Models and validation measurements of bidirectional reflectance factor for diffuse reflecting materials

A physical model developed from scattering theory by Hapke was applied to bidirectional reflectance factor (BRF) measurement data for several diffuse reflecting materials. All of the material samples were some form of polytetrafluoroethelyne (PTFE) powder. The solar illuminated diffuser for the Moderate Resolution Imaging Spectroradiometer (MODIS) was one of the samples. The BRF was characterized in seven wavelength bands, covering a spectral range of 400 nm to 2100 nm.;The BRFs were determined, using the Santa Barbara Remote Sensing (SBRS) scattering goniopolarimeter, by measuring all four linear polarization components and using those measurements in the BRF equations of Clarke. The scattering goniopolarimeter was carefully characterized in a series of measurements. It was calibrated by comparing BRF measurements to the BRF calibration values of a reflectance standard.;A detailed error analysis was done. The uncertainties for each of the four polarization components was considered individually, and then combined to obtain the total estimated uncertainty in the BRF values. The mean-square errors of the measured BRF sample averages were compared to the estimated uncertainties. Results of BRF evaluations and the measurement uncertainties for the different diffusers are presented.;A study of several variations of the Hapke scattering model was made. The models were successfully applied to each of the four polarization components of BRF, in addition to the unpolarized BRF. The quality of the models was evaluated using the "root-mean-square of the fit" merit function, RMSf.;The simplest Hapke model gave RMSf values from two percent down to less than one percent, but the vegetation canopy form of the Hapke model gave higher RMSf values, from six to ten percent. The Henyey-Greenstein single scattering phase function, even when used in the simplest Hapke model, gave RMSf values between two and eight percent, whereas Legendre polynomial phase functions resulted in RMSf values of less than one percent. Equations with an additional forward scatter term usually made a slight improvement, on the order of one to two tenths of a percent. To obtain a representative model, at least two sets of BRF data at different incidence angles were needed.