Photometric correction of Mercury's global color mosaic

Planetary and Space Science 59 (2011) 1873–1887

Contents lists available at ScienceDirect

Planetary and Space Science journal homepage: www.elsevier.com/locate/pss

Photometric correction of Mercury’s global color mosaic Deborah L. Domingue a,n, Scott L. Murchie b, Brett W. Denevi c,1, Nancy L. Chabot b, David T. Blewett b, Nori R. Laslo b, Robin M. Vaughan b, Hong K. Kang b, Michael K. Shepard d a

Planetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA c School of Earth and Space Exploration, Arizona State University, Box 871404, Tempe, AZ 85287-1404, USA d Department of Geography and Geosciences, Bloomsburg University, 400 E. Second Street, Bloomsburg, PA 17815, USA b

a r t i c l e i n f o

abstract

Article history: Received 22 October 2010 Accepted 24 March 2011 Available online 9 April 2011

During the third flyby of Mercury by the MESSENGER spacecraft, a dedicated disk-integrated photometric sequence was acquired with the wide-angle multispectral camera to observe Mercury’s global photometric behavior in 11 spectral filters over as broad a range of phase angle as possible within the geometric constraints of the flyby. Extraction of disk-integrated measurements from images acquired during this sequence required careful accounting for scattered light and residual background effects. The photometric model fit to these measurements is shown to fit observed radiances at phase angles below 1101, possibly except where both solar incidence and emission angles are high (4 701). The complexity of the scattered light at wavelengths greater than 828 nm contributes to a less accurate photometric correction at these wavelengths. The model is used to correct the global imaging data set acquired at a variety of geometries to a common geometry of incidence angle ¼301, emission angle ¼01, and phase angle ¼ 301, yielding a relatively seamless mosaic. The results here will be used to correct image mosaics of Mercury acquired in orbit. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Photometry Mercury Spectra MESSENGER

1. Introduction Analyses of laboratory measurements of the spectral properties of mineral and lunar samples as a function of illumination and viewing geometry show the importance of correcting spectral observations to a common set of photometric conditions prior to detailed compositional analyses, such as mixture modeling or comparison with analog materials. The laboratory measurements also show that to characterize the photometric behavior of a surface, the radiance of the surface should be thoroughly sampled over all possible photometric angles. To address these issues at Mercury, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft completed a dedicated disk-integrated photometric imaging sequence during the probe’s third flyby (M3) of the innermost planet on 29 September 2009. The photometric observations were conducted with MESSENGER’s Mercury Dual Imaging System (MDIS) instrument (Hawkins et al., 2007, 2009). MDIS consists of a multispectral wide-angle camera (WAC) and a monochrome narrow-angle camera (NAC).

n Correspondence to: Planetary Science Institute, 400 Teresa Marie Ct., Bel Air, MD 21015, USA. Tel.: þ1 410 868 2296. E-mail address: [email protected] (D.L. Domingue). 1 Current address: Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA.

0032-0633/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2011.03.014

The subset of observations presented in this paper was taken with the WAC, a four-element refractor with a 10.51 field of view and an 11-color (and one broadband) filter wheel (for filter specifics see Hawkins et al., 2007, 2009; Domingue et al., 2010). We also make use of MDIS images obtained during MESSENGER’s first (M1) and second (M2) flyby of Mercury on 14 January and 6 October 2008, respectively. The image sequences acquired during each flyby include both disk-integrated (where the illuminated disk of Mercury is fully contained within the image frame) and disk-resolved (where only a portion of the illuminated disk of Mercury is contained within the image frame) observations of Mercury’s surface. Monochrome and color sequences were part of each encounter’s imaging observation set. A subset of these image sequences was designed for the construction of a global color mosaic with a spatial resolution of  5 km/pixel. During MESSENGER’s first Mercury flyby two color sequences relevant to the global mosaic were acquired, one on approach and the second on departure. Although additional color sequences were obtained during the first encounter, they are not discussed in this paper. The global color mosaic sequences during M1 involved imaging Mercury’s surface at spatial resolutions of 5.05–4.83 km/pixel in 11 filters. During M2 two additional color sequences relevant to the global color mosaic were acquired, one on approach and another on departure, at similar spatial resolutions of 5.04–4.86 km/pixel.

1874

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

Additional color sequences were obtained during M2, but only a subset of these is presented in this paper, namely the five diskintegrated observations acquired during the departure phase of the flyby. The timing and trajectories of the first two flybys were such that different hemispheres of Mercury were illuminated and imaged, thus maximizing the coverage for the global mosaic. During M3, two additional color sequences relevant to the global mosaic were planned, but because of a spacecraft safe-hold event only the approach mosaic sequence was obtained, although other imaging sequences were also successful. The M3 color sequence was obtained at a spatial resolution of 5.0 km/pixel, similar in spatial resolution to the first and second flyby images. The M3 images were of a region similar to that seen during M2, but this image sequence set provided observations of Mercury’s surface that filled in some gaps in the color mosaic (Fig. 1). The image sequences for the global color mosaic discussed in this paper are shown in Table 1. The mosaic in Fig. 1 shows the regions imaged during each sequence in comparison to the coverage obtained by Mariner 10. A dedicated set of disk-resolved photometric observations was obtained during M1. Several color series were acquired of an area centered on 1.71S, 123.51E, spanning approximately 5.51 of latitude and 101 of longitude and 51–1201 phase angle. This disk-resolved data set, described in an earlier paper (Domingue et al., 2010), provided results used in this study to help constrain the initial Hapke photometric modeling parameters. Additional analyses of this disk-resolved data set are also presented by Domingue et al. (this issue). The radiometric calibration and photometric correction applied to these images, prior to the geometric registration and

projection into a mosaic, are the focus of this paper. The rationales and methodologies used for the construction of a global color mosaic are described, along with a critique of the resulting mosaic.

2. Calibrations and corrections This section provides a summary of the radiometric calibration and a description of the derivation of a photometric correction to the calibrated data to construct a global color mosaic. Details of the derivation and application of a photometric correction along with an evaluation of the resulting global color mosaic are also provided. 2.1. Radiometric calibration A detailed description of the MDIS calibration and in-flight performance was provided by Hawkins et al. (2009). The value of each pixel is converted from raw digital number (DN) to radiance values in units of W m  2 sr  1 mm  1. The conversion is given by Lðx,y,f ,T,t,bmÞ Lin½DNðx,y,f ,T,t,bm,METÞDkðx,y,f ,T,t,bm,METÞSmðx,y,t,bmÞ ¼ ½Flatðx,y,f ,bmÞt RESPðf ,bm,TÞ ð1Þ where x is the column designation of the pixel, y is the row designation, f is the filter, T is the temperature of the chargecoupled device (CCD), t is the exposure time in milliseconds, bm is the binning mode, and MET is the mission elapsed time (seconds from launch). The values for f, T, t, bm, and MET are recorded in

Fig. 1. Regions on Mercury’s surface imaged by MESSENGER during each of the sequences shown in Table 1 relative to the area imaged by Mariner 10 during its flybys of Mercury. The phase angle at which the region was imaged is also shown.

Table 1 Global color mosaic image sets. Flyby sequence

MET range (s)

Phase angle (deg)

Resolution (km/pixel)

M1 M1 M2 M2 M3

108,820,007–108,820,057 108,829,678–108,829,728 131,764,500–131,764,550 131,775,228–131,775,268 162,741,039–162,741,079

119.19–119.29 52.19–52.26 130.19–130.29 37.23–37.27 106.85–106.91

5.05–4.99 4.83–4.89 5.04–4.97 4.86–4.92 5.04–5.00

approach departure approach departure approach

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

1875

the image headers. L(x, y, f, T, t, bm) is the pixel value in radiance, Dk(x, y, f, T, t, bm, MET) is the dark level derived from a model based on exposure time and CCD temperature, Sm(x, y, t, bm) is the scenedependent frame transfer smear for each pixel, Lin is a function that corrects the small nonlinearity of the detector response, Flat(x, y, f, bm) is the correction for non-uniformity of pixel sensitivity (flat field), and RESP(f, bm, T) is the responsivity relating dark-, flat-, and smear-corrected DN per unit exposure time to radiance. The calibration is performed stepwise using calibration tables and images in the following order:

 Inversion of 12-bit to 8-bit compression (this step was skipped      

for the flyby data since all observations were obtained as 12-bit measurements). Subtraction of modeled dark level. Correction for frame transfer smear. Correction for CCD nonlinearity. Correction for flat field. Conversion of DN to radiance. Conversion of radiance to radiance factor.

The radiance factor, R(f), also denoted I/F, is the ratio of measured radiance received from the surface to the radiance expected from a perfect Lambertian surface normally illuminated by the Sun. The conversion is given by Rðf Þ ¼ Lðf Þp½ðDsolar =A2 Þ=Fðf Þ

ð2Þ

where L(f) is the calibrated radiance for an image taken in filter f at a solar distance Dsolar. A is the number of kilometers in one astronomical unit (AU), and F(f) is the effective average solar irradiance sampled under filter f. The solar spectrum used in the radiance calibration is from R.L. Kurucz.2 2.2. Photometric variability Three spectra of a single highland lunar soil sample (Apollo 16, Station 2 sample 62,231, 14) measured at the Reflectance Laboratory facility at Brown University are shown in Fig. 3. Each spectrum was acquired under different illumination and viewing geometries. The spectra are variously displayed in absolute reflectance (Fig. 2a), normalized to unity at 500 nm (Fig. 2b), and as normalized spectra between 500 and 1500 nm (Fig. 2c). Spectrum L30 was acquired at an incidence angle (i) of 301, an emission angle (e) of 01, and a phase angle (a) of 301. Spectra L20 and L110 were acquired at i¼401, e¼201, a ¼201, and i¼601, e¼501, a ¼1101, respectively. The normalized spectra emphasize the changes in slope with variation in illumination and viewing geometry, along with variations in the properties of the absorption feature centered between wavelengths of 900 and 1000 nm. Fig. 3 shows a more detailed view of the absorption feature observed in the L30 and L20 spectra (the feature is absent in the L110 spectrum). Using the reflectance values at 800 and 1100 nm, a line was derived from these points to define the continuum background in the portion of the spectrum near the absorption feature. The spectral reflectance was divided by the calculated continuum. The resulting spectra for L30 and L20 are shown in Fig. 3. This figure demonstrates how fundamental absorption feature properties, such as band depth and wavelength position of the band minimum, can vary as a function of illumination and viewing geometry. The variations in these spectra emphasize the need for photometric corrections, so that observations can be adjusted to 2 The SOLAR Irradiance by Computation. Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA. Available from the author on request, or at KURUCZ.HARVARD.EDU under IRRADIANCE in the SUN directory.

Fig. 2. The reflectance spectrum of a lunar highland soil (Apollo 16, Station 2 sample 62,231, 14) measured under three different illumination and viewing geometries. Spectrum L30 (black line) was acquired at i¼ 301, e¼01, and a ¼ 301. Spectrum L20 (dotted line, open circles) was acquired at i¼ 401, e¼201, and a ¼ 201, and spectrum L110 (dashed line, open squares) was acquired at i¼ 601, e¼501, and a ¼1101. Plotted are (a) the absolute reflectance, (b) the reflectance normalized to unity at 0.5 mm, and (c) the normalized reflectance between 0.5 and 1.5 mm, accenting the spectral region near the ’’1 mm’’ ferrous-iron absorption feature.

a common set of conditions prior to spectral analysis and compositional interpretation. A further emphasis of this point, shown in Fig. 4, comes from a comparison of lunar spectral trends (Blewett et al., 2009) with corresponding measurements taken from the three laboratory spectra of the Apollo 16 lunar highland sample. In studies of the lunar surface, plots of color ratio versus reflectance are used to examine regolith compositional and maturity relations and to indicate surface alteration or space-weathering trends (e.g., Lucey et al., 1995, 1998, 2000; Staid and Pieters, 2000). Fig. 4 presents example ratio-reflectance diagrams for the lunar nearside from Blewett et al. (2009) with corresponding plots extracted from the three spectra shown in Fig. 2. This comparison demonstrates and

1876

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

emphasizes that the trends are dependent on photometric conditions (illumination and viewing geometries) and that photometric correction to a common illumination and viewing geometry is essential prior to any reflectance or color analysis.

Fig. 3. Reflectance at wavelengths near the absorption feature seen in the lunar soil spectra shown in Fig. 2 but with the spectral continuum removed. Note the shift in the position in the band minimum and change in the band depth between the L30 (diamonds) and L20 (circles) spectra. Spectrum L110 (squares) shows no evidence of an absorption feature. These spectra of the same lunar sample were acquired under different illumination and viewing geometries.

2.3. Photometric measurements Following M1 an experiment was conducted to test the accuracy with which photometric corrections could be derived from a limited set of phase angle observations. This test was carried out using laboratory measurements made at the Bloomsburg University Goniometer (BUG) facility. The measurements were a subset of those examined by Shepard and Helfenstein (2007), who tested the correlations between the known physical properties of the measured samples with those derived from modeling the reflectance measurements using Hapke’s equations (Hapke, 1981, 1984, 1986, 2002). The BUG facility provides a measurement of the reflectance of a sample as a function of incidence, emission, and phase angles over the entire photometric phase space (both in and out of the scattering plane). This facility provides the most complete measure currently available of the reflectance phase space for a sample. The experiment conducted to test the accuracy to which photometric corrections could be derived involved: (1) modeling reflectance measurements covering as much of the photometric phase space as possible, (2) modeling reflectance when only a limited region of the phase curve is included (in this case, phase angles from 501 to 1251, corresponding to the phase angle coverage from the diskresolved photometric sequence acquired during M1), (3) using the modeling results from both cases to derive photometric corrections to the laboratory-standard geometry for reflectance measurements (i¼301, e¼01, a ¼301), and (4) comparing the results of the two

Fig. 4. (Left) Ratio-reflectance plots for the lunar nearside from Blewett et al. (2009) constructed from Galileo imaging observations. The color codes denote density of observations. The upper plot (near-infrared wavelengths) has white arrows indicating major spectral trends, one associated with increasing ferrous iron in silicates, the other related to reddening and darkening associated with maturity (space weathering). The lower plot (visible wavelengths) shows major spectral trends predominantly caused by variations in maturity or ferrous iron content in silicates (highlands) and variations in opaque mineral (ilmenite) abundances in the maria. (Right) Ratio-reflectance data for the three spectra in Fig. 2 (square is L30, triangle is L20, circle is L110). The same lunar sample will fall in markedly different portions of the plot depending on the photometric conditions (illumination and viewing geometries) at which an observation was made, therefore influencing the interpretation of the sample’s composition and state of maturity.

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

modeling efforts. The two samples used for this test included a sample of hematite and a sample of iron-rich clay (Blackbird clay by Shepard and Helfenstein, 2007). These samples are not intended to be compositional or textural analogs for Mercury’s surface, but rather were selected to illustrate the important effects that photometric geometry can have on spectra and their interpretation. For each sample, measurements were acquired at three wavelengths (450, 550, and 700 nm). The laboratory measurements were modeled using Hapke’s equations (Hapke, 1981, 1984, 1986) with the modeling methods described by Domingue et al. (2010). First the entire data set (covering the full measured photometric phase space) at each wavelength was modeled, and the model parameter values were derived from a least-squares grid search over all possible parameter values. Second, the entire data set was modeled again, but this time the opposition amplitude and width (bo and h, respectively) were constrained to the values obtained at 550 nm wavelength from the first modeling results and the surface roughness parameter (y) was set to the average obtained from each wavelength in the first modeling. This procedure mimics the constraints applied to the modeling of the combined M1 and M2 observations analyzed by Domingue et al. (2010). Domingue et al. (2010) modeled the 550 nm observations of Mallama et al. (2002) to obtain opposition parameter values because the MESSENGERderived data have no opposition measurements. They performed initial fits of each filter data set with this constraint. They then performed a final fit with the opposition parameter constraint and the surface roughness parameter at all wavelengths set to the average value across all wavelengths from the initial fit values. Third, the subset data (measurements covering phase angle ranges from 501 to 1251) were modeled using the same constraints on the opposition and surface roughness parameters as in the second modeling effort. This approach mimics not only the constraints applied to the modeling of the first and second MESSENGER flyby observations, but also represents the limited range of photometric phase space sampled in the disk-resolved photometric sequence measurements acquired during M1. To facilitate discussion, the

1877

first modeling scenario will be termed the ‘‘unconstrained full data sample (UFDS)’’, the second modeling scenario will be termed the ‘‘constrained full data sample (CFDS)’’, and the third modeling scenario will be termed the ‘‘constrained subset sample (CSS)’’. Results for the hematite and clay samples are shown in Figs. 5 and 6, respectively. The plots on the left-hand side of the figures display spectra in units of absolute reflectance, whereas the plots on the right-hand side of the figures display spectra normalized to unity at 550 nm wavelength. The top graphs represent spectra at i¼01, e¼301, and a ¼301 (outside of the subset phase angle range), whereas the graphs on the bottom represent spectra at i¼ 301, e¼601, and a ¼901 (within the subset phase angle range). Each plot compares the spectral reflectance as measured in the laboratory at the specified i and e values with the predicted spectra based on the various modeling results. The results shown in Figs. 5 and 6 demonstrate the ability of the Hapke model to describe the phase and spectral behavior and the accuracy with which the model can be used to derive photometric corrections. In the lower-reflectance hematite results, both the UFDS and CFDS spectra are within 5% of the actual measurement at the illumination and viewing geometries considered here. This agrees, in general, with results from Cheng and Domingue (2000), who demonstrated that Hapke’s model is accurate to within 2–4% for dark materials. The results from the CSS, however, are much less accurate when used to extrapolate outside of the phase angle range of the data set. This is seen in the divergence of the CSS spectrum at i¼01, e¼ 301, and a ¼301 from the actual spectrum at this illumination and viewing geometry (Fig. 5b), yet the CSS spectrum is well within the 5% variance at the geometry that falls within the data set range (i¼301, e¼601, and a ¼901). In the clay results, the accuracy of the Hapke model falls to within 5% at shorter wavelengths and to 10% at 700 nm, the error range within which the UFDS and CFDS match the actual measurement at i¼01, e¼301, and a ¼301. This outcome agrees, in general, with results from Cheng and Domingue (2000) at the lower wavelengths, but is higher than the Cheng and Domingue (2000) results at the longest wavelength measured. The results

Fig. 5. Laboratory measurements of spectra of hematite (gray diamonds) compared with model spectra. The measured spectra were acquired at the BUG facility at Bloomsburg University. The top graphs are for spectra acquired at i¼ 301, e¼01, and a ¼301, and the bottom plots show spectra acquired at i¼301, e¼ 601, and a ¼ 901. The graphs at left are in units of absolute reflectance, and those at right display the ratio of model spectrum to measured spectrum at the designated illumination and viewing geometry. Spectra derived from modeling the UFDS (dotted line) and the CFDS (dashed line) often overlie each other. Spectra derived from modeling the CSS are displayed by the solid lines and show the greatest departure from the measured spectral properties.

1878

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

Fig. 6. Laboratory measurements of spectra of iron-rich clay (gray diamonds) compared with model spectra. The measured spectra were acquired at the BUG facility at Bloomsburg University. The top graphs are for spectra acquired at i¼ 301, e ¼01, and a ¼301, and the bottom plots show spectra acquired at i¼301, e¼ 601, and a ¼ 901. The graphs at left are in units of absolute reflectance, and those at right display the ratio of model spectrum to measured spectrum at the designated illumination and viewing geometry. Spectra derived from modeling the UFDS (dotted line) and the CFDS (dashed line) often overlie each other. Spectra derived from modeling the CSS are displayed by the solid lines and show the greatest departure from the measured spectral properties.

from the CSS, however, are much less accurate when used to extrapolate outside of the phase angle range of the data set. This is seen in the divergence of the CSS spectrum at i¼ 01, e¼301, and a ¼301 from the actual spectrum at this illumination and viewing geometry (Fig. 6b), yet the CSS spectrum is well within the 5% variance at the geometry that falls within the data set range (i¼301, e¼601, and a ¼901), as are the UFDS and CFDS. The conclusions from this test are as follows: (1) more robust photometric characterization requires that the photometric phase space be well sampled, and (2) photometric corrections are more robust if the corrections are to an illumination and viewing geometry within the measurement ranges used to derive the correction. These results drove the design of the photometry measurement sequence obtained during MESSENGER’s third flyby. During the weeks surrounding M3 there was a dedicated observing campaign to measure Mercury’s phase curve at 1–21 phase angle increments. The predicted coverage included observations with all 11 filters from 145.51 to 102.31 phase angle on approach (acquired from 22 September 2009 to 29 September 2009) and 37.81 to 144.51 phase angle on departure (acquired from 3 October 2009 to 21 October 2009). Because of a spacecraft safehold event, the actual coverage in this dedicated sequence was to 145.4–101.61 phase angle on approach and 53.3–144.51 on departure. The purpose of this dedicated photometric sequence was to provide sufficient measurements to quantify the phase behavior of the global surface of Mercury in all 11 filters, thus enabling more accurate photometric corrections. These photometric corrections are essential for quantitative color studies of Mercury’s surface.

3. Photometric corrections: derivation The observations used to derive photometric corrections for the construction of a global color mosaic are described next. The details of the modeling effort, and the interpretation of the modeling results, are provided in a companion paper (Domingue

et al., this issue). This section provides a summary of the modeling methods and results that are relevant for understanding the photometric correction of the global color mosaic. 3.1. MDIS disk-integrated observations MDIS acquired 11-color image sets that contain the full illuminated disk of Mercury within its field of view during all three flybys. All three flybys also included multiple disk-resolved color observations sequences. With the exception of the diskresolved photometric sequence acquired during M1, these additional color observations are not discussed in this paper. During each flyby a disk-integrated full-color set was collected on approach. These are the same color image sequences used to construct the global color mosaic. On departure, a single diskintegrated color-set was obtained during M1 and five diskintegrated color-sets were obtained during M2. The M1 departure color sequence is also part of the global color mosaic image set. The first disk-integrated color sequence following closest approach during M2 is, again, also part of the global color mosaic image set. Following M2 closest approach, a series of color image sets were obtained to measure the point-spread-function characteristics of the MDIS WAC. Of these color sets, the first three (  741 phase angle) were useful for extracting disk-integrated measurements, since they contained no saturated pixels. The third MESSENGER flyby included a dedicated disk-integrated photometry color sequence for defining the phase curve of Mercury in 1–21 increments from 53.31 to 144.51 phase angle (the only gaps in this coverage are between 801 and 841 and between 971 and 1021 phase angle). The final color set on approach in the disk-integrated photometry color sequence is also the global color mosaic image set from M3. The initial analysis began by extracting disk-integrated reflectance values from the radiometrically calibrated images using the following process: (1) determining residual background values, (2) summing the pixel values within a box circumscribing the disk

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

of Mercury, (3) subtracting the background contribution, and (4) dividing by the number of pixels on the disk of Mercury. Residual background values were determined on an image-byimage basis. The average pixel values of four 100  100 pixel boxes was determined, where each box was 20 pixels from the edges of the image corners. In the images taken just before and just following closest approach, the disk of Mercury filled a large portion of the field of view, and the disk of Mercury was apparent in the left-hand image corners. For these images two adjacent 100  100 pixel boxes in the right-hand image corners were used for calculating residual background values. The residual background for each image was then derived by taking an average of the four box averages from each image. The average from the four box averages was the residual background used in the initial diskintegrated reflectance derivation. An alternate method for determining residual background values was examined using the first four columns of the images. These columns are masked on the MDIS CCD detector to provide a measure of the instrument dark current. An average value of these four columns was calculated and used as an alternate measure of the residual background. However, the phase curve derived from the 559.2-nm filter images using the average dark strip for the residual background value produced a steeper phase curve that was not commensurate with the Mallama et al. (2002) Earthbased observations at 560 nm. In contrast, the phase curve derived from the 559.2-nm filter images produced by using the box method for background residual determination overlapped well with the Mallama et al. (2002) measurements. Thus the box method was used for the residual background determination for all MDIS filter observations. The difference between the two methods is ascribed to a combination of factors that produce small errors in the conversion from DN to physical units, which results in a low-level (  10  6–10  8) signal contributing to the reflectance value that is apparent in the image background pixels but not the dark strip pixels. No systematic difference is observed in the differences between the two methods for calculating background, indicating that scattered light is not the sole contributor to the residual background. The second step in extracting a disk-integrated reflectance from each of the images was to sum the pixel values in a box circumscribing the disk of Mercury. This box was defined to be 6RM (where RM is Mercury’s radius) from the center of the disk on all sides. The extent of this box was determined by an examination of the pixel values as a function of distance from the limb of Mercury. The pixel values were found to decline to approximately the same order of magnitude as the residual background value at a distance well within 5RM of the limb. A more detailed discussion of the scattered light is provided below. The number of pixels within this box (pxlbox) was tracked in addition to the number of pixels actually on the disk of Mercury (pxldisk). The disk-integrated reflectance is then given by I ðSBpxlbox Þ ¼ F pxldisk

ð3Þ

where S is the sum of the pixel reflectance values in the circumscribing box and B is the residual background value. This process of disk-integrated data extraction was performed on all flyby images used to construct the photometric phase curves at each wavelength. Additional analyses of these data are discussed in the companion paper (Domingue et al., this issue). 3.2. Initial phase curves The resulting MESSENGER phase curves and modeling results for three of the 11 filters are shown in Fig. 7. Comparisons of the MESSENGER-derived phase curves with Earth-based telescopic

1879

Fig. 7. Examples of reflectance versus phase angle at three of the 11 MDIS narrowband filter wavelengths as derived with the initial data extraction methods. These methods include deriving residual background values from four 100  100 boxes, one from each corner of the image. The scattered light content is assumed to be captured within a box extending to 6RM from the planet center. The data (circles) are compared to Hapke modeling solutions (solid line) from Domingue et al. (this issue). The filter wavelengths of (a) 996.8 nm, (b) 749 nm, and (c) 430 nm, correspond to the wavelengths used in the red, green, and blue channels, respectively, for constructing color mosaics (see Fig. 8).

observations are given by Domingue et al. (this issue). The diskintegrated observations were modeled using an earlier version of Hapke’s equations (Hapke 1981, 1984, 1986). Details concerning the model, modeling methods, and parameter values are discussed by Domingue et al. (this issue). Since the surface of Mercury is of low reflectance, and studies have demonstrated that Hapke’s equations can model lower-reflectance surfaces to within 2–5% (Cheng and Domingue, 2000; this paper), this model should be sufficient for characterizing Mercury’s global photometric behavior. The phase angle coverage extends downward to  341, to provide photometric corrections for the construction of a

1880

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

global color mosaic to the standard i ¼301, e¼01, and a ¼301 photometric conditions. 3.3. Initial global color mosaics The global color mosaic, photometrically corrected to 301 phase angle with the modeling results of the MESSENGER phase curves shown in Fig. 7 and described by Domingue et al. (this issue) is shown in Fig. 8a. This mosaic was constructed using images from all three flybys and was built from the 996.8-, 749-, and 430-nm filter images in the red, green, and blue channels, respectively. Regions imaged in the M1 and M2 approach frames (taken at 119.21 and 130.21 phase angles, respectively) are comparatively darker than nearby or overlapping regions imaged in either the M1 or M2 departure frames (taken at 52.21 and 37.21 phase angles, respectively) or the M3 approach frame (taken at 106.91 phase angle). The regions observed at higher phase angles (greater than 1101) appear to have been insufficiently corrected for photometric variations. Likely sources of error affecting the photometric characterization follow from the methods used to characterize both the scattered light and the residual background contributions. These error sources are accentuated by the nature of the images from

which the photometric behavior is modeled. In the majority of these images the illuminated disk of Mercury is approximately 6–10 pixels across, nearly a point-source measurement. Scattered light measurements (Fig. 9) show that the angle over which light is scattered is large and can spread over the entire image frame for many of the MDIS filters. In order to include the scattered light from Mercury in the reflectance measurements, the signal from pixels over a large area of the image frame should be integrated. However, there are contributions to the signal in each pixel from residual background sources, which when integrated over a large area introduce a substantial contribution to the measured reflectance. The residual background sources include small errors in the calibration from raw signal to physical units, especially within the dark current subtraction. Hawkins et al. (2009) described the details of the radiometric calibration and the possible sources of error. Therefore, a more sophisticated approach to account for the scattered light and residual background is required, and one such approach is described below. 3.4. Scattered-light properties Monochrome global mosaics for each filter (corrected to 301 phase angle with the modeling results from Fig. 7) are shown in

Fig. 8. Global color mosaics obtained by the MESSENGER spacecraft: (a) This mosaic was radiometrically calibrated and photometrically corrected to 301 phase angle using the phase curve model solutions shown in Fig. 7. The darker, highly contrasting albedo seen in the approach images from the first two flybys indicates that the photometric corrections at high phase angles do not adequately model the photometric behavior of the surface at these extreme ( 41191) phase angles. The quality of the mosaic, especially in regions where the surface was observed at both high and low phase angles, indicates that perhaps scattered light has not been adequately corrected in the image suite. (b) This mosaic was radiometrically calibrated and photometrically corrected to 301 phase angle using the revised phase curve model solutions shown in Fig. 11. The darker, greener albedo seen in the approach images from the first two flybys indicates that the photometric corrections are not adequately correcting for the reflectance behavior at high phase angles (4 1101). The quality of the mosaic indicates that perhaps scattered light has still not been adequately treated at the longer wavelengths. In both mosaics the red, green, and blue channels are represented by the 996.8-, 749-, and 430-nm filter images, respectively. Similar ranges of brightness were applied to the three channels for both mosaics.

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

1881

Fig. 9. Global mosaics in each filter paired with a measurement of the point-spread function (which displays the scattered-light pattern) acquired in the same filter. Common ranges of brightness were applied to the red, green, and blue channels used to construct the mosaics. The point-spread-function images (acquired with extremely long exposure times) show a saturated disk of Mercury in the image center. Each of the point-spread-function images has been displayed at a common scale to emphasize scattered light. The scattered-light pattern becomes more complex and covers a larger portion of the image frame as wavelength increases. The scattered-light pattern is observed to extend outside of the field of view for the 948- and 996.8-nm filters.

Fig. 9 alongside images acquired on departure from M2 designed to measure the point-spread function or scattered light extent within each filter. As in the color mosaic (Fig. 8a), regions imaged on approach during the first two flybys (taken at 119.21 and 130.21 phase angles for M1 and M2, respectively) are comparatively darker than nearby or overlapping regions imaged on departure (taken at 52.21 and 37.21 phase angles for M1 and

M2, respectively) or on approach during M3 (106.91 phase angle). The contrast in albedo between these regions increases with wavelength and apparent complexity in the scattered-light pattern. The point-spread-function images have been stretched to accentuate the scattered-light patterns within each filter. As Fig. 9 illustrates, this pattern becomes more complex and extensive as filter wavelength increases. Algorithms for remediating

1882

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

the scattered light are currently under development, but a firstorder characterization has been derived here to study the impact of scattered light on the derivation of a photometric correction to produce a uniform, seamless global mosaic. The majority of the Mercury images from which the phase curves are derived were obtained at low spatial resolution. The disk of Mercury in these images is often limited to 6–10 pixels in diameter, and the number of illuminated pixels, especially at higher phase angles, is small compared with the number of pixels summed within the image to derive the disk-integrated reflectance. Thus any DN value within the background pixels (whether due to subtle radiometric calibration errors or scattered light) can make a major contribution to the disk-integrated reflectance measurement with the data extraction method described above. It is therefore necessary to fully characterize the scattered light and residual background in order to account for these effects in the photometric measurements. The scattered-light images shown in Fig. 9 were constructed from a subset of the point-spread-function measurements. Five images, taken from the fifth, tenth, 15th, 20th, and 25th color set within this sequence, were co-added. In these images the exposure time was set to saturate the pixels on the disk of Mercury in order to focus on measurement of the scattered light in the region off the disk. A median pixel value within this summed image was calculated, and this median value was subtracted from the value of each pixel. A three-by-three-pixel boxcar smoothing function was then applied to produce the images shown in Fig. 9. This processing of the pointspread-function measurements was performed to emphasize the scattered light patterns, thus making them more visible and easier to measure within the image frame. These images were then used to derive two zones within the image frame. The first zone is the scattered-light zone (SLZ), for which a box is defined that encompasses the scattered-light pattern within the point-spread-function image frame. The second zone, the residual background zone (RBZ), is the remainder of the frame outside of the SLZ that was used to measure the residual background pixel levels. The images obtained in the first three color sets of the pointspread sequence were collected with exposure times that did not saturate the pixels on Mercury’s disk. These images were used to derive a first-order scattered-light correction for the photometric measurements. This correction was constructed by first determining the median pixel value in the RBZ, thus providing a measure of the residual background exclusive of scattered light contributions. The second step was to sum the pixel values within the SLZ and subtract the residual background from each pixel. This difference is a measure of the total light reflected from Mercury (Rtotal). The third step involved examining these images to determine the extent of the scattered light halo around the disk of Mercury. This extent is a measure of the number of pixels beyond the limb of Mercury, measured radially, to which a visible halo can be distinguished. The radial distance in the line and sample domain defines a box that contains the scattered light halo. Since the scattered light pattern has a fixed angular dependence (as evidenced in the images of Fig. 9), a measure of the extent of the halo beyond the planetary limb in these images provides an estimate of the extent of the halo beyond the planetary limb in all images, regardless of the pixel diameter of Mercury within the image frame. The fourth step in determining the first-order scattered-light correction was to sum the pixel values within the box containing Mercury and the scattered light halo and subtract the residual background from each pixel. This difference is termed the Mercury-halo reflectance measurement (Rbox). This quantity can be measured in all images of Mercury, regardless of the size of Mercury within the image frame. The first-order scattered light correction, Cs, is then defined as Rbox Cs ¼ Rtotal

where Rbox is the Mercury-halo reflectance and Rtotal is the total light reflected from Mercury in the SLZ. Values for Cs were calculated from measurements taken from each of the images in the first three point-spread observation sequences. The average of these three Cs values, in each filter, was then used as the scatteredlight correction coefficient, Cs. 3.5. Residual background properties Examples of the residual background value as a function of phase angle using the four 100  100 pixel corner-box algorithm described above are shown in Fig. 10. The values show a trend with phase, where the residual value appears to decrease with solar phase angle. The residual values plotted are all from images in

Fig. 10. Trends of the residual background with phase angle for the three filters used to construct the color mosaic. The residual was calculated by averaging the pixel values in four 100  100 boxes in each corner of the MDIS images. An average of these four box averages was then calculated to determine the residual. The values plotted are those derived from the M3 photometry sequence images, in which Mercury occupies a small (6–10 pixels in diameter) fraction of the field of view. The trend with increasing phase angle is consistent with trends expected from a scattered-light contribution to the measurement, rather than dark current alone.

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

which Mercury is a small portion (6–10 pixels in diameter) of the image frame. The trend in Fig. 10 indicates that the corner-box algorithm for deriving the residual background may also be capturing scattered light. It further indicates that the residual background may be a function of number of illuminated pixels. To account for these possible characteristics a new algorithm for deriving the residual background in the photometry images was devised. Using the median pixel value for the RBZ (rRBZ) as measured from the point-spread-function images, a scene-dependent residual background was derived from the relationship

rRBZ ¼ eRbox where Rbox is the Mercury-halo reflectance measurement defined above, and e is the coefficient for extracting the residual from the Mercury-halo reflectance measurement. Thus the residual background for each image is given by eRbox.

1883

3.6. Revised photometric phase curves The disk-integrated phase curves were then re-derived using the more robust scattered-light and residual background values. The resulting phase curves, compared with the original phase curves discussed above, are shown in Fig. 11. The phase curves at wavelengths shorter than 560 nm nearly overlap, but a difference between the phase curves that increases with wavelength above 560 nm. The phase curves derived from the updated scattered-light and residual background corrections have steeper slopes, and these slopes increase with wavelength, which is the direction of the change indicated by the initial mosaic results to better correct for photometric effects within the color observations. Also shown in Fig. 11 are the revised Hapke modeling solutions, which are discussed in detail by Domingue et al. (this issue). A revised modeling approach was taken in fitting the updated phase curves. This revised approach allows values of the surface

Fig. 11. A comparison of initial phase curves (solid circles, examples shown in Fig. 7) with the revised phase curves (open circles) derived from the SLZ and RBZ measurements. The revised phase curves are steeper and show a greater absolute reflectance at 301 phase angle than previous measurements. The solid lines represent fits of Hapke’s equations to model the phase behavior of the observations after the scattered-light correction.

1884

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

Fig. 11. (Continued)

roughness parameter to vary with wavelength. Whereas the opposition parameters remain fixed, as in the initial approach described above, the single-scattering albedo, single-particle scattering function, and surface roughness parameters are determined via a least-squares grid search over the available parameter spaces that minimizes the root mean squared difference between the model and the data. The rationale and details concerning this revised modeling approach are described by Domingue et al. (this issue), but it should be stated that Hapke parameters do not have a one-to-one correspondence with the physical properties of the scattering medium (Shepard and Helfenstein, 2007). Therefore, the traditional value of the surface roughness parameter was allowed to vary in the modeling. The surface roughness varied from 121 to 191, with errors of 721. These values were compared against the disk-resolved photometric observations from the first Mercury flyby and found to be consistent with these measurements (Domingue et al., this issue). From the resulting model solutions for each filter, photometric correction factors to incidence,

emission, and phase angle values of 301, 01, and 301, respectively, were re-derived and applied to the global color mosaic images. The resulting monochrome mosaics for each filter are shown in Fig. 12. These mosaics display an improved correlation between the albedo in regions imaged at high phase angle (the M1 and M2 approach regions) and those imaged at lower phase angle (the M1 and M2 departure regions and the M3 approach region). This correlation holds especially for those mosaics at wavelengths less than 828 nm. At 828 nm and above, the correlation, though improved, still displays differences in albedo between regions imaged at phase angles above 1101 and those imaged at lower phase angles.

4. Global color mosaic Comparisons of the monochrome mosaics in Figs. 9 and 12 show that the revised method for measuring both the scattered light and residual background offers a more robust description of the surface

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

1885

Fig. 12. Global monochrome mosaics acquired in each of the 11 MDIS color filters. These mosaics have been photometrically corrected to 301 phase angle with the Hapke modeling results shown in the revised phase curves (Fig. 11). The ranges of brightness applied to the red, green, and blue channels were the same as those used for Fig. 9.

photometric behavior, leading to photometric corrections that provide a better match between the M2 and M3 approach regions. However, for filters with wavelengths greater than 828 nm, the revised method, although still an improvement, does not yet provide a satisfactory match. The scattered light patterns shown in Fig. 9 demonstrate above 828 nm wavelength the patterns are more complicated and of greater magnitude than those at lower wavelengths and thus are a contributing factor to the continued mismatch between the overlapping regions imaged on approach during M2 and M3. Another observation is that the match between the M2 departure region and the M3 approach region is very good in the revised monochrome images shown in Fig. 12. 4.1. Color comparisons The color mosaic obtained with the revised photometric modeling results, shown in Fig. 8b, may be compared with that in Fig. 8a. In both of these mosaics the 996.8-, 749-, and 430-nm filter images are presented in the red, blue, and green channels, respectively. In the initial mosaic (Fig. 8a), the regions imaged on approach during M1 and M2 appear darker and perhaps bluer than the adjacent or overlapping regions imaged during either the departure phase or during the M3 approach. An item to note is that M1 and M2 approach images were obtained at 1191 and 1301 phase angles, respectively. In comparison, the revised mosaic (Fig. 8b) shows the regions imaged on approach during the first two flybys to be darker and greener than adjacent or overlapping regions. Both mosaics are constructed with the 996.8 nm filter in the red channel; that filter has one of the more complex scattered light patterns. Fig. 14 compares two additional color mosaics that do not incorporate images with the more complex scattering properties. The top mosaic in Fig. 13 was derived with the initial photometric analysis. The bottom mosaic was obtained with the revised

photometric analysis and the updated scattered-light and residual background models. These mosaics were constructed using the 749-, 559.2-, and 480.4-nm filter images in the red, green, and blue channels, respectively. The contrast between the region imaged during the M2 approach and the overlapping region imaged during M3 is greatly diminished in the revised (bottom) mosaic. As noted above, the M2 approach images were obtained at 1301 phase angle whereas the M3 approach images were acquired at 1061 phase angle. The contrast between these overlapping regions in the initial image still shows the M2 region as much darker than the overlapping area. The agreement between the overlapping regions imaged during the M2 departure and M3 (taken at 351 and 1061 phase angle, respectively) imply that for observations made below 1101 phase angle, the revised photometric models adequately describe Mercury’s surface and provide photometric corrections sufficient for quantitative color analyses. A re-projection of the mosaics in Fig. 13 with the region imaged during M3 placed on top of the regions imaged during the M1 and M2 is shown in Fig. 14. The bottom mosaic, determined with photometric corrections derived from the phase curves generated from the updated scattered-light and residual background measurements, show some artifacts at the polar regions. These are regions of high incidence and emission angles (4701), where the photometric model is not providing accurate corrections due to the remaining scattered-light contribution. Fig. 14 also shows that the reddening at the terminators, seen in the top mosaic, is no longer present in the bottom mosaic, where the scattered light has been better measured. 4.2. MESSENGER in orbit The current observing plan for MESSENGER’s orbital mission phase provides for a global color mosaic (97% of the surface

1886

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

Fig. 13. Mosaics radiometrically calibrated and photometrically corrected to 301 phase angle. The top mosaic was constructed with photometric corrections from the initial phase curve derivations and analyses (shown in Fig. 7), whereas the bottom mosaic was constructed with photometric corrections from the revised phase curves and modeling results (shown in Fig. 11). The red, green, and blue channels are represented by the 749-, 559.2-, and 480.4-nm filter images, respectively. These filters were selected for the construction of these mosaics because they represent the spectral range from filters with the least complex scattered-light patterns (see Fig. 9). In the top mosaic, photometrically normalized reflectance values of regions imaged at high phase angle ( 41101) display lower reflectance values than overlapping regions imaged at lower phase angle. These reflectance contrasts are not seen in the bottom mosaic, which incorporates more robust measures of the scattered-light effects. Common ranges of brightness were applied to the three channels for the two mosaics.

Fig. 14. Mosaics constructed with the revised photometric corrections from the phase curve analysis derived with the updated scattered-light and residual background corrections (the phase curve models shown in Fig. 11). The regions imaged at high phase angle (4 1101) are overlaid on top of those regions imaged at lower phase (in contrast to the previous mosaics where the regions imaged at lower phase angle are overlaid on those imaged at higher phase). In the top mosaic the red, green, and blue channels are represented by the 996.8-, 749-, and 430-nm filter images, respectively. In the bottom mosaic these channels include the 749-, 559.2-, and 480.4-nm filter images, respectively. For the top mosaic the ranges in brightness levels were the same as those applied to the mosaics in Fig. 8, and for the bottom mosaic the ranges in brightness levels were the same as those applied to the mosaics in Fig. 13.

D.L. Domingue et al. / Planetary and Space Science 59 (2011) 1873–1887

imaged in eight colors) at a spatial resolution of 1 km/pixel. The median emission angle for this set of images, calculated from the mission planning software, is 8.71, with 80% of the emission angle values ranging between 2.11 and 16.51. In all cases the incidence angle has been minimized. The observation plan currently has 80% of the images with phase angle values ranging between 26.11 and 69.31. These photometric angles are well within the range for which the photometric corrections derived from the flyby images are applicable.

5. Conclusions Disk-integrated phase curve measurements were acquired during MESSENGER’s flybys of Mercury to provide a description of the planet’s global photometric properties. These measurements are dominated by images where Mercury occupies a small fraction (6–10 pixels in diameter) of the image frame, and thus extracting disk-integrated values is highly affected by scattered light and residual background (from radiometric calibration errors). The scattered-light properties become more complex with increasing wavelength. Whereas Hapke’s equations well describe the observations, the photometric corrections derived from these models break down at higher phase angles ( 41101) and extreme values ( 4701) of incidence and emission angles. Images acquired at lower ( o1101) phase angles are photometrically corrected to within  5% variability. During MESSENGER’s orbital phase, the color images that will be acquired to construct the higher-spatialresolution global color mosaic will be acquired well within the lower phase angle region ( o1101) and at lower emission angle ( o201) and minimum incidence angle. Additional photometric observation sequences are planned for orbit, to help provide more robust photometric corrections, but these photometric corrections derived from the flyby observations will enable construction of the higher-spatial-resolution global color map. Nonetheless, the remaining albedo variations currently displayed in the photometrically corrected global mosaic show that a robust, detailed determination of the scattered light properties, and a corresponding scattered light correction, are essential for spectral analysis of the image data set.

1887

References Blewett, D.T., Robinson, M.S., Denevi, B.W., Gillis-Davis, J.J., Head, J.W., Solomon, S.C., Holsclaw, G.M., McClintock, W.E., 2009. Multispectral images of Mercury from the first MESSENGER flyby: analysis of global and regional color trends. Earth Planet. Sci. Lett. 285, 272–282. Cheng, A.F., Domingue, D.L., 2000. Radiative transfer models for light scattering from planetary surfaces. J. Geophys. Res. 105, 9477–9482. Domingue, D.L., Vilas, F., Holsclaw, G.M., Warell, J., Izenberg, N.R., Murchie, S.L., Denevi, B.W., Blewett, D.T., McClintock, W.E., Anderson, B.J., Sarantos, M., 2010. Whole-disk spectrophotometric properties of Mercury: synthesis of MESSENGER and ground-based observations. Icarus 209, 101–124. Domingue, D.L., Murchie, S.L., Chabot, N.L., Denevi, B.W., Vilas, F., Mercury’s spectrophotometric properties: update from Mercury Dual Imaging System observations during the third MESSENGER flyby. Planet. Space Sci., this issue. doi:10.1016/j.pss.2011.04.012. Hapke, B., 1981. Bidirectional reflectance spectroscopy. 1. Theory. J. Geophys. Res. 68, 4571–4586. Hapke, B., 1984. Bidirectional reflectance spectroscopy. 3. Correction for macroscopic roughness. Icarus 59, 41–59. Hapke, B., 1986. Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect. Icarus 67, 264–280. Hapke, B., 2002. Bidirectional reflectance spectroscopy. 5. The coherent backscatter opposition effect and anisotropic scattering. Icarus 157, 523–534. Hawkins III, S.E., Boldt, J.D., Darlington, E.H., Espiritu, R., Gold, R.E., Gotwols, B., Grey, M.P., Hash, C.D., Hayes, J.R., Jaskulek, S.E., Kardian, C.J., Keller, M.R., Malaret, E.R., Murchie, S.L., Murphy, P.K., Peacock, K., Prockter, L.M., Watters, T.R., Williams, B.D., 2007. The Mercury Dual Imaging System on the MESSENGER spacecraft. Space Sci. Rev. 131, 247–338. Hawkins III, S.E., Murchie, S.L., Becker, K.J., Selby, C.M., Turner, F.S., Nobel, M.W., Chabot, N.L., Choo, T.H., Darlington, E.H., Denevi, B.W., Domingue, D.L., Ernst, C.M., Holsclaw, G.M., Laslo, N.R., McClintock, W.E., Prockter, L.M., Robinson, M.S., Solomon, S.C., Sterner II, R.E., 2009. In-flight performance of MESSENGER’s Mercury Dual Imaging System. In: Hoover, B., Levin, G.V., Rozanov, A.Y., Retherford, K.D. (Eds.), Instruments and Methods for Astrobiology and Planetary Missions XII, SPIE Proceedings 7441, Paper 74410Z. SPIE, Bellingham, Washington, 12 pp. Lucey, P.G., Taylor, G.J., Malaret, E., 1995. Abundance and distribution of iron on the Moon. Science 268, 1150–1153. Lucey, P.G., Blewett, D.T., Hawke, B.R., 1998. Mapping the FeO and TiO2 content of the lunar surface with multispectral imaging. J. Geophys. Res. 103, 3679–3699. Lucey, P.G., Blewett, D.T., Jolliff, B.L., 2000. Lunar iron and titanium abundance algorithms based on final processing of Clementine UVVIS data. J. Geophys. Res. 105, 20297–20306. Mallama, A., Wang, D., Howard, R.A., 2002. Photometry of Mercury from SOHO/LASCO and Earth, The phase function from 21 to 1701. Icarus 155, 253–264. Shepard, M.K., Helfenstein, P., 2007. A test of the Hapke photometric model. J. Geophys. Res. 112, 1–17. Staid, M.I., Pieters, C.M., 2000. Integrated spectral analysis of mare soils and craters: applications to eastern nearside basalts. Icarus 45, 122–139.