An assessment of the bidirectional reflectance models basing on laboratory experiment of natural particulate surfaces

- An assessment of bidirectional reflectance model is based on the measurements.
- The measurements were performed from controlled natural particulate surfaces.
- The surface properties are inadequately described by some model parameters.
- The parameter values depend on the number of measurements.
- We should make a caution when using the semi-empirical model.

The bidirectional reflectance model is commonly used to study surface structure and composition of atmosphereless celestial bodies basing on photometric measurements. We conducted a test of two bidirectional reflectance models, which are theoretically similar but with different form, to assess their ability for calculating the bidirectional reflectance of particulate surfaces and if the parameters could be confidently linked to the surface׳s property. Two types of natural particulate surfaces with controlled particle sizes vary from 300 μm to 900 μm have been measured in the visible and near-infrared wavelength with the NENULGS (Northeast Normal University Laboratory Goniospectrometer System), we only used these measurement results at 560 nm and 670 nm which are regarded to the evaluation standard of models. In this range of particle size, the bidirectional reflectance models were well match to the experimental data as the results shown in previous publications. Although some parameters of the models can be used to simulate the reflectance of particulate surface, they contain no reliable information on the physical property of our samples. Furthermore, the influence of the number of viewing angles on the precision of modeling results has been tested in this paper. It is clear that an increase of the number of viewing angles and the range of azimuth angles could allow us to improve precision on the estimation of parameters. Comparing with the best fitted model reflectance, we also found that if we used the parameters, which derived from measurements in the principal plane for individual incident zenith angle, to model the bidirectional reflectance may overestimate the computed results in the backward scattering direction and underestimate the computed results in the forward scattering direction. The difference between modeled results and measurements can reach up to 20% in the backward direction when using the parameters inverted in the principal plane. However, if we used the parameters, which derived from the combined measurements in the principal plane for two incident zenith angles, to model the bidirectional reflectance, the maximum difference reaches up to 50% in the backward direction. In the context of experimental measurement study, we suggest that there must be enough measured results at different viewing and azimuth angles when using the bidirectional reflectance models, which are considered as semi-empirical at best, to describe the scattering property or surface structure of particulate system as shown in this study.