Multiparameter Spectrophotometry Platform for Turbid Sample Measurement by Robust Solutions of Radiative Transfer Problems

Multiparameter spectrophotometer instruments based on the radiative transfer (RT) theory differ fundamentally from conventional ones in their ability to determine absorption and scattering coefficients and anisotropy factor. Ease of use and robustness of inverse solutions are of necessity for general-purpose applications. We have developed a new instrument platform design incorporating a compact three-photodiode detection configuration without integrating spheres, four-channel signal-processing unit, and Monte Carlo (MC) simulation-based software for accurate and rapid inverse solutions. To verify the platform design, two sphere suspension samples of different size distributions were measured and RT parameters were determined by a sample model with the Henyey and Greenstein (HG) phase function between 460 and 1000 nm. System validation is achieved by comparison of the RT parameters and spectral dependence against the results by Mie theory for single-sized spheres of nominal diameter values. Five wavelengths from 560 to 960 nm were selected for quantitative evaluation of the robustness of the HG sample model and two Mie theory-based sample models assuming light scattering by independent and single spheres. We found that only the HG-based sample model yields high accuracy and strong robustness for inverse determination of RT parameters even for the cases of sphere suspensions in which the assumptions of sample uniformity and scattering by independent and single spheres are not satisfied. These results demonstrate that the new platform with MC simulation-based inverse algorithm combined with the HG sample model is capable of robust and rapid measurement of RT parameters for turbid samples with optical thickness up to 30.

I. Introduction

Spectrophotometry and infrared spectroscopy often serve as the tools of choice for material analysis by their ease of use to acquire spectral data. The data can be presented in the form of either sample absorbance log(1/ or attenuation coefficient , where is wavelength, the measured signal of collimated transmittance, and the sample thickness along the direction of incident light beam. Conventional instrument designs for determination of or are founded on the assumption that light attenuation is dominated by atomic and/or molecular absorption [1]–[3]. The assumption, however, breaks down if light scattering is no longer negligible. One must then consider the effect of scattering on measured signals and solve the challenging problems of forward modeling of light scattering and inverse parameter extraction. In return, multiple sample parameters with wavelength dependence enhance markedly the ability to characterize materials by quantification of molecular composition through absorption parameter and wavelength-scaled structures through scattering parameters. Over the past decades, numerous light scattering models of different approximations have been developed and combined with efficient inverse algorithms to retrieve sample parameters from measured signals [4]–[6]. Various spectrophotometric system designs incorporated these methods to determine absorption and scattering parameters in academic laboratory settings. Nearly all designs require integrating spheres for hemispherically integrated measurement of signals and fast parameter extraction from the signals [2], [7]–[13].