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Icarus
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Mercury's global color mosaic: An update from MESSENGER'S orbital observations
Deborah L. Domingue^*, Scott L. Murchieb, Brett W. Denevib, Carolyn M. Ernstb, Nancy L. Chabotb
aPlanetary Science Institute, 1700 E. Fort Lowell, Suite 106, Tucson, AZ 85719-2395, USA b The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
ARTICLE INFO ABSTRACT
We report an update to the photometric correction used to produce global color mosaics of Mercury, derived from an analysis of photometric observations acquired during the orbital phase of MESSENGER's primary mission. Comparisons between versions of the color mosaic produced with photometric corrections derived from flyby and orbital data indicate that areas imaged at high incidence and emission angles (>50°) are better standardized to a common illumination and viewing geometry with the orbit-derived corrections. Seams between images taken at very different illumination geometries, however, are still present at visually detectable levels. Further improvements to the photometric correction await updates to the radiometric calibration that will enable data retrieval over a larger range of photometric angles.
© 2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/3XI/).
CrossMark
Article history: Received 26 June 2014 Revised 4 November 2014 Accepted 25 November 2014 Available online 6 December 2014
Keywords: Photometry Spectrophotometry Mercury Mercury, surface
1. Introduction
The trajectory of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft en route to Mercury included three flybys of the innermost planet prior to orbit insertion on 18 March 2011. Observations acquired during these flybys provided an opportunity to test the performance of the instrument suite, to practice data acquisition strategies designed for orbital operations, and to obtain early scientific measurements as a step toward achieving the mission's scientific goals. One of the first data products generated from the one-year orbital phase of MESSENGER's primary mission was a global color mosaic (97% of the surface imaged in eight colors) at a spatial sampling of 1 km/pixel (Hawkins et al., 2009). This color mosaic is one of several data products that are being used to address Mercury's surface composition and geological evolution, two of MESSENGER's primary scientific objectives (Solomon et al., 2007).
Prior to MESSENGER's orbital mission phase, a preliminary global color map was constructed from the flyby observations. Multispectral image sequences acquired during the flybys were combined to construct an initial global color mosaic, albeit a data set less complete and of lower spatial resolution (~5 km/pixel) than achievable from orbit (Domingue et al., 2011a). The flyby image acquisition plan included a series of both disk-integrated and disk-resolved color photometric observations for deriving the pho-
* Corresponding author at: 400 Teresa Marie Ct., Bel Air, MD 21015, USA. E-mail address: domingue@psi.edu (D.L. Domingue).
tometric correction necessary to construct this initial global color mosaic from the flyby observations (Domingue et al., 2011a,b).
Radiometric calibration and photometric correction of the flyby global color mosaic were described by Domingue et al. (2011a,b). Radiometric calibration transforms camera response to radiance or reflectance values, which can be compared with laboratory measurements of the spectral reflectance of minerals and mineral mixtures. However, most laboratory mineral spectra, with which the color information is compared for compositional analyses, are acquired at a standard photometric geometry specified by angles of incidence, emission, and phase values (i, e, a) of 30°, 0°, and 30°, respectively. In order to compare images acquired under different observing geometries with each other and with laboratory spectra for inferences regarding compositional information, a photometric correction must be applied to the spacecraft data. The photometric correction most often transforms the spacecraft observations to the standard laboratory geometry. Domingue et al. (2011a,b) showed, however, that photometric corrections of the MESSENGER flyby images to 30°, 0°, 30° are not sufficiently accurate for images acquired at high phase angles (>110°) and extreme values (>70°) of incidence and emission angles. Images acquired at lower (<110°) phase angles, in contrast, can be photometrically corrected to within ~5% image-to-image variability (Domingue et al., 2011a,b), and such corrected images provided a useful first-generation product for initial color analyses (Blewett et al., 2009, 2013; Kerber et al., 2011; Denevi et al., 2013).
The MESSENGER images acquired from orbit for the construction of a global color mosaic were at higher spatial resolution (1 km/
http://dx.doi.org/10.1016/j.icarus.2014.11.027 0019-1035/© 2014 The Authors. Published by Elsevier Inc.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
pixel compared with the km/pixel resolution from the flyby imagery), at lower phase angles (<110°), and with generally lower (<20°) emission and incidence angles than the images acquired during the Mercury flybys. However, application of the photometric correction derived from the flyby data resulted in obvious seams between image boundaries and variations within images as incidence angles approached values greater than 70°. The reflectance mismatches along image seams motivated a re-examination of the photometric correction, the assumptions inherent in its derivation, and possible issues with the radiometric calibration.
As with the flyby data acquisition plan, the orbital image acquisition plan included dedicated photometric observations to provide the input for an update and refinement to a global photometric correction. This paper provides an overview of the global color mosaic and photometric imaging campaigns during MESSENGER's first year in orbit, describes the derivation of an updated photometric correction based on current radiometric calibration algorithms, and presents an overview of the photometrically corrected global color mosaic of Mercury's surface delivered to NASA's Planetary Data System (PDS) in March 2013.
2. Orbital image data
messenger's Mercury Dual Imaging System (MDIS) includes both a wide-angle camera (WAC) and a narrow-angle camera (NAC) (Hawkins et al., 2009). The WAC includes a 12-position filter wheel with one broadband filter and eleven narrow spectral filters, eight of which were used during the first year in orbit to image nearly the entire surface in color. Hawkins et al. (2009) provided a preliminary description of MDIS calibration accuracy and inflight performance. This section summarizes further issues with the radiometric calibration, the need for an updated photometric correction, and the data sets used to derive an updated photometric correction and to construct the global color mosaic.
2.1. Radiometric calibration
Hawkins et al. (2009) described the conversion of each pixel within an image frame from raw digital number (DN) to radiance values (Wm~2sr_1 im-1). This conversion was reviewed by Domingue et al. (2011b) as it pertains to photometric analyses with the image data, and it incorporated all instrument performance updates as of May 2011. Analysis of the WAC responsivity during orbit demonstrated a change associated with an event on or about 24 May 2011 when MESSENGER first approached one of the planet's ''hot poles'' near spacecraft periapsis (Keller et al., 2013). That event has been interpreted as the result of deposition and subsequent loss of a contaminant on the WAC optical surfaces. An updated radio-metric calibration applied to MDIS data, including those used to construct the global color map, models and largely corrects for the effect of this contaminant by treating responsivity as a function of time. Details of the correction have been described by Keller et al. (2013). However to avoid any residual effects of that event in the photometric correction, the updated photometric parameters are derived only from images acquired prior to 24 May 2011.
2.2. Photometric imaging data sequences
MESSENGER acquired several dozen targeted series of eight-filter images to sample a range of photometric angles during its first year in orbit (18 March 2011 to 17 March 2012). Each series met the following criteria within spacecraft pointing constraints: the same region of the surface was imaged repeatedly, photometric (incidence, emission, phase) angle coverage was maximized, and photometric angles were sampled with a resolution of 5°. Two regions on Mercury's surface were targeted, near the Beethoven
and Rachmaninoff basins; however, only the Beethoven region, located between 8°S and 50°S and between 200°E and 270°E, was imaged prior to 24 May 2011. Twenty areas were selected within the Beethoven photometric region (Fig. 1a) for photometric analysis on the basis of their lack of topographic relief on the scale of the image resolution, lack of bright rays, and moderate reflectance.
Fig. 1. (a) The locations of the 20 areas selected for photometric analysis in the Beethoven photometric target region. This region, extracted from the global mosaic at 898.8 nm using the combined model (Table 1) solution for the photometric correction, is centered on 30.4°S, 247.3°E. A portion of the Beethoven basin (643 km in diameter) can be seen in the upper left corner. (b) The locations of the 10 areas selected for photometric analysis in the Matabei photometric region. This region, extracted from the global mosaic at 898.8 nm using the combined model solution for the photometric correction, includes the dark-rayed crater Matabei (23.52 km in diameter, centered at 39.84°S, 346.06°E), seen near the right center. Both images are simple-cylindrical projections, and north is up.
Unfortunately, many of the geometries under which the images for the global color mosaic were acquired were not well sampled within the photometric sequences of the Beethoven region during the limited time range of the first two months of orbital operations. Thus, in order to include more of the geometries from the global color mosaic (low incidence and emission angles), a subset of the global color image sequences was examined as a separate image set in the photometric analysis. To derive a photometric function from measurements that span the viewing geometries used to acquire the images from which the 8-color map was constructed,
a location was identified within the map region that was repeatedly imaged and maximized the photometric angle coverage prior to 24 May 2011 (Fig. 1b). That location, hereafter termed the Mata-bei photometric region, is located near the dark-rayed Matabei crater (Fig. 1b). Ten areas were selected and sampled in the region. These areas were intermediate-reflectance terrains, predominantly intercrater plains, without major shadows or bright crater rays. The selection criteria for the areas were similar to those used to select sites in the Beethoven photometric region.
The photometric angle coverage from the 20 regions in the Beethoven photometric region is shown in Fig. 2. For comparison, Fig. 2 also shows photometric angle coverage from the 10 regions in the Matabei photometric region.
2.3. Global color imaging sequences
More than 41,000 images were acquired during MESSENGER's first year in orbit as part of the 8-color global mosaic imaging campaign. The goal was to obtain global coverage of the surface at 1 km/pixel average resolution, using images acquired at a near-nadir geometry at the lowest solar incidence angle values available for the latitudes of each image. The result was >99% coverage of the surface with average values of incidence, emission, and phase angles of 45.7°, 7.8°, and 45.8° and standard deviations of ±18.5°, ±6.9°, and ±16.0°, respectively.
This image acquisition strategy contrasted with that needed to acquire the photometric image sequences; covering the greatest range of photometric angles from MESSENGER's orbit required that the highest and lowest solar incidence angle values be observed off-nadir. Thus, the photometric sequences are dominated by images with photometric angle coverage different from that for the global 8-color map (Fig. 2). With laboratory measurements, Domingue et al. (2011a,b) demonstrated that accurate photometric functions should be derived from measurements that include both the range of photometric angles observed and the angles to which the observations are to be corrected. Although the photometric angle coverage for the Matabei photometric region is less than for the Beethoven photometric region (Fig. 2), the former region includes images with geometries more representative of those in the global color mosaic sequence, as well as of the geometry to which the global color mosaic is corrected.
3. Photometric analysis methodology
3.1. Photometric model
The form of the Hapke (1981, 1984, 1986) photometric model and the application method used in this study follow those described by Domingue et al. (2011a,b). The Hapke model, derived from a radiative-transfer treatment, describes and predicts photometric behavior well (Cheng and Domingue, 2000; Shepard and Helfenstein, 2007; Bhattacharjee et al., 2011; Helfenstein and Shepard, 2011) and has thus been commonly used for establishing
Photometric Angle Coverage - E Filter (628.8 nm)
0 20 40 60 80 100 120
Incidence angle (°)
Photometric Angle Coverage - E Filter (628.8 nm)
0 Beethoven Photometric Region
0 -1-1-1-1-1-1
0 20 40 60 80 100 120
Incidence angle (°)
Fig. 2. Photometric angle coverage with the MDIS WAC 628.8-nm filter from the 20 areas in the Beethoven photometric target region (black circles) and the 10 areas in the Matabei photometric region (red diamonds). (Top) Phase angle versus incidence angle. (Bottom) Emission angle versus incidence angle. The photometric angles of diagnostic regions within the global color mosaic (locations identified in Figs. 8-13 and described in Table 5) are displayed by blue diamonds. The geometry to which the global color mosaic is corrected (30° incidence, 0° emission, 30° phase), consistent with the geometry at which most laboratory spectra are acquired, is shown by a green X.
Table 1
Data set summary.
Data set name Description
Matabei Combination of the radiance factor (i/F) values from all 10 areas sampled in the Matabei photometric region
These data are derived from images acquired during MESSENGER's orbital operations prior to 24 May 2011
Beethoven Combination of the i/F values from all 20 areas sampled in the Beethoven photometric target region
These data are derived from images acquired during MESSENGER's orbital operations prior to 24 May 2011
Combined Amalgamation of the Matabei and Beethoven data sets
Disk-integrated Disk-integrated observations of Mercury's full disk acquired during MESSENGER's flybys (Domingue et al., 2010)
Integral-combined Amalgamation of the combined and disk-integrated data sets
photometric corrections for both image and spectral data. Questions have been raised on the basis of laboratory measurements as to whether Hapke model parameters actually correspond to physical properties (Gunderson et al., 2006; Shkuratov et al., 2007; Shepard and Helfenstein, 2007; Helfenstein and Shepard, 2011). For the derivation and construction of a photometrically corrected image mosaic, however, the basic Hapke model predicts photometric behavior sufficiently accurately (<2% root mean squared residual) to support the needed photometric correction (Cheng and Domingue, 2000), regardless of any physical interpretation of the model parameters. The parameters in this model (Eq. (1)) include the single scattering albedo (w); the opposition surge function (Eq. (2)), B(a), with opposition amplitude (b0) and width (h) parameters; the single-particle scattering function, P(a), with parameters b and c; and the surface roughness function, S(i,e, 0), with roughness parameter (0):
F = (W) (lTl) [((1 + B(a))P(a)_ 1 + H(l0)H(l'))]S(i, e, a) (1)
B(a) = ^---r (2)
W A + tan(a/2)\ v '
P(a) - " - c)(1 - 3,., + c(1 - b2) ,3,, (3)
(1 - 2bcos(a) + b2) = (1 + 2bcos(a) + b2) =
where I/F is the radiance factor (Hapke, 1981). The single-particle scattering function (Eq. (3)) used is a double Henyey-Greenstein function of the same form as that used by Domingue et al. (2010, 2011a,b).
3.2. Modeling approach
A summary of the various data sets examined in this paper is given in Table 1. The data analysis was divided into three stages, each of which treated a different combination of the data sets listed in Table 1. The first stage in the analysis was modeling of the Matabei data set. Parameters in the photometric model were obtained by conducting a grid search and minimizing the root mean squared (RMS) misfit with observations, following the method described by Domingue et al. (2010, 2011a,b). The opposition parameters were set to the values (b0 = 2.3, h = 0.075) obtained by Domingue et al. (2010) from an analysis of disk-integrated measurements of the opposition surge at 560 nm (there are no opposition-regime observations in the disk-resolved data sets). A set of Hapke-equation parameters was derived independently for each MDIS WAC filter data set. The resulting parameter solutions were fit as a function of wavelength (k) by third-order polynomial functions, so as not to introduce spectral artifacts because of differences in measurements between filters and round-off errors. The final set of parameters derived from modeling the Matabei data set is provided in Table 2. Errors arising from rounding off below the fifth significant digit have been known to introduce false color variations, so parameter values are provided to eight figures to minimize correction errors.
The second stage in the analysis focused on modeling the combined data set (see Table 1). The combined data set was modeled with the same methodology as that for the Matabei data set, and the resulting parameter values are as shown in Table 3. The larger variability in the surface roughness values (0) in the combined data set analysis compared with the Matabei data set reflects the larger variability in the I/F values in the combined data set as a result of the greater photometric angle coverage. The factor of ~3-5 difference between the combined and Matabei 0 values is a reflection of the difference in angle coverage between the two data sets (Fig. 2). The broader photometric angle coverage in the combined data set, especially at larger phase angles where topography is
Table 2
Hapke model parameters for the Matabei data set.
Filter k (nm) w b c 0
F 433.2 0.21112805 0.33408532 0.62483203 26.4272511
C 479.9 0.23081363 0.32475832 0.61347319 26.0305832
D 558.9 0.25886800 0.31467599 0.60249436 25.7299549
E 628.8 0.28085382 0.30943110 0.59828747 25.7042660
G 748.7 0.31280100 0.30571239 0.59897988 25.9385751
L 828.4 0.32968258 0.30508542 0.60208940 26.1119564
J 898.8 0.34164972 0.30449374 0.60463868 26.1607118
I 996.2 0.35420316 0.30175767 0.60520495 25.8967012
Table 3
Hapke model parameters for the combined data set.
Filter k (nm) w b c 0
F 433.2 0.18085048 0.26920220 0.44368026 8.3253332
C 479.9 0.20000093 0.26089677 0.43191468 8.6543198
D 558.9 0.22769017 0.25190351 0.42347518 8.4312644
E 628.8 0.24983131 0.24754230 0.42457314 7.7171738
G 748.7 0.28310482 0.24649328 0.44079105 6.0213270
L 828.4 0.30160096 0.24934324 0.45828137 5.0584994
J 898.8 0.31545772 0.25349770 0.47585838 4.6339707
I 996.2 0.33146358 0.26112095 0.50142592 5.1581114
accented by shadows, provides a better mathematical constraint on both w and 0 values.
The final stage in the analysis involved iterative modeling between the combined data set (with its large photometric angle coverage) and the disk-integrated measurements from Domingue et al. (2010). This analysis involved what is termed the integral-combined data set in Table 1. The first step in this analysis stage began with setting the surface roughness parameter (0) value at each wavelength to the values derived from the analysis of the combined data set (Table 3). The larger photometric angle coverage provided by the combined data set allows for a solution for which the mathematical affects of w versus 0 in the model can be better separated than with either the Matabei or Beethoven data sets alone. With the 0 value fixed, the disk-integrated data at 560 nm were then modeled with the technique of Domingue et al. (2010) to derive the remaining photometric model parameter values. This modeling included solving for the opposition parameters, as the disk-integrated data set at 560 nm includes both MESSENGER measurements and Earth-based observations (Mallama et al., 2002) that sampled the opposition region. With these newly derived opposition parameter values, the remaining MDIS disk-integrated photometric data sets for the other filters were modeled. For those models, the surface roughness parameter was set to the value derived from the combined model solutions, and the opposition parameter values were set to those derived from modeling the 560-nm measurements. The resulting photometric model parameters were fit to a polynomial function (degree 6 6) of wavelength. The second step was to re-model the combined data set, by setting the opposition values to those obtained in the first step along with setting the single-scattering albedo (w) values to those derived from the disk-integrated modeling analysis completed in the first step. Thus the only model parameters allowed to vary in this second step were the single-particle scattering function parameters (b and c) and 0. The remaining model parameter values obtained in this second step were fit with a low-order polynomial function of wavelength to provide the next iteration of values.
The final step was to re-model the disk-integrated data sets, beginning with the 560 nm data set. Single-scattering albedo and surface roughness parameters were constrained to the values from the second step and not allowed to vary. This procedure allowed re-examination of the opposition surge parameters, in addition to
the single-particle scattering function parameters. The opposition parameter values were then fixed and used to model the remaining wavelengths in the disk-integrated data set. The final values for the opposition parameters are 3.086 and 0.090 for the opposition amplitude (b0) and opposition width (h), respectively. The model solutions for the single-particle scattering function parameters were fit with a low-order polynomial function of wavelength. The final results are shown in Table 4. Note that the integral-combined solutions include parameter sets for all 11 filters (compared with the 8 filters included for the Matabei and combined solution sets) given that the disk-integrated data were acquired with all 11 MDIS filters.
Comparisons of the Hapke model parameters from each solution are displayed in Fig. 3, and the characteristics of the single-particle scattering function are shown in Fig. 4 for those wavelengths used to create the color mosaics presented in the next section. It is interesting to note that at the two longer wavelengths (748.7 and 996.2 nm) the single-particle scattering functions for the flyby, Matabei, and combined solutions have both
Table 4
Hapke model parameters from the integral-combined data analysis.
Filter k (nm) w b c e
F 430 0.13472888 0.19192497 0.07364995 8.0168815
C 480.4 0.16054888 0.17889916 0.09040433 9.0361850
D 559.2 0.18509333 0.16461793 0.07097318 8.6778805
E 628.7 0.19874286 0.15908048 0.03902138 7.4793528
A 698.8 0.21091492 0.16026608 0.01602333 6.2476317
G 749 0.22059260 0.16486528 0.01267853 5.6137731
L 828.6 0.23878951 0.17696133 0.03406310 5.1900252
J 898.1 0.25644630 0.18988636 0.07458267 5.2438422
H 948 0.26829380 0.19867014 0.10855348 5.2669540
I 996.8 0.27711813 0.20528799 0.13716673 4.9859014
K 1010 0.27873073 0.20654023 0.14288327 4.8159446
forward- and backward-scattering components, whereas the integral-combined solution is predominantly a backward-scattering single-particle scattering function. The scattered-light contribution increases with wavelength and may be compensated by the model with a forward-scattering component in the data set that includes the disk-integrated data (which will be highly affected by scattered light). At 433.2 nm the flyby solution is predominantly backward scattering whereas the scattering functions for the other solutions remain consistent with the longer-wavelength properties. The Matabei solution displays a dominant forward-scattering component at three wavelengths, whereas the combined solution displays scattering functions with comparable backward and forward scattering directions, though at the two shorter wavelengths the scattering function for this solution is slightly more backward scattering.
4. Global color mosaic
Four versions of the global color mosaic, each derived with one of the photometric corrections discussed above (flyby, Matabei, combined, and integral-combined), are compared in Fig. 5. Each mosaic is stretched to the same dynamic range to accentuate seams and color variations along image boundaries, so as to enable an examination of the quality of the photometric correction. The incidence, emission, and phase angles of the images used to construct these mosaics are displayed in Fig. 6, and, as discussed further below, the quality of the mosaics varies. Three sub-areas in the mosaics (Fig. 7) were selected (Caloris area A, northern area B, and southern area C) to show examples of the quality of the various photometric corrections under different illumination and viewing conditions. These examples qualitatively distinguish those photometric corrections that provide the fewest or most subtle seams between images comprising the mosaic. A more quantitative examination is provided in Section 5.
Single-scattering albedo (w)
0.350.3 5 0.25 0.2
v" ..'*> .JSr''
y •«• Flyby •*>'Matabei
/ ^-Lomoinea ^^Integral-Combined
600 700 800 Wavelength (nm)
30 25 ■ 2015 -
Surface roughness (6)
».......e-"®-
......s--••«—
•<»• Flyby "O'Matabei
—^^Combined-
-°-lntegral-Combined
600 700 800 Wavelength (nm)
Single-particle scattering function parameter b
Single-particle scattering function parameter c
a.. •••o ......O /\
••a....
•^•MataDei
^^Combined
"^Integral-Combined
600 700 800 Wavelength (nm)
0.6 0.5 0.4 0.3 0.2 0.1
...•©•••o-Flyby
•<>• Matabei
^"Integral-Combined
600 700 800 Wavelength (nm)
Fig. 3. Comparisons of Hapke parameter values as a function of wavelength for the flyby (open circles, dotted line), Matabei (open diamonds, dotted line), combined (filled diamonds, solid line), and integral-combined (filled circles, solid line) solutions. Like symbols are connected by straight lines.
Fig. 4. Comparisons of the single-particle scattering functions from the flyby (solid black line), Matabei (solid gray line), combined (dotted gray line), and integral-combined (dotted black line) solutions for the wavelengths corresponding to the red (996.2 nm), green (748.7 nm), and blue (433.2) channels in the mosaics presented in the next section.
4.1. Caloris area A
The first sub-area, labeled "A" and outlined in red in Fig. 7, is centered on the Caloris basin. This sub-region from all four versions of
the mosaic is displayed in Fig. 8 with corresponding photometric angles displayed in Fig. 9. Several points are identified on the "combined" mosaic panel (Fig. 8), and their corresponding locations are shown on the emission angle map (Fig. 9, center). These points
Fig. 6. Mosaics of the photometric angles that correspond to the images in the color mosaics shown in Fig. 5. These simple cylindrical projections are centered on 0°N, 180°E. The top, center, and bottom panels display variations in incidence, emission, and phase angle, respectively; light shades of gray represent high angles and dark shades represent low angles. Linear gray scales correspond to incidence, emission, and phase angle value ranges of 5.83-87.82°, 0.85-66.41°, and 23.42-86.66°, respectively. Regions where there is no image coverage are shown in black.
are labeled for illustrative comparisons and discussed below. The photometric angles for these points are provided in Table 5.
There are several image seams visible within the Caloris basin in all four area A mosaic panels (Fig. 8), though these seams are least apparent in the mosaic constructed with the Matabei photometric correction. In the lower left corner of each mosaic panel there are additional visible seams, along which one of the images appears "greener" than the adjacent images. Points 1 through 6 are within the Caloris basin, and points 7 and 8 are examples from contrasting images in the lower left corner of area A (see Table 5). Note that the contrasting images (points 1 and 4) within the Caloris basin were acquired at high (>50°) emission angles whereas the adjacent images (points 2, 3, 5, and 6) were acquired at low (<30°) emission angles. The contrasting images in the lower left were acquired at comparable incidence angles (~7° difference), but contrasting emission and phase angles. The acquisition geometries are such that the image represented by point 7 was acquired in the forward-scattering direction and the image represented by point 8 was acquired in the backward-scattering direction. The photometric angles of the portions of the mosaic at these points
Fig. 7. (Top) Areas chosen for closer examination (red outline, area A; blue outline, area B; yellow outline, area C) superposed on the global color mosaic from Fig. 5 obtained with the photometric correction derived from the Matabei solution. (Bottom) Corresponding mosaic of emission angle from Fig. 6.
may be compared with the photometric angles of the data from which the photometric corrections were derived; such a comparison is displayed in Fig. 2 (blue diamond symbols). Points 1 through 4 and point 6 are at geometries not present in any of the photometric data sets. In addition, points 1, 4, 5, 6, and 7 represent photometric geometries outside the dominant illumination and viewing conditions (30° < i < 60°, 0° < e < 60°) within the photometry data set, where the model is least constrained.
4.2. Northern area B
Mosaics of the second sub-area, labeled "B" and outlined in blue in Fig. 7, are displayed in Fig. 10 for all four photometric corrections. This area was imaged predominantly under uniformly varying illumination and viewing conditions (Fig. 11). Several points are identified on the "combined" mosaic panel (Fig. 10), and their corresponding locations are shown on the emission angle map (Fig. 11, center). These points are labeled for illustrative comparisons and discussion. The photometric angles for these diagnostic points are listed in Table 5. Point 10 denotes a string of images taken at higher emission angle than background images, represented by point 9. It is difficult to discern any seams between this string of images and the surrounding images in any of the four versions of the mosaic. Points 11 and 12 were acquired under high (>50°) incidence angle but comparable (~7° difference) emission angles. Though the images acquired at these points differ in photometric angles (Fig. 11), the color mosaics do not display obvious reflectance contrasts. The image at point 11 was acquired in a backward-scattering orientation, whereas the image at point 12 was acquired in a forward-scattering orientation. Of the four points, only point 10 was imaged at a photometric geometry outside the dominant illumination and viewing conditions (30° < i < 60°, 0° < e < 60°) for the photometry data set.
Fig. 8. Mosaics of area A (Fig. 7), centered on Caloris basin, in a simple cylindrical projection. Each version of the mosaic was built with a photometric correction derived from a different modeling solution, as labeled. The red, green, and blue channels are the 1000-nm, 750-nm, and 430-nm filter map planes, respectively. Images were stretched to enhance contrasts and seams resulting from photometric variations (red range: 0.07-0.14, green range: 0.06-0.12, blue range: 0.03-0.08). Seams are clearly seen within the Caloris basin and in the lower left of these mosaics. These seams correspond to abrupt boundaries in the photometric geometries (Fig. 9) by which the images were acquired. The numbered locations in the "combined" mosaic panel correspond to the numbered locations in Fig. 9 and Table 5.
Table 5
Photometric angles used to acquire the images at numbered locations on the global color mosaic.
Fig. 9. Mosaics of the photometric angles for the images in the color mosaics of area A shown in Fig. 8, displayed with the same gray scale as in Fig. 6. Variations in incidence, emission, and phase angle are shown in the top, center, and bottom images, respectively. Locations are marked and numbered in the emission angle mosaic. The photometric angles of the images acquired at these locations are given in Table 5.
Pointa i e a
1 40.18 70.57 31.00
2 33.47 2.98 33.92
3 33.95 2.59 34.18
4 25.14 55.47 32.25
5 25.96 21.93 29.10
6 16.94 9.02 26.30
7 26.25 24.39 50.67
8 33.28 8.15 27.40
9 56.91 8.88 55.25
10 45.46 27.32 51.68
11 65.04 13.62 54.81
12 55.54 6.35 59.74
13 24.50 6.21 28.80
14 16.80 41.68 57.96
15 25.33 5.71 27.63
16 9.58 33.25 32.74
17 15.22 12.45 26.80
18 58.96 29.4 30.23
19 53.86 14.11 59.72
20 72.79 16.84 62.76
21 66.70 34.66 42.69
22 62.33 16.02 70.74
23 56.56 27.67 35.95
24 66.81 20.18 53.13
25 71.17 37.84 38.44
26 72.16 19.27 65.61
Bold entries denote illumination and viewing conditions outside the dominant conditions (30° < i < 60°, 0° < e < 60°) for the observations from which the photometric corrections were derived. a Point numbers correspond to the numbered locations in Figs. 8-13.
Points 13 through 17 were imaged with viewing geometries that were not represented in any of the photometry data sets from which the photometric corrections were derived (Fig. 2). The grouping of points 13, 14, and 15 contributes image seams that are barely discernable in any of the versions of the color mosaic.
Fig. 10. Mosaics of area B (Fig. 7) in a simple cylindrical projection. Each version of the mosaic was built with a photometric correction derived from a different modeling solution, as labeled. The red, green, and blue channels are represented by the 1000-nm, 750-nm, and 430-nm map planes, respectively. Images were stretched to enhance contrasts and seams due to photometric variations (red range: 0.07-0.14, green range: 0.06-0.12, blue range: 0.03-0.08). The photometric angles for this segment of the mosaic are shown in Fig. 11. The numbered locations in the "combined" mosaic panel correspond to the numbered locations in Fig. 11 and Table 5.
The apparent reflectance contrast is greatest in the mosaics created with the photometric corrections derived from the flyby and integral-combined solutions. Though all these images were acquired in a forward-scattering orientation, the image at point 14 was acquired at higher emission angle than the adjacent images. No seam is evident between points 16 and 17 in the color mosaics, the images of which were acquired at low photometric angles (see Table 5). This area of the global color mosaic appears to be one in which the photometric variability has been well removed by each of the corrections.
4.3. Southern area C
The third area, labeled ''C'' and outlined in yellow in Fig. 7, is displayed in Fig. 12 for all four photometric corrections. The area was imaged under a variety of illumination and viewing conditions (Fig. 13). Several points are identified on the ''combined'' mosaic panel (Fig. 12), and their corresponding locations are shown on the emission angle map (Fig. 13, center). The photometric angles for these points are provided in Table 5. Points 18 through 26 display a variety of contrasting seams that are visible in all of the color mosaics, but to differing degrees. Points 18 and 19 are near one another and were imaged at high (>50°) incidence angles and low (<30°) emission angles. However, the image of point 18 was acquired in a backward-scattering orientation whereas that for point 19 was acquired in a forward-scattering orientation (accounting for the large contrast in phase angles between the two locations). Images for nearby points 20 and 21 were also acquired at high (>60°) incidence angles; both images were acquired in a backward-scattering orientation, but the difference in emission angles results in a ~20° difference in phase angles. In addition, images of both points 20 and 21 were acquired at photometric geometries outside the dominant illumination and viewing conditions (30° < i < 60°, 0° < e < 60°) for the photometry data sets. Points 22 and 23 also represent adjacent images imaged at high
Fig. 11. Mosaics of the photometric angles for the images in the color mosaics of area B shown in Fig. 10, displayed with the same gray scale as Fig. 6. Variations in incidence, emission, and phase angle are shown in the top, center, and bottom images, respectively. Locations are marked and numbered in the emission angle mosaic. The photometric angles of the images acquired at these locations are given in Table 5.
Fig. 12. Mosaics of area C (Fig. 7) in a simple cylindrical projection. Each version of the mosaic was built with a photometric correction derived from a different modeling solution, as labeled. The red, green, and blue channels are represented by the 1000-nm, 750-nm, and 430-nm map planes, respectively. Images are stretched to enhance contrasts and seams resulting from photometric variations (red range: 0.07-0.14, green range: 0.06-0.12, blue range: 0.03-0.08). The photometric angles for this segment of the mosaic are shown in Fig. 13. The numbered locations in the "combined" mosaic panel correspond to the numbered locations in Fig. 13 and Table 5.
(>50°) incidence angles, but the image of point 22 was acquired in a forward-scattering direction and that for 23 was acquired in a backward-scattering direction. Like the images of points 20 and 21, the image of point 22 represents a viewing geometry outside the dominant parameters of the photometry data sets. As discussed in the next section, these points illustrate a relation between the quality of the photometric correction and the scattering direction with which the images were acquired.
Images of points 24, 25, and 26 were all acquired at high (>60°) incidence angles and with photometric geometries outside the dominant illumination and viewing conditions for the photometry data set. The image of point 25 was acquired in a backward-scattering direction and has the smallest phase angle of those sampled. Images of points 24 and 26 were also acquired in a backward-scattering direction, but at a higher phase angle. All of these points in area C show seams in the four color mosaics, but the reflectance contrast is smallest in the mosaic constructed with the photometric correction from the combined solution.
-41.85-
-41.85
5. Analysis of quality of fit
There are two metrics that have been applied to the data to assess the quality of the modeling solutions. The first is the RMS misfit used to select the best set of model parameters. The RMS values are defined as
y/CRobT
Fig. 13. Mosaics of the photometric angles for the images in the color mosaics of area C shown in Fig. 12, displayed with the same gray scale as Fig. 6. Variations in incidence, emission, and phase angle are shown in the top, center, and bottom images, respectively. Locations are marked and numbered in the emission angle mosaic. The photometric angle values of the images acquired at these locations are given in Table 5.
where Robs is the observed reflectance, Rmodei is the model-derived reflectance, and N is the number of data points. A comparison of the RMS values for the four different model solutions is shown in Fig. 14. These graphs demonstrate that the RMS values, and thus the quality of fit, tends to become worse with increasing
O.OOE+OO
Combined Data Set
600 700 800 Wavelength (nm)
Matabei Data Set
400 500 600 700 800 900 1000 1100 Wavelength (nm)
Fig. 14. RMS value as a function of wavelength for the four modeling solutions (diamonds, flyby solution; circles, Matabei solution; squares, combined solution; triangles, integral-combined solution). (a) RMS values for the combined disk-resolved data set; (b) RMS values for the Matabei data set.
1.6 1.4
0 1.2 'C
Ï 0.8
œ 0.6 0.4
Beethoven Region
<c 1.2
u C nj
! ( >—< l-« h— r r—« »---- ----, *
550 650 750 Wavelength (nm)
Matabei Region
1 ►-< - - 1 )
f\ >-f J-«*, ---__ !..........«
) ( 7 1 1-( t-—
650 750 850 Wavelength (nm)
Fig. 15. The median reflectance ratio value as a function of wavelength for the four modeling solutions (diamonds, flyby solution; circles, Matabei solution; squares, combined solution; triangles, integral-combined solution). (a) Reflectance ratio values for the Beethoven data set; (b) reflectance ratio values for the Matabei data set.
wavelength. This behavior is related to the scattered light issues reported by Domingue et al. (2011a,b). It also indicates that the Matabei solution best describes the Matabei photometric region, whereas the combined model solution best describes the combined data set with measurements from both the Matabei and Beethoven photometric regions.
The second metric is the reflectance ratio, defined as Robs/ Rmodel. For a perfect model solution this ratio is unity. A comparison of the reflectance ratio for the four different model solutions is shown in Fig. 15. These plots show the median reflectance ratio as a function of wavelength, and the errors shown are from the minimum to the maximum values of the reflectance ratio. Within these errors the solutions appear indistinguishable from each other, but the errors shown represent more the scatter in the measurements than uncertainties in the median values. The differences in the reflectance ratios are similar to the differences seen in the mosaics constructed with the different photometric solutions. As with the RMS values, the Matabei solution best describes the photometric data from the Matabei region, whereas it is the worst solution to describe the photometric data from the Beethoven region.
The data set from the Matabei photometric region were acquired with geometries that most closely resemble those under which the global color mosaic images were acquired. The RMS and reflectance ratio analysis both show that this latter data set is best described by the Matabei solution. Inspection of the mosaics created with each photometric solution also show that the Matabei solution displays the fewest seams, or that the seams display less contrast.
6. Concluding discussion
Examination of the MESSENGER global color mosaic generated with the four different photometric corrections shows that systematic errors in the correction to an incidence angle of 30°, emission angle of 0°, and phase angle of 30° occur when the incidence and emission angles of the original data were high (>50°), or when the image was acquired at a forward-scattering geometry that results in a high (>50°) phase angle. Table 6 summarizes the comparison of several adjacent image pairs that support this conclusion. The photometric corrections derived with the Matabei solution work best in reducing image seam contrasts under conditions of large differences in emission angle when the incidence and phase angles are low (<50°). The photometric corrections derived with the "combined" solution work best in reducing, but not eliminating, seam contrasts under conditions in which incidence angles are large (>50°) and either emission or phase angles are large (>50°). The "integral-combined" solution, although derived from observations that include all 11 MDIS filters, is heavily influenced by the disk-integrated observations that do not capture the reflectance variability with incidence and emission angle. This solution underscores the importance of including disk-resolved measurements at geometries relevant to both the observational ranges and the correction geometry. The MESSENGER imaging team chose to use the Mata-bei solution for the photometric correction applied to the global color mosaic delivered to the PDS in March 2013 because it performs better on most of the data that were used to create that mosaic product.
Table 6
Summary of image comparisons.
Point #/scattering direction
Point #/scattering direction
Photometric angle comparisons
Seam visible?
7 Forward
11 Backward 14 Forward
16 Backward 18 Backward
20 Backward 22 Forward
8 Backward
12 Forward 15 Forward
17 Backward 19 Forward
21 Backward 23 Backward
Both <35°, within 10°
Both >50° Both <30°
Both <20° Both >50°
Both >50° Both >50°
, within 10° , within 10°
within 10° within 10°
, within 10°
, within 10°
Both <25°
Both <15°, within 10° Both <50°
Both <35°
Both <30°, within 20° Both <35°, within 20° Both <35°, within 20°
7: >50° 8: <30° Both >50° 14: >50° 15: < 30° Both <35° 18: -30° 19: >50° 20: >50° 21: <50° 22: >50° 23: <40°
Yes Yes
Yes Yes
Promising directions for improving the photometric corrections and removing the remaining photometric artifacts include improving the radiometric calibration, expanding the photometric data set, and considering alternative models. For instance, there is currently no correction for scattered light applied as part of the radio-metric calibration algorithm. As shown by Hawkins et al. (2009), scattered light in the WAC is strongly wavelength dependent, increasing from a contribution over large areas at short wavelengths to a contribution at the longest wavelengths. Although Hapke's model has been demonstrated to predict photometric reflectance behavior, alternative, simpler models (e.g., Helfenstein and Shepard, 2011; Shkuratov et al., 2011) should also be examined and applied to the growing photometric data sets acquired by the MESSENGER mission.
Acknowledgments
The authors thank the MESSENGER mission operations, engineering, and MDIS instrument operations teams, without whom the scientific work presented in this paper would not have been possible. The authors also thank L.R. Nittler, S.C. Solomon, and two anonymous reviewers for their insightful comments and suggestions. The MESSENGER mission is supported by the NASA Discovery Program under contracts NAS5-97271 to The Johns Hopkins University Applied Physics Laboratory and NASW-00002 to the Carnegie Institution of Washington.
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