An evaluation of the influence of measurement geometry on the uncertainties of photometric model results based on the laboratory measurements of particulate surfaces

- Measurements of samples with different particle size were performed over a wide viewing angle.
- The influence of measurement geometric on the model parameters and results was analyzed.
- The empirical relation between model parameters and particle size was verified.
- Several favorable measurement geometrics both in the laboratory and field were proposed.

Sunlight reflected by particulate surfaces carries important information about its physical properties. Modeling the reflectance of different types of particulate samples is an attractive field of study, so estimating the favorable measurement geometry for accurate inversion of photometric model parameters is necessary. This research examines the distribution of the bidirectional reflectance factor (BRF) with different particle sizes by multi-angular reflectance. Two types of particulate samples (one with low reflectance and the other with moderate reflectance) with particle sizes of 0.3, 0.45 and 0.9 mm were measured over a wide viewing range under the assumption of left-to-right symmetry of the BRF. Based on these measurements, we computed the reflectance of particulate surfaces by a photometric model and analyzed the influence of measurement geometry (different combinations of incident zenith angle, viewing zenith angle and azimuth angle) on the inverted parameters and the results modeled by the best-fit parameters. The results show that by using the measurements in the single azimuth (including the principal plane) to invert the model parameters, the difference between the modeled results and measured results will exceed the reflectance change caused by the samples' particle size; this difference is also found when we used the combined measurements at two different incident zenith angles. Including the measurements in the principal plane, an increase in the number of azimuth angles will improve the match between the modeled results and measurements. Our results also confirm that the single-scattering albedo is the only model parameter that could be empirically used to determine the particle sizes of our samples over a wide range of measurement directions. This study proposes several favorable combinations of measurement geometry and also appears to provide a promising empirical reference for the particulate surfaces similar to ours in future laboratory experiments.