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Polarization of visible light by desert pavements
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Remote Sensing of Environment 112 (2008) 1808 – 1819 www.elsevier.com/locate/rse
Polarization of visible light by desert pavements Charles A. Hibbitts a,⁎, Alan R. Gillespie b a
b
Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd., Laurel, Md. 20723, United States W. M. Keck Remote Sensing Laboratory, Department of Earth & Space Sciences, University of Washington, Seattle, Wa. 98195, United States Received 16 December 2005; received in revised form 7 September 2007; accepted 9 September 2007
Abstract Desert pavements can be detected through multi-spectral polarization measurements of reflected sunlight both in and out of the solar principle plane. The combination of polarization and color distinguishes desert pavements from other desert landforms and vegetation. Desert pavements linearly polarize and impart a blueness to sunlight reflected at visible wavelengths. The polarization and color of skylight reflected at high emission angles is also preserved. The polarization properties of desert pavements are dominated by Fresnel reflection at large phase angles and by multiple scattering at low phase angles, causing significant positive and small negative polarization, respectively. © 2007 Published by Elsevier Inc. Keywords: Desert pavements; Desert varnish; Polarization
1. Introduction Identifying the composition and structures of surfaces with remote sensing has evolved into a complex science utilizing passive and active instruments to image the energy reflected and emitted from the surface. Desert pavements can be quite large, covering up to many km2 and thus are potentially well-suited for detection and mapping by remote sensing (e.g. Gillespie et al., 1984; Rivard et al., 1992). The compositions and physical structure of pavements also make them well-suited for detection with reflected sunlight and thermal emission. Reflectance and emission spectroscopy has proven capable of detecting pavements (e.g. Christensen and Harrison, 1993; Crouvi et al., 2003; Kahle, 1987; Rivard et al., 1993; Spatz et al., 1987). Here, we explore an alternative approach, visible-wavelength polarization combined with color imaging. As a broad band imaging technique, it has the potential to be a simple yet effective tool for mapping these landforms over large areas at high spatial resolution and high signal-to-noise. In this paper, we investigate the capabilities and limitations of this combined color and polarization approach, which can be used from the ground and air, and potentially from near-space and space.
⁎ Corresponding author. Tel.: +1 443 778 2834. E-mail address: [email protected] (C.A. Hibbitts). 0034-4257/$ - see front matter © 2007 Published by Elsevier Inc. doi:10.1016/j.rse.2007.09.004
Using color from the visible through shortwave infrared, pavements can be distinguished from many other terrains (e.g. Rivard et al., 1992), especially from vegetated terrain. Pavements are typically composed of smooth cobbles coated with rock varnish, a dark mineral coating which further smoothes affected surfaces. Thus pavements polarize reflected sunlight (e.g. Shepard and Arvidson, 1999), further distinguishing them from surrounding, rougher terrains. Adding color information enables us to create an even more effective technique for distinguishing pavements from other terrains. We explore using visible polarization of reflected sunlight at three colors (blue, green, red) for discerning desert pavements from other terrains. The investigations consist of a series of field and laboratory measurements exploring the combined color and polarization properties of desert pavements and individual varnished stones. The polarization of pavements and clasts is explored in the solar principal plane; the polarization of pavements is also measured normal to the plane. 2. Background 2.1. Physical characteristics of varnished rocks and desert pavements Despite their name, desert pavements are not mechanically strong surfaces, but are a mosaic of flat-lying stones commonly
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darkened by a thin and smooth coating called ‘desert varnish’ (e.g. Engle and Sharp, 1958; Hunt, 1954; Laudermilk, 1931). Desert pavements, and the varnish covering the clasts, develop over hundreds to thousands of years (e.g. Dorn, 1991) with the dark color of the varnish caused by an accumulation of manganese oxide (McKeown and Post, 2001; Potter and Rossman, 1977). The stone mosaic of pavements is generally a single layer thick, and can camouflage a dusty layer of silt tens of centimeters thick or less (Fig. 1). Thus, although appearing to offer a strong surface for traversing, pavements can be readily disrupted by vehicular and pedestrian traffic to expose this fine-grained silt for redistribution by wind to be a dust problem when dry. Weather-resistant fine-grained mafic and siliceous rocks dominate the lithology of clasts that develop the thickest, most continuous varnished surfaces because of the physical and chemical stability of the rocks (e.g. Mabbutt, 1977). Varnish development on coarse-grained rocks such as granites is impeded by the rock and grains fragmenting to expose fresh, unvarnished surfaces. Such rocks rarely form pavements nor become thickly coated by varnish. The mechanical weathering of granites can often, however, create grus that fills the interstices between the stones of the pavements (Fig. 1). Soft rocks such as limestone abrade and chemically weather sufficiently quickly so that when they do form pavements, varnish coatings on the clasts tend to be thin or absent (Crouvi et al., 2003). Rock varnish forms as complex layers growing up and out from nucleation points (Perry and Adams, 1978). Each layer, a few micrometers thick, is comprised of botryoidal structures that lead to non-uniformity on horizontal and vertical scales of a few micrometers. The thicknesses of varnishes vary from stains of only a few micrometers to tough weather-resistant coatings over 100 μm thick (Dragovich, 1988, 1994, 1998). Such nonuniformity in thickness can occur on individual rocks where thick varnish accumulates in small pits, leaving tops of bumps free or nearly free of varnish. The bulk composition of the varnish is dominated by amorphous silica, possibly hydrated (Perry et al., 2006), with a lesser amount of clay present at
Fig. 1. A schematic cross section of a well-developed desert pavement. Each aspect of this idealized caricature, (clast spacing, grus, thickness of the vesicular Av horizon of aeolian silt, thickness and uniformity of the varnish coating, etc.) will vary among pavements. Poorly developed pavements have greater interclast distances, fewer varnished stones with generally thinner varnish, a thinner Av, and more silt exposed between the stones.
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∼10–20% (Potter and Rossman, 1978). It is derived from materials external to the rock, and thus distinct from a weathering rind. The source of the manganese and the method of its fixation have been of much debate, with the possibility of microbial mediation having been extensively explored after their discovery within varnishes (Dorn and Oberlander, 1981). However, a microbial origin for either the varnish or the Mnfixation has yet to be established, and recent experiments suggests the origin of both may be inorganic (Perry et al., 2006), with microbes merely being trapped during varnish formation. 2.2. Spectroscopy and polarimetry of varnished rocks Several remote-sensing techniques have been explored over the years for detecting desert pavements. Approaches such as visible and infrared reflectance spectroscopy as well as emittance (thermal) spectroscopy have proven sensitive to pavements. Although limitations exist, spectral signatures in the short and longwave infrared have been used to identify pavements (e.g. Christensen and Harrison, 1993; Crouvi et al., 2003; Kahle, 1987; Rivard et al., 1993; Spatz et al., 1987). However, spectroscopic measurements cannot always provide definitive detection of pavements. Robust identification of varnish via spectroscopy depends upon the varnish being spectrally distinct from unvarnished rocks and surrounding terrain. For instance, the ∼2.2-μm clay absorption band is present in the reflectance spectra of varnish because of the presence of clays. In the thermal infrared, the clay in the varnish also provides an absorption band centered near 9.6 μm [e.g. Hibbitts et al., 2004; Potter, and Rossman, 1977], although it also can appear similar to spectra of other silicate coatings (Kraft et al., 2003) as well as some mafic rocks. Clays are also present in weathering rinds, wind-blown dust, and in spectra of other terrain such as playas [e.g. Lyon, 1994; Rivard et al., 1992, 1993] making it an unreliable marker for pavements. Varnish darkens and reddens rocks in the visible through shortwave infrared. However, this spectrally broad effect can be confused with photometric or compositional variations. There may also be a potential for identifying varnished rocks through the non-linear mixing of light emitted from the rock substrate with that emitted from the varnish (Hibbitts et al., 2004). Again, though, reliably separating these mixing effects from the spectra of incredibly diverse lithologies of clasts may prove insurmountable. Polarization of sunlight reflected from varnished rocks is an alternative approach for detecting pavements. Varnished rocks were shown by Guinness et al. (1997) to polarize reflected sunlight. They were able to derive Hapke constants for individual varnished stones, demonstrating the importance of both reflection and scattering in light reflected from varnished rocks. Shepard and Arvidson (1999) explored the angular dependence in the polarization of light reflected from varnished basalt rocks at visible (red) wavelengths. They also demonstrate that the reflectance and polarization properties of dark varnished basaltic clasts are consistent with a surface that specularly (mirror-like) reflects light multiple times as well as slightly scattering it. They interpreted the large positive polarization at high phase angles to be due to the multiple specular reflections and the significant
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Fig. 2. The flat-field response of the (a) red and (b) blue channels (1600 × 1200 pixels) interpolated over 50 pixels. Each pixel has been normalized to the average of the image. A value of ‘1’ would represent no difference from the image average and thus no flat-field correction. Scaled between 0.9 and 1.05, the flat-field variation for each channel is significant, although the two responses are similar. These separate flat-field corrections are applied to the blue and red channels during calibration.
negative polarization at low phase angles indicative of a phenomenon associated with scattering, shadow-hiding, either on the surface or by scattering centers within the varnish. Our work focuses on the polarization of light reflected from pavements, with some laboratory measurements of individual clasts to help interpret the results. We also explore the utility of using color to help emphasize the optical characteristics of pavements and rock varnish. 3. Camera calibration Before interpreting the field and laboratory measurements, it is important to understand the camera performance to interpret the significance and limitations of those measurements
accurately. Standard image calibration procedures were performed, including geometric flat-field characterization, the measurement of responsivity with signal level (linearity), and noise estimation and correction for these effects. A tripod-mounted Cannon A60 digital 1.9 mega-pixel (effective) camera with a rotating linear polarizer mounted in front of the aperture was used to obtain the measurements. The focal plane array is a 4:3 ratio CCD detector with 1600 × 1200 pixels and micro-filters in a Bayer pattern to produce a color image. The spectral responsivity was not measured, but is assumed to be the typical broad response of filter color arrays used on compact digital cameras. Blue responsivity peaks ∼450 nm, green ∼540 nm, and red ∼625 nm (Kodak, 2006). With a fullwidth half-maximum of the response varying between 50 and
Fig. 3. Camera responsivity (y-axis) vs. integration time (scaled). Calculated blue channel (black line) and red channel (gray line) responses diverge at high signal levels. The symbols are the average value for several observations. The ‘o’ and ‘+’ designate the parallel and perpendicular components of the (mostly) unpolarized light from the outdoor calibration. The ‘x’ points are from the indoor calibration where no polarizer was used. The 1 − σ error for the indoor calibration is b5 DN, and for the outdoor calibration is b10 DN.
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100 nm, there is overlap in sensitivity between the green filter and both the blue and red filters, but the blue and red filters are spectrally distinct. A detector size of 5.27 mm × 3.96 mm equates to an individual pixel size of ∼3.3 μm, typical for these types of cameras (Bockaert, 2005). Although compact digital cameras are not designed for quantitative measurements of illumination, through basic calibration efforts to determine detector response and focal plane flat field we developed a calibration procedure that can be applied to determine relative reflectance. Relative reflectance is sufficient for calculating reflectance ratios such as the polarization ratios we explore in this study. The pixel-to-pixel response has been calibrated with the specific settings used to give the field measurements better than 10% accuracy (typically much better). Changes in the absolute responsivity from image to image are sufficiently small that time-lapse comparisons can also be made. No attempt was made to derive an absolute radiometric calibration. The signal-response curve and flat-field uniformity were derived separately for each color channel with the calibration target extremely out-of-focus to ensure greatest image uniformity. The flat-field response of the detector is non-uniform primarily due to vignetting and is different for the red and blue channels. Because of significant pixel-to-pixel spatial variation in the raw flat-field measurements due to compression artifacts, the flat-field data were interpolated over a 50-pixel region to remove the high-frequency variations while preserving the regional variations characteristic of flat-field responses (Fig. 2). The flat-field variations of the blue and red channels each exceed 10% and have similar structure. The ∼3% difference between the channels' flat-field responses warranted the use of a separate flat-field calibration for each. Separately determining the responsivity of the red and blue channels removed any dependence on the color of the calibration source/target, although spatial uniformity was still required for the flat-field characterization. Calibrated measurements obtained under indoor fluorescent illumination and outdoor solar illumination could therefore be evaluated together for characterizing instrument noise and response linearity with signal level. The response curves are combinations of multi-order polynomials and spline functions fit to the average response for each channel at each integration time (Fig. 3). The curve is non-linear with signal. Because CCD response to signal is usually biased to be linear until nearing detector saturation, there may be signal processing occurring within the camera before image recording. Regardless of its origin, the shape of the response curve is invariant, making reliable calibration possible. After scaling the outdoor and indoor measurements to overlap, the shapes of the camera response to signal are nearly identical. The consistency demonstrates that there is no strong integration-time dependent response although the greater scatter in the response under bright illumination implies that detector responsivity is more variable under strong illumination (shorter integration time) or with a warmer detector. The ambient air temperature during the field measurements at times exceeded 38 °C (100°F). The field measurements were conducted under direct-sunlight similar in illumination geometry and sky conditions to the outdoor calibration effort. In most
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analyses, averages of thousands of pixels are used to reduce measurement error further as well as to reduce the effects of variations in the pavement surfaces. The greatest challenge to a quantitative analysis has been the lossy compression storage used by the camera software. It is the noise introduced by this lossy compression scheme that ultimately limits the accuracy of the calibration, and is largely manifested as aliasing between high-contrast pixels. This aliasing has been minimized by spatially smoothing each image using a 1-pixel wide Photoshop™ Gaussian resampling function. Some aliasing remains, especially at clast boundaries in more nadir images where the higher-albedo grus and silt adjacent to the low albedo varnished clasts is resolved. The degradation of spatial resolution associated with this resampling did not degrade subsequent multi-pixel characterizations. 4. Field site Field measurements were conducted in the desert of southern California, near the town of Mecca Hills. Images were obtained of three pavements located on a single fan (Table 1 and Fig. 4) throughout a day. The solar incidence angle ‘i’ (illumination angle measured from nadir) decreased from ∼ 40 to ∼25° during the experiment, but was constant for any single observation. For most observations, the camera was oriented in the solar principal plane and facing into the sun to best measure the polarization of reflected sunlight (Fig. 5). A few observations were also obtained in the solar principal plane facing away from the sun to measure the color and polarization of reflected skylight. Still other observations were made perpendicular to the solar plane. For most observations, context was provided by capturing an unimproved road surface in the background, horizontally transecting the image. Other features commonly included in an image are leafy and dry vegetation, sky, and sometimes, disrupted or poorly-developed pavements. The phase angles, ‘g’, of the field measurements extend from less than 0° to greater than 100° with the incident angle, ‘i’, ranging from ∼ 14 to 38° and the emission angles ‘e’ (angle from nadir of reflected light) spanning ± 19.6° of the detector's center pixel. Multiple images were taken of each site from each
Table 1 Locations and measurement conditions for the desert pavements near Mecca Hills, California Begin and end times (PDT)
Sun incidence Latitude/ angle (average, longitude range)
Description
Site 1 1005, 1015
37.6°, 3°
Site 2 1025, 1042
32.5°, 3°
Site 3 1055, 1105
27.6°, 2°
Well-developed pavement Well-developed and disturbed pavements Well-developed pavement Poorly developed and disturbed pavement Partially disturbed pavement
Site 4 1110, ∼ 1120 25.0°, 2° Site 5 1310, ∼ 1320 14.0°, 1°
33°40.325N 115°58.203W 33°40.128N 115°58.224W 33°40.030N 115°58.315W 33°39.352N 115°59.161W 33°43.702N 116°07.958W
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Fig. 4. Images of pavements from study area. Camera height for each image ∼ 1.23 m (4 feet). (a) Site 1. Well-developed pavement. Pen is ∼ 102 cm from camera and 15 cm long. (b) Site 2. Well-developed pavement. Pen is ∼ 102 cm from camera. (c). Site 3. Well-developed pavement. Road is 15 m from camera. (d) Poorly developed pavement with some sparse vegetation. The leafless shrub in the center of the image is 52 m from the camera, the edge of the hill which blocks the dirt road from the foreground is 96 m distant, and the dirt road is ∼ 390 m away.
camera position to obtain a large range of emission angles. As a result, for some observations in the solar principal plane, the phase angle of the measurement passes through the specular angle (e = i, and g = e + i). 5. Results and discussion 5.1. Polarization Light reflected by a smooth, mirror-like (specular) surface is linearly polarized, as described by the Fresnel equations, which assume reflection occurs on the uppermost surface and that light which penetrates the rock does not scatter back out through the surface. The polarization of the reflected component, P, is the difference between the perpendicular (R⊥) and parallel (R∥) components of the reflected light, divided by the sum of the two (i.e. the total reflected light). P ¼ ðR8 ROÞ=ðR8 þ ROÞ
Light polarized by reflecting from desert pavements possesses a quasi-specular behavior characteristic of specular reflection plus scattering from a rough surface (Shepard and Arvidson, 1999). Reflected light that is a combination of multiple specular reflections always has positive polarization (R⊥ N R∥) and its reflectance dramatically increases near the specular angle. However, sunlight reflected from pavements behaves differently. There is no surge in reflectance near the specular angle and the polarization begins negative at low phase angle, increasing to positive values at moderate and large phase angles, and continues to increase as the emission angle becomes equal to and exceeds the incident angle (i.e. passes through the specular angle). Fig. 6 demonstrates this effect for both the blue and red colors.
ð1Þ
For a specular surface, the perpendicular component is larger than the parallel component, especially at incidence angles of 30° or more (e.g. Bohren and Huffman, 1983). However, any penetration of light into the varnish and scattering, such as from a particulate medium, would change the magnitude and photometric dependence of the polarization.
Fig. 5. Schematic of the instrument set-up and illumination geometry of measurements within the solar principal plane looking towards the sun.
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Fig. 6. Pc of mature desert pavement at Site 1. Each image is a mosaic of two pictures, with the vehicle in the distance at ∼ e = 90°, and the closest stone clasts e ∼ 20°. The pen, near e = 40°, is ∼ 102 cm from the camera and is 15 cm long. The specular angle is approximately e = 38°. (a) The RGB image of the perpendicularly polarized component of the reflected sunlight. The blueness of the image increases with increasingly grazing view angle. (b) The RGB image of the parallel component. (c) The vertical profile along sight of the image. P for the blue channel (blue line) and red channel (red line) are contrasted with the two formulations of color polarization: Pc1 (thick black line) and Pc2 (thick gray line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6a,b shows the perpendicular and parallel components of the reflected sunlight for the sum of the red, green, and blue channels for a mosaic of two images. The perpendicular component is brighter and appears bluer. Fig. 6c contains profiles of different polarization calculations derived from the two images that compose the mosaic (the spatial overlap is evident in overlapping profiles near e = 50°). Each profile is calculated using a different formulation for polarization and is a running average, with each point on the profile an average of the entire row plus all points for ten rows above and below the current position. Pixels containing the vehicle are excluded from the average for this and all other observations when present. Averaging emphasizes the role of photometry on the polarization of reflected sunlight by dramatically reducing the sharp variations in the profile caused by changes in the pavement and the lossy compression used by the camera. Some effects due to variations in pavement development remain and manifest themselves as both sharp and broad features in the profiles that are also consistent between the profiles. The 1 −σ noise for each profile is about equal to the width of the line. The red and blue profiles represent the polarization associated with only these two channels, ‘Pr’ and ‘Pb,’ respectively, where ‘b’ and ‘r’ correspond the blue and red channels. For the other two profiles, color information is included while maintaining the structure for the definition of polarization (Eq. (1)): Pc ¼ ðRc18 Rc2OÞ=ðRc18 þ Rc2OÞ
ð2Þ
where ‘c1’ and ‘c2’ are two colors, and ‘Pc’ represents what we refer to as “color polarization.” The following variations to the color polarization equation directly follow: Pc1 ¼ ðRb8 RrOÞ=ðRb8 þ RrOÞ
ð3Þ
Pc2 ¼ ðRr8 RbOÞ=ðRr8 þ RbOÞ
ð4Þ
The profiles derived with these equations are plotted in Fig. 6c. Pc1 emphasizes the polarization at blue wavelengths and Pc2
emphasizes the polarization in the red channel. Because these equations mix independent physical measurements, they no longer represent an easily interpretable physical quantity, although they provide quantitative information. 5.2. Field measurements 5.2.1. Single-color polarization characteristics of desert pavements As demonstrated by Fig. 6, Pb is greater than Pr for welldeveloped desert pavements, especially at grazing angles. Pb and Pr both decrease ∼ linearly to slightly below zero as ‘e’ decreases to a minimum of ∼20°. Non-pavement terrain has significantly lower P. Both Pb and Pr are low for the unimproved road, with Pb N Pr at all ‘e’. Scene-wide variations in pavement maturity result in a slight decrease in Pb and Pr at e ∼75° to 80°. Other high-frequency variations that are present in both the Pb and Pr profiles are also real variations in the pavement development. Pr and Pb from several observations of additional sites of mature pavements (Fig. 7) consistently show similar trends. With the additional observations acquiring lower ‘e’ (and thus lower ‘g’) values, the linear trend in ‘P’ is found to sharply flatten at low ‘g’ (also low ‘e’). However, Pb remains greater than Pr at all angles. Both Pb and Pr are slightly negative at ‘g’ b ∼ 40°. In both profiles, the curve flattens at g b 20°, and Pr may increase again at very low ‘g’. The presence of a negative branch in P of pavements at low ‘g’ is consistent with multiple scattering by a particulate surface (Hapke, 1993). Egan (1985: his Fig. 10.1) also noted this phenomenon in rock fragments of ilmenite with smooth clean faces, including having a positive Pr at larger ‘g’ that is similar in sign and magnitude to that of the pavements. High-albedo, rough surfaces such as roughened glass have a negative polarization branch that extends to larger ‘g’ that is almost as large in amplitude as the positive branch, due to significant multiple scattering with little absorption in the glass (Hapke, 1993: his Fig. 14.2) and is different than the P observed for pavements.
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Fig. 7. Polarization vs. phase angle for the (a) blue channel and (b) red channel. Values for the blue channel values are greater than for the red channel, showing that polarization calculation using the blue channel is sensitive to the presence of reflected blue skylight. The shape is consistent with quasi-specular reflection from mineral faces (Egan, 1985). The dashed line in each is a model based upon Hapke theory (e.g. Hapke, 1993), assuming no multiple scattering.
For sunlight polarized by desert pavements, there is no peak at the specular angle. Instead, ‘P’ increases as observing angles become increasingly grazing crossing from negative to positive at g ∼ 50°. This positive polarization can be modeled assuming a surface composed of subpixel, partially randomly oriented, specular reflectors (Fig. 7). Following directly from Woessner and Hapke (1987), the polarization is: P ¼ f ðwÞ⁎ðF8 FO Þ=½2⁎r⁎ð1 þ cosðeÞ=cosðiÞÞ;
ð5Þ
where f (ψ) is a characteristic constant, in this case 0.5, and signifies a non-uniform distribution in the orientation of the subpixel reflectors. The specular reflection coefficients ‘F⊥’ and ‘F∥’ are controlled by the real portion of the complex index of refraction. The reflection of the surface ‘r’ is largely controlled by the single-scattering albedo ‘w’ (grossly related to the albedo), with a directional distribution assumed to be consistent with a Lommel–Seeliger phase function, the single-particle angular scattering function, and terms describing the single- and multiplescattering albedo. A real index of refraction (n) = 1.45 for both the red and blue channels best describes the polarization curves of the varnish. This value is consistent with clay minerals (Klein and Hurlbut, 1993), though slightly low, and is significantly lower than the index of refraction for opaque oxides such as the Mn oxide, birnessite. For the red channel, we find that w = 0.4 provides the best fit to the data, and for the blue channel w = 0.35
is better. These values are consistent with those previously derived for varnished basalts (Guinness et al., 1997), and with the observation that pavements are more reflective (brighter) at longer wavelengths, resulting in the reddish/brown color of the pavement. These choices are also consistent with the empirical observations that surfaces dominated by low-albedo materials are more polarizing than brighter surfaces (Hapke, 1993). Thus, it appears that the positive portion of the polarization of sunlight by desert pavements is dominated by specular reflection likely associated with the varnished clasts. The negative polarization is due to multiple scattering, either inside the varnish and/or by unvarnished clasts, grus, and dust in the pavement. 5.2.2. Two-color polarization of desert pavements The two profiles of color polarization in Fig. 6c are noticeably different from each other as well as from Pb and Pr. Pc1 emphasizes features in both Pb and Pr. The differences between the redder, dusty road surface and the bluer varnish of the pavement are more apparent in Pc1 and the variations in the pavement are exaggerated. The negative spike in the Pc1 of the unimproved road is greater than for either Pb or Pr. The slope of Pc1 is greater as well. The greater slope is primarily due to lower Pb and Pr at low ‘e’. Reflected sunlight polarized by desert pavements is bluer than unpolarized reflected sunlight because specular reflection not strongly color-dependent and the blue light is not absorbed as much as it would otherwise be. When the surface is not specular, but diffusely scatters sunlight, Rb⊥ is small and thus Rb⊥ −Rr∥ can
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be very negative as observed for the unimproved road. At large ‘e’, Rb⊥ is large and the Pc profile converges with Pb and PR. In contrast, for Pc2 the distinctiveness of the unimproved road is largely absent and the effects of pavement variations are reduced. Because the unimproved road does not strongly polarize reflected sunlight and is red, the numerator in Pc2 is large at all angles. This results in a large Pc2 with a shallow slope. However, variations in the profile of Pc2 remain significant. The Pc2 of the unimproved road is slightly greater than for the pavement and is slightly b 0, which implies slight polarization. A nonpolarizing surface would have equal perpendicular and parallel components for a particular channel ( Rb⊥ =Rb∥ and Rr⊥ =Rr∥) resulting in Pc1 =−Pc2. The observed minimum value of Pc1 = −0.185 and the maximum Pc2 = 0.193 for the unimproved road is consistent with a largely nonpolarizing surface and the difference may be due to slightly different amounts of polarization by multiple scattering. Pc1 (from now on simply referred to as Pc) consistently emphasizes the varnished surfaces of mature pavements (Fig. 8)
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and increases with increasing ‘e’. In contrast, the Pc of an unimproved road surface near ‘e’ = 85° is again negative,∼b−0.2. In Fig. 8a, the Pc profile also dips at the top of the image because of a large swath of vegetation. In Fig. 8b,c the effects of vegetation are obscured by more abundant varnished terrain, with all profiles truncated at the boundary with the sky. Also the Pc of vegetated terrain tends to be higher than for an unimproved road because vegetation is less red (these bushes were green at this time of year) and because the leaves can slightly polarize reflected light (e.g. Egan, 1985; Duggin et al., 1997; Raven et al., 2002). The orientation of the road also affects the profile of Pc. When the road is ∼ perpendicular to the field of view, the transition in the profile from pavement to road is sharp; an oblique road orientation results in a wide transition (Fig. 8c). The other sharp features in the profiles correspond to significant changes in the pavement. Disturbed pavement, where clasts are overturned and dust is exposed, has a low Pc (Fig. 9). In a panchromatic image insensitive to both polarization and color (Fig. 9a), disturbed pavements will
Fig. 8. Pc of three different mature pavements. (a) Site 1, different perspective than in Fig. 6. Vehicle is 4.2 m long. (b) Site 2. (c) Site 3 and same image as in Fig. 4c. Each pixel along the vertical profile is an average across the row, excluding pixels containing artifacts such as automobiles, if present. Pc N 0 for paved surfaces. Pc b 0 for the unimproved road. Total reflected light is the sum of the reflected perpendicular and parallel components.
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Fig. 9. Color polarization of disturbed pavement. (a) Total reflected illumination from disturbed pavement on the far side of unimproved road present in site 2; scaled to emphasize the disturbed pavement. Vehicle tracks are pre-existing, and of unknown age. (b) Image of Pc scaled over same range as the profile in (c) — from − 0.1 to +0.4. The high-Pc rock near center of image to left of the cross section is ∼20 cm across. The dashed line is center location of the pixels used to generate the profile in (c). (c) Pc for pixels along the dashed line in the images. Each pixel along the profile is an average of 50 pixels centered on the line.
appear either bright (because of dust) or dark (because of shadows casts by dislodged clasts). In contrast, disturbed pavements consistently appear dark in an image of Pc (Fig. 9b). Thus, areas of disturbance difficult to discern in unpolarized images can be more easily detected using color polarization. Even small
disturbances difficult to detect in Fig. 9a become obvious in the image of Pc. Using Pc to discern pavement does have its limitation: it will not work over long distances when scattered skylight becomes significant, resulting in a large Pc obscuring the signature of the ground.
Fig. 10. Color polarization of reflected skylight. (a) Site 1, looking away from sun. The profile is from two images from same position taken at two different camera angles. Scale is provided by the sheet of notebook paper at e ∼ 82° along image centerline. (b) Site 2, looking away from sun (thick lines) and perpendicular to sun (thin line). The image is a mosaic of the two observations looking directly away from the sun. The shadow of the camera head is ∼76 cm from the camera.
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5.2.3. Reflected skylight As Fig. 9b shows, skylight can affect the calculation of Pc for a surface. In that example, the presence of skylight (which is blue and partially polarized) obscured the surfaces of very distant objects. However, when reflected from a nearby surface, skylight can augment the sensitivity of Pc to pavements. Both the polarization and blueness of skylight will be partially preserved in reflection from pavement. When there is a significant component of skylight in the reflected illumination, it can make it possible to distinguish pavement from other surfaces oriented other than in the solar principal plane and facing into the sun. Polarized skylight is greatest when looking directly away from the sun but also is present in other geometries not in the solar principal plane. Thus, to explore the possible effect of reflected skylight on Pc of pavements, we obtained images of well-developed pavements in Sites 1 and 2, both looking away from the sun while in the solar principal plane (Fig. 10a,b) as well as oriented perpendicular to the solar principal plane (Fig. 10b). When in the solar principal plane and facing directly away from the sun, Pc is significantly negative, but increases considerably at ‘e’ N ∼70° and is greater for pavement than for a vegetated surface. When viewing perpendicular to solar principal plane surface-scattered sunlight may contribute to the illumination (Fig. 10b). The unimproved road again has a very low Pc for observation both orthogonal and in the solar principal plane, which are similar in magnitude to Pc observed when facing the sun, suggesting that skylight light does not significantly contribute to its reflected illumination at any angle. The greater Pc at moderate ‘e’ for site 2 in Fig. 10b compared to site 1 in Fig. 10a may be characteristic of these pavements, although this difference isn't seen when viewed into the sun (Fig. 8a,b).
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5.3. Laboratory measurements It has been shown above that the polarization of sunlight reflected from desert pavements is a combination of light reflected from varnished clasts, unvarnished clasts, and interstitial dust and grus. The positive polarization is a consequence of the smooth varnish on the clasts whereas the negative polarization is due to scattering possibly both within the varnish and from the other unvarnished surfaces. In order to understand the polarization contribution from only the varnished clasts, laboratory measurements were made of varnished and unvarnished stones. Six varnished clasts from the pavements were analyzed, to include varnished basalts and schists and lightly varnished coarse-grained granites. Two smooth, unvarnished stones were chosen, one from a stream channel and the other a sample of cut, but unpolished, marble. The selection was chosen to maximize the possibility for polarization to better understand the signal that could be expected from a worst-case natural, but unvarnished surface. To provide consistency with the field measurements, a constant i = 30° was maintained for the laboratory measurements. The ‘e’ of the center camera pixel was varied in 10° increments from 10° to 60°. This resulted in ‘g’ ranging from 40° to 90°. Samples were consistently placed in the center of the camera field of view so that the average ‘e’ of the illuminated pixels was equivalent to ‘e’ of the center pixel. No flat-field correction was applied because we derived a single polarization value for the illuminated area, illuminated the same portion of the detector each time, and did no spatial analyses. The laboratory polarization measurements were obtained for the green channel, Pg, because it provided the greatest signal-to-noise.
Fig. 11. Polarization data from individual clasts and mature pavements. The Pb and Pr of pavements (gray lines) is less positive and more negative polarization than for individual varnished clasts (solid black circles and gray ‘x’). The Pg of unvarnished but smooth clasts (black ‘x’) is low and specular. Pr of heavily varnished basalt clasts (gray ‘x’) measured by Shepard & Arvidson (1999) is greatest for large phase angles. The range in Pg of varnished and unvarnished clasts is ∼+− 0.05.
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The range in Pg for varnished stones results from the variation in varnish development on each clast. Fig. 11 shows how the Pg data of the clasts compare with the Pb and Pr of mature desert pavement. The best-fit trends for Pb and Pr of the pavements (Fig. 7) are consistently smaller than the Pg of the varnished clasts. This lower Pb and Pr of the pavements may be due to the presence of unvarnished clasts and other unvarnished materials in the pavements. The positive wing of Pg for the clasts is modeled with Eq. (5) (black line) as was previously used to model the Pb and Pr of mature pavements. However, a smaller w = 0.28, and larger n = 1.75 is required to fit the Pg of the clasts. These values suggest that a dark material, such as manganese oxide, contributes more significantly to the polarization of light from individual clasts than was determined from the observations of pavements. The ‘Pg’ of unvarnished stones is lower than for all varnished clasts and may have a peak near the specular angle. A small amount of unvarnished rocks such as these could thus have a significant effect on the polarization properties of desert pavements, explaining their low P compared to P of individual varnished clasts. Also, at low phase the inter-clast fine-grained material is observable in pavements. As discussed in Section 6.1.1., the dust and fine-grained grus between the clasts may also be responsible for a portion of this negative polarization in pavements. The greater ‘Pr’ of varnished basaltic clasts measured by Shepard and Arvidson (1999), implies those were more heavily varnished than the clasts for the Mecca hills pavements. 6. Conclusions Desert pavements strongly and positively polarize reflected sunlight at large phase angles and large emission angles within the solar principal plane. The shape and amplitude of the polarization curve is consistent with multiple specular reflections from the pavement surface, with a multiple-scattering contribution inducing a few percent negative polarization at small phase angles. The positive polarization of well-developed pavements is less, and the negative polarization is greater, than for individual clasts. This suggests that the pavement structure, possibly the interstitial grus and dust, as well as any unvarnished clasts, has a significant effect on the polarization properties of pavements. When modeled by Hapke theory, the positive polarization of pavements appears to be dominated by the optical properties of the silicate component of the varnish, whereas the positive polarization of heavily varnished individual clasts is more consistent with a darker material such as Mnoxide. Including color information with polarization combines compositional and structural information to emphasize the presence of rock varnish. This can aid in the discrimination of desert pavements from other landforms (dirt roads, vegetation, disrupted pavements). Polarized and blue skylight is also reflected from pavements. Its contribution to the reflected illumination can be significant, especially at e N 70° and may be useful in the identification of pavements. Because color polarization effects can highlight pavements over a large range of emission and incidence angles, pavements can be detected from the air as well as ground, and potentially from space platforms.
Acknowledgments We would like to acknowledge the helpful reviews of the two anonymous reviewers. This research was begun under a DCI Postdoctoral program and continued under a Federal Contract and under NASA's ASTER program. References Bockaert, V. (2005). http://www.dpreview.com Bohren, C. F., & Huffman, D. R. (1983). Absorption and scattering of light by small particles (pp. 35). New York: J. Wiley & Sons. Christensen, P. R., & Harrison, S. T. (1993). Thermal infrared emission spectroscopy of natural surfaces; application to desert varnish coatings on rocks. Journal of Geophysical Research, 98, 19,819−19,834. Crouvi, O., Ben-Dor, E., Beyth, M., Avigad, D., Kaufmann, H., Scholdlok, M., et al. (2003). Relative dating of alluvial surfaces using reflective hyperspectral remote sensing; a new tool for geomorphic mapping, (abstract). XVI INQUA, 16, 230. Dorn, R. I. (1991). Rock Varnish. American Scientist, 79, 542−553. Dorn, R. I., & Oberlander, T. M. (1981). Microbial origin of desert varnish. Science, 213, 1245−1247. Dragovich, D. (1988). A preliminary electron probe study of microchemical variations in desert varnish in western New South Wales, Australia. Earth Surface Processes and Landforms, 13, 259−270. Dragovich, D. (1994). Fire, climate, and the persistence of desert varnish near Dampier, Western Australia. Palaeogeography, Palaeoclimatology, Palaeoecology, 111, 279−288. Dragovich, D. (1998). Microchemistry of small desert varnish samples, western New South Wales, Australia. Earth Surface Processes and Landforms, 23, 445−453. Egan, W. G. (1985). Photometry and Polarization in Remote Sensing. New York: Elsevier Press. Engle, C. G., & Sharp, R. P. (1958). Chemical data on desert varnish. Bulletin of the Geological Society of America, 69, 487−518. Duggin, M. J., Kinn, G. J., & Schrader, M. (1997). Enhancement of vegetation mapping using Stokes parameter images. Proceedings SPIE, 3121, 307−313. Guinness, E. A., Arvidson, R. E., Clark, I. H., & Shepard, M. (1997). Comparing terrestrial varnished basalts to rocks at the Viking lander sites. GSA (abstract), 29(6), 214. Gillespie, A. R., Kahle, A. B., & Palluconi, F. D. (1984). Mapping alluvial fans in Death Valley, California, using multispectral thermal infrared images. Geophysical Research LettersGeophysical Research Letters, 11, 1153−1156. Hapke, B. (1993). Theory of reflectance and emittance spectroscopy. New York: Cambridge Univ. Press. Hibbitts, C. A., Gillespie, A., & Hansen, G. B. (2004). Identifying varnished rocks on Mars using thermal infrared spectroscopy, AGU Fall Meeting, #P11A-0955. Hunt, C. B. (1954). Desert Varnish. Science, 120, 183−184. Kahle, A. B. (1987). Surface emittance, temperature, and thermal inertia derived from Thermal Infrared Multispectral Scanner (TIMS) data for Death Calley, California. Geophysics, 52, 858−874. Klein, C., & Hurlbut, C. (1993). Manual of Mineralogy, 21st Edition. Kodak (2006). Device Performance Specification Rev 1.0 MTD/PS-0938 (pp. 5). Kraft, M. D., Michalski, J. R., & Sharp, T. G. (2003). Effects of pure silica coatings on thermal emission spectra of basaltic rocks: Considerations for Martian surface mineralogy. Geophysical Research Letters, 30, 2288. doi:10.1029/2003GL018848 Laudermilk, J. D. (1931). On the origin of desert varnish. American Journal of Science, 21(121), 51−66. Lyon, R. J. P. (1994). Weathering and desert varnish in arid terrains: Spectral effects in deeply-weathered mafic, ultrabasic, and felsic rocks, Yilgarn Block, central Western Australia. IARACE (abstract) (pp. 257−268). Mabbutt, J. A. (1977). Desert Landforms (pp. 119−150). Canberra: Australian National Univ. Press.
C.A. Hibbitts, A.R. Gillespie / Remote Sensing of Environment 112 (2008) 1808–1819 McKeown, D. A., & Post, J. E. (2001). Characterization of manganese oxide mineralogy in rock varnish and dendrites using X-ray absorption spectroscopy. American Mineralogist, 86, 701−713. Perry, R. S., & Adams, J. B. (1978). Desert varnish; evidence for cyclic deposition of manganese. Nature, 276, 489−491. Perry, R. S., Lynne, B. Y., Sephton, M. A., Kolb, V. M., Perry, C. C., & Staley, J. T. (2006). Baking black opal in the desert: The importance of silica in desert varnish. Geology, 34, 537−540. Potter, R. M., & Rossman, G. R. (1977). Desert varnish: The importance of clay minerals. Science, 196, 1446−1448. Potter, R. M., & Rossman, G. R. (1978). The manganese- and iron-oxide mineralogy of desert varnish. Chemical Geology, 25, 79−94. Raven, P. N., Jordan, D. L., & Smith, C. E. (2002). Polarized directional reflectance from laurel and mullein leaves. Optical Engineering, 41(05), 1002−1012.
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Rivard, B., Arvidson, R. E., Duncan, I. J., Sultan, M., & El Kaliouby, B. (1992). Varnish, sediment, and rock controls on spectral reflectance of outcrops in arid regions. Geology, 20, 295−298. Rivard, B., Petroy, S. B., & Miller, J. R. (1993). Measured effects of desert varnish on the mid-infrared spectra of weathered rocks as an aid to TIMS imagery interpretation. IEEE Transactions on Geoscience and Remote Sensing, 31, 284−291. Shepard, M. K., & Arvidson, R. E. (1999). The opposition surge and photopolarimetry of fresh and coated basalts. Icarus, 141, 172−178. Spatz, D. M., Taranik, J. V., & Hsu, L. C. (1987). Desert varnish on volcanic rocks of the Basin and Range Province: composition, morphology, distribution, origin and influence on Landsat imagery. Proceedings of the International Symposium on Remote Sensing of Environment, 21, 843−852. Woessner, P., & Hapke, B. (1987). Polarization of light scattered by clover. Remote Sensing of Environment, 21, 243−261.
Remote Sensing of Environment 112 (2008) 1808 – 1819 www.elsevier.com/locate/rse
Polarization of visible light by desert pavements Charles A. Hibbitts a,⁎, Alan R. Gillespie b a
b
Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Rd., Laurel, Md. 20723, United States W. M. Keck Remote Sensing Laboratory, Department of Earth & Space Sciences, University of Washington, Seattle, Wa. 98195, United States Received 16 December 2005; received in revised form 7 September 2007; accepted 9 September 2007
Abstract Desert pavements can be detected through multi-spectral polarization measurements of reflected sunlight both in and out of the solar principle plane. The combination of polarization and color distinguishes desert pavements from other desert landforms and vegetation. Desert pavements linearly polarize and impart a blueness to sunlight reflected at visible wavelengths. The polarization and color of skylight reflected at high emission angles is also preserved. The polarization properties of desert pavements are dominated by Fresnel reflection at large phase angles and by multiple scattering at low phase angles, causing significant positive and small negative polarization, respectively. © 2007 Published by Elsevier Inc. Keywords: Desert pavements; Desert varnish; Polarization
1. Introduction Identifying the composition and structures of surfaces with remote sensing has evolved into a complex science utilizing passive and active instruments to image the energy reflected and emitted from the surface. Desert pavements can be quite large, covering up to many km2 and thus are potentially well-suited for detection and mapping by remote sensing (e.g. Gillespie et al., 1984; Rivard et al., 1992). The compositions and physical structure of pavements also make them well-suited for detection with reflected sunlight and thermal emission. Reflectance and emission spectroscopy has proven capable of detecting pavements (e.g. Christensen and Harrison, 1993; Crouvi et al., 2003; Kahle, 1987; Rivard et al., 1993; Spatz et al., 1987). Here, we explore an alternative approach, visible-wavelength polarization combined with color imaging. As a broad band imaging technique, it has the potential to be a simple yet effective tool for mapping these landforms over large areas at high spatial resolution and high signal-to-noise. In this paper, we investigate the capabilities and limitations of this combined color and polarization approach, which can be used from the ground and air, and potentially from near-space and space.
⁎ Corresponding author. Tel.: +1 443 778 2834. E-mail address: [email protected] (C.A. Hibbitts). 0034-4257/$ - see front matter © 2007 Published by Elsevier Inc. doi:10.1016/j.rse.2007.09.004
Using color from the visible through shortwave infrared, pavements can be distinguished from many other terrains (e.g. Rivard et al., 1992), especially from vegetated terrain. Pavements are typically composed of smooth cobbles coated with rock varnish, a dark mineral coating which further smoothes affected surfaces. Thus pavements polarize reflected sunlight (e.g. Shepard and Arvidson, 1999), further distinguishing them from surrounding, rougher terrains. Adding color information enables us to create an even more effective technique for distinguishing pavements from other terrains. We explore using visible polarization of reflected sunlight at three colors (blue, green, red) for discerning desert pavements from other terrains. The investigations consist of a series of field and laboratory measurements exploring the combined color and polarization properties of desert pavements and individual varnished stones. The polarization of pavements and clasts is explored in the solar principal plane; the polarization of pavements is also measured normal to the plane. 2. Background 2.1. Physical characteristics of varnished rocks and desert pavements Despite their name, desert pavements are not mechanically strong surfaces, but are a mosaic of flat-lying stones commonly
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darkened by a thin and smooth coating called ‘desert varnish’ (e.g. Engle and Sharp, 1958; Hunt, 1954; Laudermilk, 1931). Desert pavements, and the varnish covering the clasts, develop over hundreds to thousands of years (e.g. Dorn, 1991) with the dark color of the varnish caused by an accumulation of manganese oxide (McKeown and Post, 2001; Potter and Rossman, 1977). The stone mosaic of pavements is generally a single layer thick, and can camouflage a dusty layer of silt tens of centimeters thick or less (Fig. 1). Thus, although appearing to offer a strong surface for traversing, pavements can be readily disrupted by vehicular and pedestrian traffic to expose this fine-grained silt for redistribution by wind to be a dust problem when dry. Weather-resistant fine-grained mafic and siliceous rocks dominate the lithology of clasts that develop the thickest, most continuous varnished surfaces because of the physical and chemical stability of the rocks (e.g. Mabbutt, 1977). Varnish development on coarse-grained rocks such as granites is impeded by the rock and grains fragmenting to expose fresh, unvarnished surfaces. Such rocks rarely form pavements nor become thickly coated by varnish. The mechanical weathering of granites can often, however, create grus that fills the interstices between the stones of the pavements (Fig. 1). Soft rocks such as limestone abrade and chemically weather sufficiently quickly so that when they do form pavements, varnish coatings on the clasts tend to be thin or absent (Crouvi et al., 2003). Rock varnish forms as complex layers growing up and out from nucleation points (Perry and Adams, 1978). Each layer, a few micrometers thick, is comprised of botryoidal structures that lead to non-uniformity on horizontal and vertical scales of a few micrometers. The thicknesses of varnishes vary from stains of only a few micrometers to tough weather-resistant coatings over 100 μm thick (Dragovich, 1988, 1994, 1998). Such nonuniformity in thickness can occur on individual rocks where thick varnish accumulates in small pits, leaving tops of bumps free or nearly free of varnish. The bulk composition of the varnish is dominated by amorphous silica, possibly hydrated (Perry et al., 2006), with a lesser amount of clay present at
Fig. 1. A schematic cross section of a well-developed desert pavement. Each aspect of this idealized caricature, (clast spacing, grus, thickness of the vesicular Av horizon of aeolian silt, thickness and uniformity of the varnish coating, etc.) will vary among pavements. Poorly developed pavements have greater interclast distances, fewer varnished stones with generally thinner varnish, a thinner Av, and more silt exposed between the stones.
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∼10–20% (Potter and Rossman, 1978). It is derived from materials external to the rock, and thus distinct from a weathering rind. The source of the manganese and the method of its fixation have been of much debate, with the possibility of microbial mediation having been extensively explored after their discovery within varnishes (Dorn and Oberlander, 1981). However, a microbial origin for either the varnish or the Mnfixation has yet to be established, and recent experiments suggests the origin of both may be inorganic (Perry et al., 2006), with microbes merely being trapped during varnish formation. 2.2. Spectroscopy and polarimetry of varnished rocks Several remote-sensing techniques have been explored over the years for detecting desert pavements. Approaches such as visible and infrared reflectance spectroscopy as well as emittance (thermal) spectroscopy have proven sensitive to pavements. Although limitations exist, spectral signatures in the short and longwave infrared have been used to identify pavements (e.g. Christensen and Harrison, 1993; Crouvi et al., 2003; Kahle, 1987; Rivard et al., 1993; Spatz et al., 1987). However, spectroscopic measurements cannot always provide definitive detection of pavements. Robust identification of varnish via spectroscopy depends upon the varnish being spectrally distinct from unvarnished rocks and surrounding terrain. For instance, the ∼2.2-μm clay absorption band is present in the reflectance spectra of varnish because of the presence of clays. In the thermal infrared, the clay in the varnish also provides an absorption band centered near 9.6 μm [e.g. Hibbitts et al., 2004; Potter, and Rossman, 1977], although it also can appear similar to spectra of other silicate coatings (Kraft et al., 2003) as well as some mafic rocks. Clays are also present in weathering rinds, wind-blown dust, and in spectra of other terrain such as playas [e.g. Lyon, 1994; Rivard et al., 1992, 1993] making it an unreliable marker for pavements. Varnish darkens and reddens rocks in the visible through shortwave infrared. However, this spectrally broad effect can be confused with photometric or compositional variations. There may also be a potential for identifying varnished rocks through the non-linear mixing of light emitted from the rock substrate with that emitted from the varnish (Hibbitts et al., 2004). Again, though, reliably separating these mixing effects from the spectra of incredibly diverse lithologies of clasts may prove insurmountable. Polarization of sunlight reflected from varnished rocks is an alternative approach for detecting pavements. Varnished rocks were shown by Guinness et al. (1997) to polarize reflected sunlight. They were able to derive Hapke constants for individual varnished stones, demonstrating the importance of both reflection and scattering in light reflected from varnished rocks. Shepard and Arvidson (1999) explored the angular dependence in the polarization of light reflected from varnished basalt rocks at visible (red) wavelengths. They also demonstrate that the reflectance and polarization properties of dark varnished basaltic clasts are consistent with a surface that specularly (mirror-like) reflects light multiple times as well as slightly scattering it. They interpreted the large positive polarization at high phase angles to be due to the multiple specular reflections and the significant
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Fig. 2. The flat-field response of the (a) red and (b) blue channels (1600 × 1200 pixels) interpolated over 50 pixels. Each pixel has been normalized to the average of the image. A value of ‘1’ would represent no difference from the image average and thus no flat-field correction. Scaled between 0.9 and 1.05, the flat-field variation for each channel is significant, although the two responses are similar. These separate flat-field corrections are applied to the blue and red channels during calibration.
negative polarization at low phase angles indicative of a phenomenon associated with scattering, shadow-hiding, either on the surface or by scattering centers within the varnish. Our work focuses on the polarization of light reflected from pavements, with some laboratory measurements of individual clasts to help interpret the results. We also explore the utility of using color to help emphasize the optical characteristics of pavements and rock varnish. 3. Camera calibration Before interpreting the field and laboratory measurements, it is important to understand the camera performance to interpret the significance and limitations of those measurements
accurately. Standard image calibration procedures were performed, including geometric flat-field characterization, the measurement of responsivity with signal level (linearity), and noise estimation and correction for these effects. A tripod-mounted Cannon A60 digital 1.9 mega-pixel (effective) camera with a rotating linear polarizer mounted in front of the aperture was used to obtain the measurements. The focal plane array is a 4:3 ratio CCD detector with 1600 × 1200 pixels and micro-filters in a Bayer pattern to produce a color image. The spectral responsivity was not measured, but is assumed to be the typical broad response of filter color arrays used on compact digital cameras. Blue responsivity peaks ∼450 nm, green ∼540 nm, and red ∼625 nm (Kodak, 2006). With a fullwidth half-maximum of the response varying between 50 and
Fig. 3. Camera responsivity (y-axis) vs. integration time (scaled). Calculated blue channel (black line) and red channel (gray line) responses diverge at high signal levels. The symbols are the average value for several observations. The ‘o’ and ‘+’ designate the parallel and perpendicular components of the (mostly) unpolarized light from the outdoor calibration. The ‘x’ points are from the indoor calibration where no polarizer was used. The 1 − σ error for the indoor calibration is b5 DN, and for the outdoor calibration is b10 DN.
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100 nm, there is overlap in sensitivity between the green filter and both the blue and red filters, but the blue and red filters are spectrally distinct. A detector size of 5.27 mm × 3.96 mm equates to an individual pixel size of ∼3.3 μm, typical for these types of cameras (Bockaert, 2005). Although compact digital cameras are not designed for quantitative measurements of illumination, through basic calibration efforts to determine detector response and focal plane flat field we developed a calibration procedure that can be applied to determine relative reflectance. Relative reflectance is sufficient for calculating reflectance ratios such as the polarization ratios we explore in this study. The pixel-to-pixel response has been calibrated with the specific settings used to give the field measurements better than 10% accuracy (typically much better). Changes in the absolute responsivity from image to image are sufficiently small that time-lapse comparisons can also be made. No attempt was made to derive an absolute radiometric calibration. The signal-response curve and flat-field uniformity were derived separately for each color channel with the calibration target extremely out-of-focus to ensure greatest image uniformity. The flat-field response of the detector is non-uniform primarily due to vignetting and is different for the red and blue channels. Because of significant pixel-to-pixel spatial variation in the raw flat-field measurements due to compression artifacts, the flat-field data were interpolated over a 50-pixel region to remove the high-frequency variations while preserving the regional variations characteristic of flat-field responses (Fig. 2). The flat-field variations of the blue and red channels each exceed 10% and have similar structure. The ∼3% difference between the channels' flat-field responses warranted the use of a separate flat-field calibration for each. Separately determining the responsivity of the red and blue channels removed any dependence on the color of the calibration source/target, although spatial uniformity was still required for the flat-field characterization. Calibrated measurements obtained under indoor fluorescent illumination and outdoor solar illumination could therefore be evaluated together for characterizing instrument noise and response linearity with signal level. The response curves are combinations of multi-order polynomials and spline functions fit to the average response for each channel at each integration time (Fig. 3). The curve is non-linear with signal. Because CCD response to signal is usually biased to be linear until nearing detector saturation, there may be signal processing occurring within the camera before image recording. Regardless of its origin, the shape of the response curve is invariant, making reliable calibration possible. After scaling the outdoor and indoor measurements to overlap, the shapes of the camera response to signal are nearly identical. The consistency demonstrates that there is no strong integration-time dependent response although the greater scatter in the response under bright illumination implies that detector responsivity is more variable under strong illumination (shorter integration time) or with a warmer detector. The ambient air temperature during the field measurements at times exceeded 38 °C (100°F). The field measurements were conducted under direct-sunlight similar in illumination geometry and sky conditions to the outdoor calibration effort. In most
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analyses, averages of thousands of pixels are used to reduce measurement error further as well as to reduce the effects of variations in the pavement surfaces. The greatest challenge to a quantitative analysis has been the lossy compression storage used by the camera software. It is the noise introduced by this lossy compression scheme that ultimately limits the accuracy of the calibration, and is largely manifested as aliasing between high-contrast pixels. This aliasing has been minimized by spatially smoothing each image using a 1-pixel wide Photoshop™ Gaussian resampling function. Some aliasing remains, especially at clast boundaries in more nadir images where the higher-albedo grus and silt adjacent to the low albedo varnished clasts is resolved. The degradation of spatial resolution associated with this resampling did not degrade subsequent multi-pixel characterizations. 4. Field site Field measurements were conducted in the desert of southern California, near the town of Mecca Hills. Images were obtained of three pavements located on a single fan (Table 1 and Fig. 4) throughout a day. The solar incidence angle ‘i’ (illumination angle measured from nadir) decreased from ∼ 40 to ∼25° during the experiment, but was constant for any single observation. For most observations, the camera was oriented in the solar principal plane and facing into the sun to best measure the polarization of reflected sunlight (Fig. 5). A few observations were also obtained in the solar principal plane facing away from the sun to measure the color and polarization of reflected skylight. Still other observations were made perpendicular to the solar plane. For most observations, context was provided by capturing an unimproved road surface in the background, horizontally transecting the image. Other features commonly included in an image are leafy and dry vegetation, sky, and sometimes, disrupted or poorly-developed pavements. The phase angles, ‘g’, of the field measurements extend from less than 0° to greater than 100° with the incident angle, ‘i’, ranging from ∼ 14 to 38° and the emission angles ‘e’ (angle from nadir of reflected light) spanning ± 19.6° of the detector's center pixel. Multiple images were taken of each site from each
Table 1 Locations and measurement conditions for the desert pavements near Mecca Hills, California Begin and end times (PDT)
Sun incidence Latitude/ angle (average, longitude range)
Description
Site 1 1005, 1015
37.6°, 3°
Site 2 1025, 1042
32.5°, 3°
Site 3 1055, 1105
27.6°, 2°
Well-developed pavement Well-developed and disturbed pavements Well-developed pavement Poorly developed and disturbed pavement Partially disturbed pavement
Site 4 1110, ∼ 1120 25.0°, 2° Site 5 1310, ∼ 1320 14.0°, 1°
33°40.325N 115°58.203W 33°40.128N 115°58.224W 33°40.030N 115°58.315W 33°39.352N 115°59.161W 33°43.702N 116°07.958W
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Fig. 4. Images of pavements from study area. Camera height for each image ∼ 1.23 m (4 feet). (a) Site 1. Well-developed pavement. Pen is ∼ 102 cm from camera and 15 cm long. (b) Site 2. Well-developed pavement. Pen is ∼ 102 cm from camera. (c). Site 3. Well-developed pavement. Road is 15 m from camera. (d) Poorly developed pavement with some sparse vegetation. The leafless shrub in the center of the image is 52 m from the camera, the edge of the hill which blocks the dirt road from the foreground is 96 m distant, and the dirt road is ∼ 390 m away.
camera position to obtain a large range of emission angles. As a result, for some observations in the solar principal plane, the phase angle of the measurement passes through the specular angle (e = i, and g = e + i). 5. Results and discussion 5.1. Polarization Light reflected by a smooth, mirror-like (specular) surface is linearly polarized, as described by the Fresnel equations, which assume reflection occurs on the uppermost surface and that light which penetrates the rock does not scatter back out through the surface. The polarization of the reflected component, P, is the difference between the perpendicular (R⊥) and parallel (R∥) components of the reflected light, divided by the sum of the two (i.e. the total reflected light). P ¼ ðR8 ROÞ=ðR8 þ ROÞ
Light polarized by reflecting from desert pavements possesses a quasi-specular behavior characteristic of specular reflection plus scattering from a rough surface (Shepard and Arvidson, 1999). Reflected light that is a combination of multiple specular reflections always has positive polarization (R⊥ N R∥) and its reflectance dramatically increases near the specular angle. However, sunlight reflected from pavements behaves differently. There is no surge in reflectance near the specular angle and the polarization begins negative at low phase angle, increasing to positive values at moderate and large phase angles, and continues to increase as the emission angle becomes equal to and exceeds the incident angle (i.e. passes through the specular angle). Fig. 6 demonstrates this effect for both the blue and red colors.
ð1Þ
For a specular surface, the perpendicular component is larger than the parallel component, especially at incidence angles of 30° or more (e.g. Bohren and Huffman, 1983). However, any penetration of light into the varnish and scattering, such as from a particulate medium, would change the magnitude and photometric dependence of the polarization.
Fig. 5. Schematic of the instrument set-up and illumination geometry of measurements within the solar principal plane looking towards the sun.
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Fig. 6. Pc of mature desert pavement at Site 1. Each image is a mosaic of two pictures, with the vehicle in the distance at ∼ e = 90°, and the closest stone clasts e ∼ 20°. The pen, near e = 40°, is ∼ 102 cm from the camera and is 15 cm long. The specular angle is approximately e = 38°. (a) The RGB image of the perpendicularly polarized component of the reflected sunlight. The blueness of the image increases with increasingly grazing view angle. (b) The RGB image of the parallel component. (c) The vertical profile along sight of the image. P for the blue channel (blue line) and red channel (red line) are contrasted with the two formulations of color polarization: Pc1 (thick black line) and Pc2 (thick gray line). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 6a,b shows the perpendicular and parallel components of the reflected sunlight for the sum of the red, green, and blue channels for a mosaic of two images. The perpendicular component is brighter and appears bluer. Fig. 6c contains profiles of different polarization calculations derived from the two images that compose the mosaic (the spatial overlap is evident in overlapping profiles near e = 50°). Each profile is calculated using a different formulation for polarization and is a running average, with each point on the profile an average of the entire row plus all points for ten rows above and below the current position. Pixels containing the vehicle are excluded from the average for this and all other observations when present. Averaging emphasizes the role of photometry on the polarization of reflected sunlight by dramatically reducing the sharp variations in the profile caused by changes in the pavement and the lossy compression used by the camera. Some effects due to variations in pavement development remain and manifest themselves as both sharp and broad features in the profiles that are also consistent between the profiles. The 1 −σ noise for each profile is about equal to the width of the line. The red and blue profiles represent the polarization associated with only these two channels, ‘Pr’ and ‘Pb,’ respectively, where ‘b’ and ‘r’ correspond the blue and red channels. For the other two profiles, color information is included while maintaining the structure for the definition of polarization (Eq. (1)): Pc ¼ ðRc18 Rc2OÞ=ðRc18 þ Rc2OÞ
ð2Þ
where ‘c1’ and ‘c2’ are two colors, and ‘Pc’ represents what we refer to as “color polarization.” The following variations to the color polarization equation directly follow: Pc1 ¼ ðRb8 RrOÞ=ðRb8 þ RrOÞ
ð3Þ
Pc2 ¼ ðRr8 RbOÞ=ðRr8 þ RbOÞ
ð4Þ
The profiles derived with these equations are plotted in Fig. 6c. Pc1 emphasizes the polarization at blue wavelengths and Pc2
emphasizes the polarization in the red channel. Because these equations mix independent physical measurements, they no longer represent an easily interpretable physical quantity, although they provide quantitative information. 5.2. Field measurements 5.2.1. Single-color polarization characteristics of desert pavements As demonstrated by Fig. 6, Pb is greater than Pr for welldeveloped desert pavements, especially at grazing angles. Pb and Pr both decrease ∼ linearly to slightly below zero as ‘e’ decreases to a minimum of ∼20°. Non-pavement terrain has significantly lower P. Both Pb and Pr are low for the unimproved road, with Pb N Pr at all ‘e’. Scene-wide variations in pavement maturity result in a slight decrease in Pb and Pr at e ∼75° to 80°. Other high-frequency variations that are present in both the Pb and Pr profiles are also real variations in the pavement development. Pr and Pb from several observations of additional sites of mature pavements (Fig. 7) consistently show similar trends. With the additional observations acquiring lower ‘e’ (and thus lower ‘g’) values, the linear trend in ‘P’ is found to sharply flatten at low ‘g’ (also low ‘e’). However, Pb remains greater than Pr at all angles. Both Pb and Pr are slightly negative at ‘g’ b ∼ 40°. In both profiles, the curve flattens at g b 20°, and Pr may increase again at very low ‘g’. The presence of a negative branch in P of pavements at low ‘g’ is consistent with multiple scattering by a particulate surface (Hapke, 1993). Egan (1985: his Fig. 10.1) also noted this phenomenon in rock fragments of ilmenite with smooth clean faces, including having a positive Pr at larger ‘g’ that is similar in sign and magnitude to that of the pavements. High-albedo, rough surfaces such as roughened glass have a negative polarization branch that extends to larger ‘g’ that is almost as large in amplitude as the positive branch, due to significant multiple scattering with little absorption in the glass (Hapke, 1993: his Fig. 14.2) and is different than the P observed for pavements.
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Fig. 7. Polarization vs. phase angle for the (a) blue channel and (b) red channel. Values for the blue channel values are greater than for the red channel, showing that polarization calculation using the blue channel is sensitive to the presence of reflected blue skylight. The shape is consistent with quasi-specular reflection from mineral faces (Egan, 1985). The dashed line in each is a model based upon Hapke theory (e.g. Hapke, 1993), assuming no multiple scattering.
For sunlight polarized by desert pavements, there is no peak at the specular angle. Instead, ‘P’ increases as observing angles become increasingly grazing crossing from negative to positive at g ∼ 50°. This positive polarization can be modeled assuming a surface composed of subpixel, partially randomly oriented, specular reflectors (Fig. 7). Following directly from Woessner and Hapke (1987), the polarization is: P ¼ f ðwÞ⁎ðF8 FO Þ=½2⁎r⁎ð1 þ cosðeÞ=cosðiÞÞ;
ð5Þ
where f (ψ) is a characteristic constant, in this case 0.5, and signifies a non-uniform distribution in the orientation of the subpixel reflectors. The specular reflection coefficients ‘F⊥’ and ‘F∥’ are controlled by the real portion of the complex index of refraction. The reflection of the surface ‘r’ is largely controlled by the single-scattering albedo ‘w’ (grossly related to the albedo), with a directional distribution assumed to be consistent with a Lommel–Seeliger phase function, the single-particle angular scattering function, and terms describing the single- and multiplescattering albedo. A real index of refraction (n) = 1.45 for both the red and blue channels best describes the polarization curves of the varnish. This value is consistent with clay minerals (Klein and Hurlbut, 1993), though slightly low, and is significantly lower than the index of refraction for opaque oxides such as the Mn oxide, birnessite. For the red channel, we find that w = 0.4 provides the best fit to the data, and for the blue channel w = 0.35
is better. These values are consistent with those previously derived for varnished basalts (Guinness et al., 1997), and with the observation that pavements are more reflective (brighter) at longer wavelengths, resulting in the reddish/brown color of the pavement. These choices are also consistent with the empirical observations that surfaces dominated by low-albedo materials are more polarizing than brighter surfaces (Hapke, 1993). Thus, it appears that the positive portion of the polarization of sunlight by desert pavements is dominated by specular reflection likely associated with the varnished clasts. The negative polarization is due to multiple scattering, either inside the varnish and/or by unvarnished clasts, grus, and dust in the pavement. 5.2.2. Two-color polarization of desert pavements The two profiles of color polarization in Fig. 6c are noticeably different from each other as well as from Pb and Pr. Pc1 emphasizes features in both Pb and Pr. The differences between the redder, dusty road surface and the bluer varnish of the pavement are more apparent in Pc1 and the variations in the pavement are exaggerated. The negative spike in the Pc1 of the unimproved road is greater than for either Pb or Pr. The slope of Pc1 is greater as well. The greater slope is primarily due to lower Pb and Pr at low ‘e’. Reflected sunlight polarized by desert pavements is bluer than unpolarized reflected sunlight because specular reflection not strongly color-dependent and the blue light is not absorbed as much as it would otherwise be. When the surface is not specular, but diffusely scatters sunlight, Rb⊥ is small and thus Rb⊥ −Rr∥ can
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be very negative as observed for the unimproved road. At large ‘e’, Rb⊥ is large and the Pc profile converges with Pb and PR. In contrast, for Pc2 the distinctiveness of the unimproved road is largely absent and the effects of pavement variations are reduced. Because the unimproved road does not strongly polarize reflected sunlight and is red, the numerator in Pc2 is large at all angles. This results in a large Pc2 with a shallow slope. However, variations in the profile of Pc2 remain significant. The Pc2 of the unimproved road is slightly greater than for the pavement and is slightly b 0, which implies slight polarization. A nonpolarizing surface would have equal perpendicular and parallel components for a particular channel ( Rb⊥ =Rb∥ and Rr⊥ =Rr∥) resulting in Pc1 =−Pc2. The observed minimum value of Pc1 = −0.185 and the maximum Pc2 = 0.193 for the unimproved road is consistent with a largely nonpolarizing surface and the difference may be due to slightly different amounts of polarization by multiple scattering. Pc1 (from now on simply referred to as Pc) consistently emphasizes the varnished surfaces of mature pavements (Fig. 8)
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and increases with increasing ‘e’. In contrast, the Pc of an unimproved road surface near ‘e’ = 85° is again negative,∼b−0.2. In Fig. 8a, the Pc profile also dips at the top of the image because of a large swath of vegetation. In Fig. 8b,c the effects of vegetation are obscured by more abundant varnished terrain, with all profiles truncated at the boundary with the sky. Also the Pc of vegetated terrain tends to be higher than for an unimproved road because vegetation is less red (these bushes were green at this time of year) and because the leaves can slightly polarize reflected light (e.g. Egan, 1985; Duggin et al., 1997; Raven et al., 2002). The orientation of the road also affects the profile of Pc. When the road is ∼ perpendicular to the field of view, the transition in the profile from pavement to road is sharp; an oblique road orientation results in a wide transition (Fig. 8c). The other sharp features in the profiles correspond to significant changes in the pavement. Disturbed pavement, where clasts are overturned and dust is exposed, has a low Pc (Fig. 9). In a panchromatic image insensitive to both polarization and color (Fig. 9a), disturbed pavements will
Fig. 8. Pc of three different mature pavements. (a) Site 1, different perspective than in Fig. 6. Vehicle is 4.2 m long. (b) Site 2. (c) Site 3 and same image as in Fig. 4c. Each pixel along the vertical profile is an average across the row, excluding pixels containing artifacts such as automobiles, if present. Pc N 0 for paved surfaces. Pc b 0 for the unimproved road. Total reflected light is the sum of the reflected perpendicular and parallel components.
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Fig. 9. Color polarization of disturbed pavement. (a) Total reflected illumination from disturbed pavement on the far side of unimproved road present in site 2; scaled to emphasize the disturbed pavement. Vehicle tracks are pre-existing, and of unknown age. (b) Image of Pc scaled over same range as the profile in (c) — from − 0.1 to +0.4. The high-Pc rock near center of image to left of the cross section is ∼20 cm across. The dashed line is center location of the pixels used to generate the profile in (c). (c) Pc for pixels along the dashed line in the images. Each pixel along the profile is an average of 50 pixels centered on the line.
appear either bright (because of dust) or dark (because of shadows casts by dislodged clasts). In contrast, disturbed pavements consistently appear dark in an image of Pc (Fig. 9b). Thus, areas of disturbance difficult to discern in unpolarized images can be more easily detected using color polarization. Even small
disturbances difficult to detect in Fig. 9a become obvious in the image of Pc. Using Pc to discern pavement does have its limitation: it will not work over long distances when scattered skylight becomes significant, resulting in a large Pc obscuring the signature of the ground.
Fig. 10. Color polarization of reflected skylight. (a) Site 1, looking away from sun. The profile is from two images from same position taken at two different camera angles. Scale is provided by the sheet of notebook paper at e ∼ 82° along image centerline. (b) Site 2, looking away from sun (thick lines) and perpendicular to sun (thin line). The image is a mosaic of the two observations looking directly away from the sun. The shadow of the camera head is ∼76 cm from the camera.
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5.2.3. Reflected skylight As Fig. 9b shows, skylight can affect the calculation of Pc for a surface. In that example, the presence of skylight (which is blue and partially polarized) obscured the surfaces of very distant objects. However, when reflected from a nearby surface, skylight can augment the sensitivity of Pc to pavements. Both the polarization and blueness of skylight will be partially preserved in reflection from pavement. When there is a significant component of skylight in the reflected illumination, it can make it possible to distinguish pavement from other surfaces oriented other than in the solar principal plane and facing into the sun. Polarized skylight is greatest when looking directly away from the sun but also is present in other geometries not in the solar principal plane. Thus, to explore the possible effect of reflected skylight on Pc of pavements, we obtained images of well-developed pavements in Sites 1 and 2, both looking away from the sun while in the solar principal plane (Fig. 10a,b) as well as oriented perpendicular to the solar principal plane (Fig. 10b). When in the solar principal plane and facing directly away from the sun, Pc is significantly negative, but increases considerably at ‘e’ N ∼70° and is greater for pavement than for a vegetated surface. When viewing perpendicular to solar principal plane surface-scattered sunlight may contribute to the illumination (Fig. 10b). The unimproved road again has a very low Pc for observation both orthogonal and in the solar principal plane, which are similar in magnitude to Pc observed when facing the sun, suggesting that skylight light does not significantly contribute to its reflected illumination at any angle. The greater Pc at moderate ‘e’ for site 2 in Fig. 10b compared to site 1 in Fig. 10a may be characteristic of these pavements, although this difference isn't seen when viewed into the sun (Fig. 8a,b).
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5.3. Laboratory measurements It has been shown above that the polarization of sunlight reflected from desert pavements is a combination of light reflected from varnished clasts, unvarnished clasts, and interstitial dust and grus. The positive polarization is a consequence of the smooth varnish on the clasts whereas the negative polarization is due to scattering possibly both within the varnish and from the other unvarnished surfaces. In order to understand the polarization contribution from only the varnished clasts, laboratory measurements were made of varnished and unvarnished stones. Six varnished clasts from the pavements were analyzed, to include varnished basalts and schists and lightly varnished coarse-grained granites. Two smooth, unvarnished stones were chosen, one from a stream channel and the other a sample of cut, but unpolished, marble. The selection was chosen to maximize the possibility for polarization to better understand the signal that could be expected from a worst-case natural, but unvarnished surface. To provide consistency with the field measurements, a constant i = 30° was maintained for the laboratory measurements. The ‘e’ of the center camera pixel was varied in 10° increments from 10° to 60°. This resulted in ‘g’ ranging from 40° to 90°. Samples were consistently placed in the center of the camera field of view so that the average ‘e’ of the illuminated pixels was equivalent to ‘e’ of the center pixel. No flat-field correction was applied because we derived a single polarization value for the illuminated area, illuminated the same portion of the detector each time, and did no spatial analyses. The laboratory polarization measurements were obtained for the green channel, Pg, because it provided the greatest signal-to-noise.
Fig. 11. Polarization data from individual clasts and mature pavements. The Pb and Pr of pavements (gray lines) is less positive and more negative polarization than for individual varnished clasts (solid black circles and gray ‘x’). The Pg of unvarnished but smooth clasts (black ‘x’) is low and specular. Pr of heavily varnished basalt clasts (gray ‘x’) measured by Shepard & Arvidson (1999) is greatest for large phase angles. The range in Pg of varnished and unvarnished clasts is ∼+− 0.05.
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The range in Pg for varnished stones results from the variation in varnish development on each clast. Fig. 11 shows how the Pg data of the clasts compare with the Pb and Pr of mature desert pavement. The best-fit trends for Pb and Pr of the pavements (Fig. 7) are consistently smaller than the Pg of the varnished clasts. This lower Pb and Pr of the pavements may be due to the presence of unvarnished clasts and other unvarnished materials in the pavements. The positive wing of Pg for the clasts is modeled with Eq. (5) (black line) as was previously used to model the Pb and Pr of mature pavements. However, a smaller w = 0.28, and larger n = 1.75 is required to fit the Pg of the clasts. These values suggest that a dark material, such as manganese oxide, contributes more significantly to the polarization of light from individual clasts than was determined from the observations of pavements. The ‘Pg’ of unvarnished stones is lower than for all varnished clasts and may have a peak near the specular angle. A small amount of unvarnished rocks such as these could thus have a significant effect on the polarization properties of desert pavements, explaining their low P compared to P of individual varnished clasts. Also, at low phase the inter-clast fine-grained material is observable in pavements. As discussed in Section 6.1.1., the dust and fine-grained grus between the clasts may also be responsible for a portion of this negative polarization in pavements. The greater ‘Pr’ of varnished basaltic clasts measured by Shepard and Arvidson (1999), implies those were more heavily varnished than the clasts for the Mecca hills pavements. 6. Conclusions Desert pavements strongly and positively polarize reflected sunlight at large phase angles and large emission angles within the solar principal plane. The shape and amplitude of the polarization curve is consistent with multiple specular reflections from the pavement surface, with a multiple-scattering contribution inducing a few percent negative polarization at small phase angles. The positive polarization of well-developed pavements is less, and the negative polarization is greater, than for individual clasts. This suggests that the pavement structure, possibly the interstitial grus and dust, as well as any unvarnished clasts, has a significant effect on the polarization properties of pavements. When modeled by Hapke theory, the positive polarization of pavements appears to be dominated by the optical properties of the silicate component of the varnish, whereas the positive polarization of heavily varnished individual clasts is more consistent with a darker material such as Mnoxide. Including color information with polarization combines compositional and structural information to emphasize the presence of rock varnish. This can aid in the discrimination of desert pavements from other landforms (dirt roads, vegetation, disrupted pavements). Polarized and blue skylight is also reflected from pavements. Its contribution to the reflected illumination can be significant, especially at e N 70° and may be useful in the identification of pavements. Because color polarization effects can highlight pavements over a large range of emission and incidence angles, pavements can be detected from the air as well as ground, and potentially from space platforms.
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