On Leaf BRDF Estimates and Their Fit to Microfacet Models
Benjamin D. Roth, M. Grady Saunders, Charles M. Bachmann, Jan van Aardt
Abstract
Remote sensing provides high accuracy/precision for quantifying forest biophysical parameters needed for ecological management. Although the significant impact of bidirectional scattering distribution functions (BSDFs) on remote sensing of vegetation is well known, current forest metrics derived from sensor data seldom take leaf BSDF into account, and despite the importance of BSDF effects, leaf directional scattering measurements are almost nonexistent. Previous studies have been limited in the spectral coverage and resolution of observed electromagnetic radiation and lacked models to interpolate all source-sensor angles beyond measurements. This study captured deciduous broadleaf bidirectional reflectance distribution functions (BRDFs) from the visible through shortwave infrared spectral regions (350–2500 nm) and accurately modeled the BRDF for extension to any illumination angle, viewing zenith, or azimuthal angle. We measured biconical directional reflectance factor of leaves from three species of large trees, Norway maple ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Acer platanoides</i> ), American sweetgum ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Liquidambar styraciflua</i> ), and northern red oak ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Quercus rubra</i> ). We then fit the data through nonlinear regression to physical, microfacet BRDF models, resulting in normalized root-mean-square errors of less than 8%, averaged across all wavelengths (excluding low signal-to-noise spectral regions). We extracted leaf physical parameters, including the index of refraction and a relative physical roughness from the microfacet models delineating the three species. The implications for forestry remote sensing are important, as rigorous models to represent leaves allow for the creation of more accurate forest scenes for radiative transfer modeling. Such accuracy enables higher fidelity sensor evaluations and data processing algorithms.