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We performed continuum removal over the entire spectrum for each of the samples used in this study over the spectral range of 400 nm to 2350 nm. We excluded spectral bands outside of this range from the present analysis due to the potential for poor signal-to-noise ratio in these regions. We plot the results of performing continuum removal over this spectral range for the case when the incident illumination was oriented at a zenith angle of 25◦and 55◦ in Figures 5.20 and 5.21, respectively. Note that in each of these figures, the continuum removal is plotted separately in the forward and backward scattering regimes, where the designation of forward scattering is for a viewing azimuth of 90 degrees to 270 degrees. We do this to characterize if the shadowing in the forward scattering direction had a significant effect on spectral dependency of macroscopic roughness.

Figure 5.20: Continuum removal performed on the bidirectional reflectance spectra for several samples used in this experiment when the light was oriented at 25 degrees zenith. From top to bottom: smooth sample, Grid-1, Grid-2, Wave-1, Wave-2. In the left image the backward scattered reflectance is plotted and in the right image the forward scattered reflectance is plotted.

Figure 5.21: Continuum removal performed on the bidirectional reflectance spectra for several samples used in this experiment when the light was oriented at 55 degrees zenith. From top to bottom: smooth sample, Grid-1, Grid-2, Wave-1, Wave-2. In the left image the backward scattered reflectance is plotted and in the right image the forward scattered reflectance is plotted.

Figure 5.22: The variance in continuum removed reflectance performed on the bidirectional reflectance spectra for several samples used in this experiment when the light was oriented at 25 degrees zenith. From top to bottom: smooth sample, Grid-1, Grid-2, Wave-1, Wave- 2. In the left image the backward scattered reflectance is plotted and in the right image the forward scattered reflectance is plotted.

From Figures 5.20 and 5.21, it is clear that the continuum removed reflectance varies significantly over the entire spectral range depending on the sensor viewing orientation. In general, it does not appear that the variance in continuum removed reflectance is dependent on whether the viewing orientations are in the forward or backward scattering region. We observe the most striking regions over which the continuum removed reflectance exhibits variance are from 1000 nm to 1700 nm and from 1840 nm to 2100 nm. In addition, it is clear that the variance in continuum removed reflectance is greater in magnitude in the case where the light is oriented at an oblique zenith angle of 55 degrees than when the light is oriented at 25 degrees zenith angle. In order to investigate the observed spectral dependencies on roughness more fully, the variance was calculated as a function of wavelength and plotted in Figures 5.22 and 5.23.

From Figures 5.22 and 5.23, we can see that the variance in continuum removed re- flectance shows a substantial increase in magnitude over the range of 1000 nm to 1700 nm. I believe that these results should be taken with caution due to the fact that sensor

Figure 5.23: The variance in continuum removed reflectance performed on the bidirec- tional reflectance spectra for several samples used in this experiment when the light was oriented at 55 degrees zenith. From top to bottom: smooth sample, Grid-1, Grid-2, Wave- 1 (perpendicular to principal plane), Wave-2 (perpendicular to principal plane). In the left image the backward scattered reflectance is plotted and in the right image the forward scattered reflectance is plotted.

diometer has 3 different sensors. One such sensor focuses on the VNIR spectral range and samples over the range of 350 nm to 1000 nm. The other two InGaAs Photodiode sensors focus on the SWIR spectral range and sample over the range of 1001 nm to 1800 nm and 1801 nm to 2500 nm, respectively. [4] It is possible that the locally higher variance in these regions is due to sensor noise that results from a transition between sensors.

In addition to the variance observed over these broad spectral regions, we can also see that there is a locally higher continuum removed variance within an absorption feature that is centered at approximately 1900 nm, that has been associated with water absorption. [68] This result matches results that were seen in the previous laboratory study that focused on clay sediments. The continuum removed variance in this region appears to be of similar orders of magnitude between both backward and forward scattered reflectance regions. In addition, the magnitude of the continuum removed variance is far higher in the case where the light is oriented at an oblique zenith angle of 55 degrees rather than 25 degrees. This spectral absorption feature is outside of the range of sensor transition points, making it likely that this variance is correlated with macroscopic surface roughness. This absorption feature will be discussed in more detail in the next subsection.

In order to more closely analyze the effects of macroscopic surface roughness on con- tinuum removed variance, a metric denoted as the Total Continuum Removed Variance (TCRV) was calculated by summing the continuum removed variance over the entire spec- tral domain for each sample used in this study. The results are plotted as a function of the mean slope angle parameter in Figures 5.24 and 5.25. Note that in these figures, the samples in which ridges are oriented in differing azimuthal orientations to the principal plane of the illumination are also plotted. The mean slope angle parameter was chosen as a roughness parameter in these plots due to its ability to account for the slope distribution of the surface microfacets.

From Figures 5.24 and 5.25, we can see that the magnitude of the TCRV is far higher in the case where incident illumination is oriented at an oblique zenith angle of 55 degrees. In addition, we can see that the magnitude of the variance in continuum-removed reflectance is similar for the case where the sensor viewing orientations are in the forward scattered and backward scattered directions.

An interesting result becomes evident from these plots when observing the TCRV for the wavelike roughness profiles. When the wavelike roughness profile is oriented parallel to the principal plane, there is almost no variance in continuum-removed reflectance, and the magnitude is similar to the magnitude of the smooth surface samples. When the samples were rotated into a 45 degree orientation or a 90 degree rotation relative to the principal plane, the samples exhibited a higher degree of variance in continuum removed reflectance. This is despite the fact that these samples had the exact same magnitude of roughness across all of these BRDF measurements.

Figure 5.24: The Total Continuum-Removed Variance plotted as a function of the sample’s mean slope angle for the various samples used in this study when the incident illumination was oriented at a zenith angle of 25 degrees. The legend denotes the samples markers in the scatter plot.

Figure 5.25: The Total Continuum-Removed Variance plotted as a function of the sample’s mean slope angle for the various samples used in this study when the incident illumination was oriented at a zenith angle of 55 degrees. The legend denotes the samples markers in the scatter plot.

Figure 5.26: The Total Continuum-Removed Variance calculated within the 1900 nm absorption feature. Results are plotted as a function of the sample’s mean slope angle for the various samples used in this study when the incident illumination was oriented at a zenith angle of 25 degrees. The legend denotes the samples markers in the scatter plot.

in magnitude than in the case of the wave-like roughness profiles. This is despite the fact that these samples had very similar orders of roughness magnitudes for both the random roughness metric and the mean slope angle metrics.