Chapter 2 - Theoretical Concepts in Spectrophotometric Measurements

Abstract

Abstract This chapter will describe some of the theoretical concepts of obtaining optical properties from spectrophotometric measurements. The optical properties of interest can be the spectrophotometric quantities themselves or the calculated optical constants (complex refractive index, absorption, and scattering coefficients). At first, the different radiometric quantities, describing radiance, irradiance, and radiometric intensity will be introduced. The relationships between these quantities and the electromagnetic fields will then be described. Then, the spectrophotometric quantities, such as spectral regular reflectance and transmittance, radiance, irradiance, emittance, diffuse reflectance, diffuse transmittance, and the bidirectional reflectance distribution function will be defined. The Kirchhoff relationship between the reflectance and emittance will be derived. A review of the Fresnel relations will be given, including expressions appropriate for thin films and thick films. Finally, three models for light scattering will be reviewed, including the theory of Kubelka and Munk, important for measuring highly diffuse, volume scattering materials for color formulation applications, scattering from rough surfaces in the facet approximation, useful for very rough surfaces, and vector first-order perturbation theory, useful for smooth surfaces.