Distance-weighted reflectance for arbitrary source-detector geometries from a single pencil-beam Monte Carlo...

Modeling reflectance for finite source-detector geometries typically requires Monte Carlo simulations with explicit illumination and collection areas. We present a distance-weighted formulation that computes reflectance for arbitrary overlapping, concentric, and non-overlapping source-detector geometries from a single, localized (quasi-pencil-beam) Monte Carlo simulation. Reflectance is expressed as an integral of the radial reflectance profile weighted by the distribution of source-detector separations. The method incorporates finite launch and detection numerical apertures and extends to non-uniform illumination and detection through an appropriate effective distance distribution. Monte Carlo validation against full source-detector simulations shows agreement in both reflectance and pathlength distributions for geometries relevant to fiber-based reflectance spectroscopy. This provides a general and efficient framework for laterally homogeneous media.