrophotometry. This is due to the relationship between attenuation and absorption coefficient becoming nonlinear; hence, the use of the Lambert–Beer law becomes invalid. It has previously been shown that application of polarization techniques can reduce these effects, resulting in a more linear relationship. Here we quantify the impact of this improvement on measurement of the ratio of concentrations for two general absorbing species and show that measurement using polarization-maintaining light is more accurate. This is performed using a generalized version of theory previously dependent on selection of isosbestic wavelengths. For the absorbing species and geometries considered here, the mean error on the estimation of absorber concentration ratio is 18.2% for the case of detection without polarization discrimination. When polarization-maintaining light is extracted, mean errors of 1.2% and 5.1% are achieved for linear and circular polarizations, respectively. The improvement provided by the polarization techniques is observed regardless of the illuminating wavelengths but is achieved at the expense of a reduced signal-to-noise ratio. Taking this into account, for the detection scheme considered with a detector well capacity of 4 × 10⁵ electrons the improvement provided by linear polarization-maintaining light is reduced to a factor of 3.6 and for circular polarizations a factor of 2.2.