Non-Contact Diffuse Reflectance Using Center-Illuminated-Area-Detection to Assess Inter-Layer Absorption: A “Capsule” Model

Non-contact diffuse reflectance to below-surface absorption disguised by a thick superficial layer is challenging to instrument and model. We develop a semi-empirical “capsule” model of non-contact diffuse reflectance, configured as center-illuminated-area-detection (CIAD), to model below-surface absorption. The “capsule” approach extends a principle of modeling the effect of a thin (<1 mm) top layer on radially resolved diffuse reflectance for contact probing to the effect of a thick (1~3 mm) surface layer on radially integrated CIAD diffuse reflectance for non-contact probing. The model treats diffuse reflectance of CIAD from a two-layer medium by weighing between two limiting cases of monolayer taking either the top or bottom of the two-layer properties. The semi-empirical model of CIAD diffuse reflectance over an area of a radius of ≤15 mm responding to variation of single inter-layer contrast is examined against Monte Carlo simulations of two-layer media with a 1–3 mm top layer, three orders of magnitude change in absorption, and two orders of magnitude change in reduced scattering. Compared to MC simulations, the modeled CIAD diffuse reflectance of the two layers gives total ensemble errors of up to 18.6% and 12.2% over the range of a single inter-layer contrast of absorption and reduced scattering, respectively. The results provide insights into the challenges of using CIAD diffuse reflectance to assess spectral absorption of the below-surface layer, which will be examined experimentally in a subsequent paper.