Calibration, Projection, and Final Image Products of MESSENGER’s Mercury Dual Imaging System

Abstract

We present an overview of the operations, calibration, geodetic control, photometric standardization, and processing of images from the Mercury Dual Imaging System (MDIS) acquired during the orbital phase of the MESSENGER spacecraft’s mission at Mercury (18 March 2011–30 April 2015). We also provide a summary of all of the MDIS products that are available in NASA’s Planetary Data System (PDS). Updates to the radiometric calibration included slight modification of the frame-transfer smear correction, updates to the flat fields of some wide-angle camera (WAC) filters, a new model for the temperature dependence of narrow-angle camera (NAC) and WAC sensitivity, and an empirical correction for temporal changes in WAC responsivity. Further, efforts to characterize scattered light in the WAC system are described, along with a mosaic-dependent correction for scattered light that was derived for two regional mosaics. Updates to the geometric calibration focused on the focal lengths and distortions of the NAC and all WAC filters, NAC–WAC alignment, and calibration of the MDIS pivot angle and base. Additionally, two control networks were derived so that the majority of MDIS images can be co-registered with sub-pixel accuracy; the larger of the two control networks was also used to create a global digital elevation model. Finally, we describe the image processing and photometric standardization parameters used in the creation of the MDIS advanced products in the PDS, which include seven large-scale mosaics, numerous targeted local mosaics, and a set of digital elevation models ranging in scale from local to global.

1 Introduction

The Mercury Dual Imaging System (MDIS) was the eyes of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft and provided not only our first view of much of Mercury’s surface, but an extensive dataset optimized for a variety of geologic investigations. MDIS included a monochrome narrow-angle camera (NAC) with a single medium-band filter, and a wide-angle camera (WAC) with a filter wheel that held eleven narrow-band filters and one clear filter (Table 1). The NAC and WAC each had identical $1024 \times 1024$ charge-coupled device (CCD) detectors. The NAC was an off-axis reflector with a 1.5° field of view (FOV), and the WAC was a four-element refractor with a 10.5° FOV. The cameras were controlled by shared electronics, meaning only one camera could operate at a time, and they were mounted on a pivot with a 90° calibrated range of motion, which enabled a much wider range of imaging than would have been possible given the spacecraft’s fairly strict pointing restrictions (Leary et al. 2007) and the observing requirements of other instruments. A full description of MDIS was given by Hawkins et al. (2007).

Table 1 Spectral responsivity of the WAC filters and NAC, and their use in imaging campaigns

MDIS operated successfully from MESSENGER’s launch on 3 August 2004 through a six-and-a-half-year cruise phase that included a flyby of Earth (2 August 2005), two of Venus (24 October 2006, 5 June 2007), and three of Mercury (14 January 2008, 6 October 2008, 29 September 2009), and an orbital phase at Mercury that lasted more than four years (18 March 2011–30 April 2015). MDIS accomplished the first global mapping of Mercury, completing the initial view of the $\sim55\%$ of the surface not seen by Mariner 10 during its flybys of Mercury in 1974 and 1975 and substantially improving upon the image resolution, multispectral coverage, and range of illumination conditions viewed for each portion of the surface. To do this within the available downlink and onboard storage, pixel binning and lossless and lossy compression were used as needed. Binning was done either only at the focal plane on-chip ($2\times2$ binning from $1024\times1024$ pixels to $512\times512$ pixels), or additionally in the spacecraft main processor (for a total of $4\times4$ binning to $256\times256$ pixels). Twelve-bit data were converted to 8-bit using a look-up table—standard Mercury imaging largely employed look-up Table 2 from Fig. 4 of Hawkins et al. (2007)—and could be wavelet compressed to varying degrees.

Here we provide an overview of MDIS operations and imaging during the orbital phase of MESSENGER’s mission, as well as the calibration and processing of final products delivered to the NASA Planetary Data System (PDS). The following sections serve as a guide for anyone who wishes to understand the details of how and why MDIS data were acquired, the full range of data available, and their strengths and limitations.

2 MDIS Operations and Images Acquired

Scheduling and commanding the seven scientific instruments on MESSENGER was largely controlled by SciBox, a software library that automated planning, simulation, and visualization of most observations (Choo et al. 2014). SciBox proved invaluable for minimizing conflicts, prioritizing and optimizing observations, and ensuring that science and observing requirements for each instrument were met. For MDIS and other instruments, requirements were codified as rule-based protocols into “opportunity analyzers.” For example, a campaign to image a region with a particular illumination and viewing geometry would be assessed using an opportunity analyzer that found all possible opportunities to observe that region during a defined period of time and ranked the candidate observations that best matched the specified conditions. Desired observations were then assembled in a prioritized fashion into a timeline of commanded operations, mutually deconflicted, and checked against operational constraints.

The science planning process was organized into advanced science planning (ASP, 6 weeks ahead) and near-term science planning (NTSP, 1 week ahead) cycles. For each ASP cycle, SciBox rules were modified to accommodate large changes, such as adding a new observing campaign, and simulations of the resulting observing schedule were run to assess their effects on other science observations; rules were then modified and the schedule re-simulated as needed. SciBox also generated a long-term prediction of the available solid-state recorder (SSR) space given the predicted downlink. This information was used to select pixel binning and image compression settings for images to fit within the predicted available SSR space during times when downlink was limited, and to schedule additional observations to maximize data acquisition during times of high downlink rates. High-resolution “ride-along” NAC images of opportunity were acquired whenever downlink rates permitted. For MDIS, planned images in each NTSP cycle were reviewed to ensure correct settings (e.g., maximum exposure time, compression settings) and to adjust the imaging plan given updated predictions of space available on the SSR.

Orbital imaging of Mercury was planned as a series of campaigns that are summarized in Table 2, each of which was designed to characterize Mercury and its environment in a specific fashion, or to track the radiometric and geometric calibration of MDIS over time. The field of OBSERVATION_TYPE in the header of each image was used to track images associated with a given imaging campaign. In general, the campaigns each fell into one of five categories:

• (1) Regional to global maps were acquired to characterize the morphology, relief, or spectral reflectance properties of the Mercurian surface. A moderate-incidence monochrome mosaic, its stereo complement, north and south polar mosaics, and an eight-color mosaic were acquired mostly during the 1-Earth-year primary mission. Additional mosaics were acquired to attain color imaging at higher spatial resolution, to characterize subtle spectral properties of Mercury’s northern smooth plains, to provide stereo coverage less interrupted by shadows, and to highlight subtle topographic features. The opportunity analyzers strove to provide regional continuity in the local solar time (LST) at which images were acquired, resulting in maps that are a montage of different, but slowly varying, illumination geometries. Pixel binning and compression were modulated to fit within available downlink.

• (2) Local area images or mosaics were designed to investigate features of high scientific interest in greater detail. During the primary mission, such image products were dominated by high-resolution NAC image strips and WAC 3-color observations of albedo features; the local-area images became more diverse in configuration as the mission progressed. Because the global campaigns typically used the WAC and pixel binning in the northern hemisphere, or were acquired under specific illumination and viewing conditions, targeted (especially NAC) images provided higher spatial resolution or alternate views of the surface. Targeting was managed with the Applied Coherent Technologies (ACT) Rapid Environmental Assessment Composition Tools (REACT) software. REACT enables views of available images and the selection of targets with desired imaging conditions. Once targets were input by the science team and assigned a priority level, a target list was generated by REACT and incorporated into the SciBox planning process during each ASP cycle.

• (3) “Ride-along” NAC images that provided higher-resolution views of the surface than did typical mapping campaigns were taken opportunistically without specific pointing, to take advantage of available downlink.

• (4) Images of astronomical targets were acquired to search for Mercurian moons and vulcanoid asteroids. Typically these were taken as multiple long exposures covering the volume within which the possible target bodies might be located. Images of comets Encke and ISON were taken while those objects were in the vicinity of Mercury.

• (5) Images of Mercury’s surface and stellar fields were taken routinely to monitor drift in MDIS radiometric calibration, solve for focal length and distortion, and track alignment of the cameras relative to each other and to the star cameras. Time variations in radiometric and geometric calibration may have been produced by the extreme thermal environment at Mercury’s distance from the Sun.

Table 2 MDIS imaging campaigns during the MESSENGER orbital mission

By the end of the mission, 291,008 images (277,928 images from orbit about Mercury) were commanded and received on the ground. For comparison, the initial 1-Earth-year primary imaging plan originally proposed to the Discovery Program included only on the order of 10,000 images.

3 Instrument Thermal Performance

The MDIS thermal regulation system was a key factor in successful operation of the instrument in the harsh Mercury environment. The orbital mission design often resulted in a substantial heat flux to the instrument, particularly during short intervals near periapsis of the initial 12-h orbit, when the illuminated surface of Mercury subtended a large solid angle. The MDIS cameras were designed to operate between $-10~^{\circ}\mbox{C}$ and $-45~^{\circ}\mbox{C}$ to minimize the effects of dark current in the CCD detectors, and in order to remain within this temperature range, a specialized MDIS thermal system was required to manage the heating effects on the camera system during these periods. As the exterior of the instrument heated, thermal diode heat pipes disconnected the heat path to the CCDs from the beryllium radiators. To absorb heat leaked through parasitic paths, the CCDs were thermally tied to a paraffin (dodecane) phase-change material thermal reservoir or “wax pack,” which partially melted to absorb heat. As the exterior of the instrument cooled, the heat pipes resumed circulation, radiating heat through the radiator, refreezing the paraffin, and preparing the instrument for the next periapsis (Hawkins et al. 2007).

The thermal design proved successful over the primary mission (one Earth year from March 2011 through March 2012, approximately equivalent to two Mercury solar days) in maintaining the instrument within its operational limits over all orbits and seasons. The maximum CCD temperature was bounded by the melting temperature of the paraffin in the wax pack ($-9.6~^{\circ}\mbox{C}$), and after accounting for parasitic heat losses between the wax pack and the CCD, the CCD temperature never exceeded $-7~^{\circ}\mbox{C}$. Thermostatically controlled compensation heaters provided the power required to maintain the minimum temperature limit of the detectors, ensuring that the CCD temperatures were never colder than $-43~^{\circ}\mbox{C}$. The instrument was calibrated over this operational range of temperatures, and the algorithms developed as a result of the ground and in-flight calibration proved successful in modeling variations in dark current and responsivity within these limits (see Sect. 4.4).

In April 2012, after completion of the primary mission, the MESSENGER spacecraft transitioned from a 12-h orbit period to an 8-h orbit period for the duration of its extended mission. This change impacted the thermal performance of MDIS in a number of ways. The change in the orbital period reduced the maximum altitude above Mercury, that is, reduced the orbital apoapsis. Although this change provided more opportunities for higher-resolution imaging, the reduction of the orbital eccentricity meant that there was a flattening of the orbit. The period during which the planet subtended large solid angles, and therefore exposed MDIS to the high heat flux from surface, was lengthened by this flattening. Further, the reduced orbital period also meant that MESSENGER had less time far from the planet to allow the wax to refreeze. To minimize heating and the amount of time outside the MDIS nominal range, the operations team adjusted the attitude of the spacecraft to orient the MDIS radiator away from the planet whenever possible. An example of a cycle when these operations allowed the CCD to remain within the designed temperature range is shown in Fig. 1. However, the increase in heat flux at times still exceeded the design limits for the amount of latent heat in the wax packs, and it ultimately meant that all of the wax melted for short periods of time during the hottest portion of the Mercury solar day throughout the remainder of the mission. Once the wax pack was completely melted, the temperature of the CCD would continue to rise as long as heat continued to enter the system, resulting in a spike in temperatures higher than $-7~^{\circ}\mbox{C}$ (Fig. 2). Images collected during such times, when temperatures exceeded the operational range within which the instrument was calibrated, have increased uncertainty in calculated radiance; updates to the in-flight calibration of the temperature-dependent CCD responsivity were not successful in completely correcting for these effects at the highest temperatures (Sect. 4.4).

Fig. 1

The WAC CCD temperature is shown as a function of time over approximately two Mercury years. The low-frequency modulation in this figure provides insight into the seasonal effects on the CCD temperature, with the lows capped by compensation heaters and the highs limited by the wax-pack system. The high-frequency oscillations are caused by changes in the CCD temperature resulting from orbital variations and spacecraft orientation. During this time period, the temperature remained within designed limits

Fig. 2

The cyclic temperature of the NAC CCD is shown through a portion of the mission when the spacecraft was in an 8-h orbit. Low-frequency temperature swings of the CCD track each Mercury solar day. Periods when the wax pack melted completely resulted in spikes to temperatures $>-7~^{\circ}\mbox{C}$ (indicated in red)

4 In-flight Radiometric Calibration

Radiometric calibration of MDIS is the transformation of raw image data number (DN) into units of radiance, through the expression:

$$ L ( x,y,f,T,t,b ) = \frac{\mathit{Lin} [ \mathit{DN} ( x,y,f,T,t,b ) -Dk ( x,y,T,t,b ) -Sm ( x,y,t,b ) ]}{\mathit{Flat} ( x,y,f,b ) \times t \times \mathit{Resp} ( f,b,T )} $$

(1)

where $L(x,y,f,T,t,b)$ is radiance in units of $\mbox{W}/(\mbox{m}^{2}\,\upmu \mbox{m}\,\mbox{sr})$, measured by the pixel in column $x$ and row $y$ through filter $f$, at CCD temperature $T$ and exposure time $t$, for binning mode $b$; $\mathit{DN}(x,y,f,T,t,b)$ is the raw DN measured by a given pixel; $Dk(x,y,T,t,b)$ is the dark level in a given pixel, derived from a model based on exposure time and CCD temperature; $Sm(x,y,t,b)$ is the scene-dependent frame transfer smear for the pixel; Lin is a function that corrects the small nonlinearity of detector response; $\mathit{Flat}(x,y,f,b)$ is the non-uniformity or “flat-field” correction; and $\mathit{Resp}(f,b,T)$ is the responsivity, relating dark-, flat-, and smear-corrected DN per unit exposure time to radiance.

Extensive MDIS radiometric calibrations were performed before launch (Hawkins et al. 2007) and during cruise (Hawkins et al. 2009), and that work continued during MESSENGER’s orbital mission phase. The initial 18-day commissioning period after Mercury orbit insertion was used to validate the calibration of the NAC and WAC; at that time the only updates that had been made were to several of the WAC flat fields. As the orbital phase of the mission progressed, other updates were made to the NAC and WAC frame-transfer smear correction, the WAC flat fields, NAC and WAC temperature-dependent responsivity, and most notably WAC responsivity as a function of time. These updates are described in the following sections and are reflected in the calibrated data record (CDR) version 5 data archived in the PDS.

4.1 Dark Model

During ground calibrations, the measured signal from the CCD was extensively sampled in the absence of incident photons as a function of temperature, exposure time, and binning. Four models of dark current were generated for each sensor: binned and not-binned, and forward and backward (Hawkins et al. 2007). The forward model computed the expected dark current as a function of CCD pixel position, exposure time, and temperature; the backward model estimated it as a function of detector row on the basis of the measured value in a set of detector columns at one side of the CCD covered by a metallic mask. Given that the MESSENGER mission extended three years past the primary mission, and that time-dependent corrections were required for other radiometric calibration components, a search was conducted for evidence of temporal changes in the dark current.

An approximation of photon-free images could be obtained from sequences of star images taken over a time window sufficiently short so that the detector temperatures remained relatively unchanged. Nominally, this time window was thirty minutes. The motion of the spacecraft displaces the point source signatures of the stars across the detector, so each image sequence should contain photon-free pixels at every row and column in the readout. For the WAC, 201 star images were selected, and, for the NAC, 937 frames were chosen. Star images were acquired during both the cruise and orbital phases of the mission, from which 201 WAC images and 937 NAC images were selected from August 2004 through November 2013. For images within each half-hour sequence, frames were grouped by binning mode and exposure time. Exposure times ranged from 1 to 9989 ms, while CCD temperatures ranged from −45 to $-7~^{\circ}\mbox{C}$. After excluding near-saturated values, defined as 95% of saturation (a threshold set to accommodate high-temperature data), a composite dark image was created from each group of 2–93 images, through a pixel-by-pixel search for the minimum DN value within the group. To remove any residual star signatures in sequences that contained only a small number of images, the pixel minima in the composite were clipped to fall within a range of the mean plus or minus the standard deviation multiplied by a factor of 1.4. With this procedure, 39 WAC and 186 NAC composite dark images were synthesized (e.g., Fig. 3).

Fig. 3

An example composite dark image created from WAC data collected on 28 April 2005. These data were collected at $-41.9~^{\circ}\mbox{C}$ at an exposure time of 9989 ms. A dark image calculated from the WAC not-binned forward model for the same exposure time and CCD temperature had an absolute mean pixel per pixel difference of 0.68 DN

The dark model was evaluated by comparing the composite dark images to the dark model. For nominal exposure times used for imaging Mercury, and for temperatures below $-20~^{\circ}\mbox{C}$, the dark model matched the composite dark images to within 1–5 DN. Some of this residual difference may be due to the use of the minimum DN value in creating the composite dark image rather than the median; read noise of the detectors is $\sim1~\mbox{DN}$, so using a minimum can account for the low end of $\sim1~\mbox{DN}$ of error. For temperatures greater than $-20~^{\circ}\mbox{C}$, the residual differences were often larger, but they were random in amplitude, included frequent sign reversals, and exhibited no meaningful trend. The search for temporal change in the composite dark images proved inconclusive. For cold temperatures, the residual difference between the composite dark images and the model for the not-binned NAC showed a linear temporal trend from −2.1 to $-4.4~\mbox{DN}$ between July 2008 and July 2010, but this time period provided the only evidence of a tendency toward temporal drift in any of the data. Thus, for both detectors, no updates were made to the dark models derived from ground calibrations (Hawkins et al. 2007).

4.2 WAC Frame-Transfer Smear Correction

After the nominal exposure time, an image is transferred line by line across the imaging zone of the CCD (responsive to light) to the readout zone of the CCD (masked from light) for image digitization. The transfer of each line takes a fixed amount of time, during which time the remaining lines are still exposed to incident light and accumulate excess signal, known as frame-transfer smear. A standard algorithm to remove this frame-transfer smear is used for the NAC and WAC (Hawkins et al. 2007) and requires knowledge of the time it takes to transfer each line to the memory. During the initial calibration, this frame-transfer time was determined empirically to be 3.84 ms for the full frame, and thus 3.75 μs for each of the 1024 lines (Hawkins et al. 2007). Subsequent in-flight calibration found values ranging from 3.4 to 4.2 μs/line (Hawkins et al. 2009). In some cases, residual effects of frame-transfer smear were observed in images with short exposure times; further analysis was thus conducted to determine the correct read-time of each line.

A review of vendor-provided documentation revealed that there are 16 lines that are not part of the image but are read out first. Thus an offset of $16\times$ the line-read time was added to the frame-transfer smear correction algorithm of Hawkins et al. (2007). To evaluate the frame-transfer time, images with high contrast (either the bright disk of a planet against space, or a sunlit region of the surface next to a shadow) were analyzed following an approach similar to that of Hawkins et al. (1997) and Murchie et al. (1999). Nine short-exposure (1–7 ms) binned and not-binned flyby images of Earth, Venus, and Mercury from the WAC and NAC were selected and dark-corrected. The frame-transfer smear algorithm was then applied, varying the line-read time from 3.20 to 3.92 μs. To eliminate edge effects, 28 pixels at the margins of the frame were trimmed for not-binned images (14 pixels for binned images). To quantify the maximum smear signature, 5% (25 binned, 51 not-binned) of the remaining rows with the largest frame-transfer smear effects were averaged along the columns and displayed (Fig. 4). The correct line-read time was chosen as the time that resulted in the least residual signal in the averaged line (signal is the flattest, with smear effects at the level of the noise, Fig. 4). From the flyby data, a line-read time of 3.40 μs provided the best correction to both WAC and NAC images. Since each instrument used identical readout electronics, the read time was expected to be the same.

Fig. 4

An example of a flyby image used to determine the best line-read time (WAC image EW0131717385B of a crescent Mercury). The red box on the image shows the region averaged; the uncorrected DN values are plotted below for this averaged region. The averaged region is also plotted after frame-transfer correction using line-read times of 3.30, 3.35, 3.40, 3.45, and 3.50 μs. The signal due to frame-transfer smear is minimized with a line-read time of 3.40 μs

Given the limited set of flyby images (e.g., Fig. 4), orbital data were also analyzed in a similar manner. Fifty-nine WAC and NAC images were selected, each with short exposure times (1–16 ms) and illuminated and shadowed regions oriented such that shadowed terrain was transferred to memory after illuminated terrain (dark below, bright above, Fig. 5). Given the variability in each scene, the readout smear analysis was restricted to portions of each frame as appropriate. Images were again corrected for frame-transfer smear with a variety of line-read times, and the dynamic ranges of each corrected row was tracked. The dynamic range was plotted as a function of line-read time (Fig. 5), with the expectation that the correct line-read time would yield the lowest dynamic range. Because the background scenes were more variable, not every analysis resulted in a single minimum, but for both the WAC and the NAC, 3.40 μs was the most commonly occurring value. Thus a line-read time of 3.40 μs was adopted and used for production of the final version of calibrated images.

Fig. 5

An example orbital image used to evaluate the frame-transfer smear correction (WAC image EW1022482170B). (a) Uncorrected image stretched to show smear. (b) Image after correcting for frame-transfer smear with a line-read time of 3.40 μs, stretched to show smear removal. (c) Plot showing the dynamic range (maximum to minimum) of a dark region after correction for frame-transfer smear using a range of line-read times. The lowest dynamic range (best correction) is found with a line-read time of 3.40 μs

4.3 WAC Flat Fields

Laboratory measurements of the WAC responsivity non-uniformity matrix, also known as a “flat field,” had several known problems. The unobstructed view of an integrating sphere that was the flat-field reference was obtained at room temperature and in air. High dark-current noise at room temperature led to artifacts, particularly in the long exposure times required in the F and C filters because of low levels of short-wavelength light, for which dark current resulted in partial saturation (Hawkins et al. 2007, 2009).

Additionally, particulates on the cover glass of the CCDs resulted in shadows (“dust donuts”), which moved during launch. The flat fields were re-derived during cruise, when it was possible to orient the spacecraft such that a Spectralon calibration target was illuminated (Hawkins et al. 2009). However, because glint from the radiator led to non-uniform illumination of the calibration target, these flat fields were not ideal and their high-spatial-frequency variation was merged with the low-spatial-frequency portion of the laboratory flats (Hawkins et al. 2009). These are the version-4 flat field files in the PDS calibration archive. WAC flat fields were thus reexamined during the commissioning phase of MESSENGER’s orbital operations, by averaging observations of Mercury, even though the number of images available at that point in the mission was insufficient to simulate observations of a truly “flat” source. Still, because of the issues with the laboratory measurements through the F and C filters, those two flat fields were updated at that point (version-5 files in the PDS).

To derive flat fields from orbital data, images of Mercury acquired without wavelet compression were selected in each filter, for which the four corners of the image were on the planet and incidence angles ranged from 0° to 70°. Because the various imaging campaigns resulted in more images in some filters than in others (Table 1), the incidence angle range was adjusted as needed to restrict or increase the number of included images. For example, the analysis of the F, G, and I filters (used in all color imaging campaigns) each included approximately 2000 not-binned images. In contrast, the A, H, and K filters were used only for selected targeted opportunities, and thus only around 200 not-binned images were available for each filter. Images with wavelet compression were excluded because although they did not appear to affect the flat field analysis for not-binned images, their inclusion resulted in a “fabric” in the binned flat field. This observation suggests that compression artifacts result in a consistent pattern.

The selected images were calibrated to subtract dark current, corrected for frame-transfer smear and for temperature-dependent responsivity, and then photometrically corrected using the most recent analysis (Sect. 7). Each image was normalized to a value of unity by dividing by the average value for the center $150\times150$ (binned) or $300\times300$ (not-binned) pixels. Flat fields were derived separately for binned and not-binned images because on-chip binning led to spatially dependent fixed-pattern variations. For each filter, binned and not binned, the median value of all images was calculated at each pixel. For most filters, the resulting product appeared qualitatively like previous versions of the flat field (Fig. 6), but with differences in low-frequency gradients and fewer high-frequency artifacts that had been attributed to the limitations in the laboratory set-up, as described above. For the three filters used exclusively for targeted images during orbital operations (filters A, H, and K), the input dataset proved to be too limited to derive a reliable flat field, largely because a substantial portion of the targeted images were centered on bright, rayed impact craters.

Fig. 6

Example of the flat fields for binned filter F. In the laboratory measurements, the top lines were saturated in this filter and thus filled in with the average value. The cruise and commissioning flat fields used the low-frequency portion of the laboratory flat field (top lines extrapolated from the median of the 32 lines below), with newly derived high-frequency components. The bottom right shows the results of compiling thousands of orbital images of Mercury and taking the median value at each pixel. Each flat field is stretched the same, from 0.92 to 1.05; the three black columns at left are masked on the detector. The general darkening of the flat fields toward the corners is an optical effect of field angles, the small circular features are “dust donuts,” and the horizontal bars are characteristics of the detector

For the eight filters for which the above procedure yielded results that were qualitatively similar to earlier flat fields, a low-pass filter ($31\times31$ pixels and $61\times61$ pixels, binned and not binned, respectively) was applied twice in succession, and the result was subtracted from the median product to leave only the high-frequency component of the scene (Fig. 7). Two low-pass filters with the same box sizes were then run in succession on the laboratory flat fields, and this result was added to the high-frequency component derived from orbital data (Fig. 7). This procedure was followed because of concerns that variable out-of-field scattered light could result in differing gradients across the scene in orbital data. Out-of-field scattered light, which would have been more uniform, likely also affected ground flat fields. This final result was then compared with the previous flat field for each filter, binned and not binned. For not-binned flat fields, filters C and F showed improvement and were updated (version 6 in the PDS); for the remaining filters there were no substantial changes and the previous flat fields (version 4, the combined laboratory and cruise measurements) were considered to have been validated. For the binned flat fields, filters C, D, E, F, G, I, and L showed improvement and were updated; filter J showed no substantial difference and was not updated.

Fig. 7

An example from filter F of the creation of the latest version of flat fields. The top left panel shows the results of two subsequent low-pass filters on the laboratory flat field, and the top right panel shows the high-frequency portion of the median-merged products. The sum of these two resulted in the version-6 orbital flat field (bottom left panel). The difference between this and the cruise flat field (version 4) is shown in the lower right panel as a ratio, stretched from 0.985 to 1.015

4.4 NAC and WAC Temperature-Dependent Sensitivity

The responsivity of the MDIS CCDs varied with their operating temperature and the wavelength of incident light (i.e., the charge generated and converted to DN is larger in filters at wavelengths $>850~\mbox{nm}$ and smaller in shorter-wavelength filters as temperature increases). A linear correction for this variation in sensitivity was developed during the ground calibration by collecting measurements through each filter at three different temperatures (Hawkins et al. 2007); however, the temperature range across which MDIS operated while in orbit around Mercury had been insufficiently sampled in the ground measurements. The calibration of temperature-dependent responsivity was first updated by adding approach and departure data from the first two Mercury flybys to the ground calibration data. The linear correction derived from the ground calibration alone was found to overcorrect for temperature effects at longer wavelengths; therefore, a quadratic correction was derived to fit all available data points (Hawkins et al. 2009). These data still did not adequately sample the higher detector temperatures experienced later during orbit.

The variations in CCD responsivity were reevaluated twice during the orbital mission, once following the commissioning phase, and once at the completion of the MESSENGER mission. The commissioning phase update is recorded in the version-5 responsivity tables archived in the PDS and will not be further described, as it has been superseded by version 6 derived from a much more complete dataset. This dataset included all images of Mercury masked to include only those pixels within restricted ranges of illumination and viewing angles (incidence angle 30–60°, emission angle 0–5°, and phase angle 30–60°) and spanned a range of temperatures from −45.6 to $9.3~^{\circ}\mbox{C}$. For each frame that contained at least 100 unmasked pixels, the median of those pixels was taken as the representative value for the image; however, natural geologic variations and other factors such as stray light increase scatter in the data. The data were calibrated according to Eq. (1), but without a correction for temperature, and then converted to radiance factor ($I/F$, where $I$ is measured radiance and $F$ is solar flux divided by $\pi$). The $I/F$ values were standardized to common illumination and viewing angles (Sect. 7). These $I/F$ values were normalized to 1.0 at $-30.3~^{\circ}\mbox{C}$ and plotted versus temperature in raw instrument counts (where 1060 DN is equivalent to $-30.3~^{\circ}\mbox{C}$). A linear fit to the data in each filter (Fig. 8) yielded a slope and an offset at each wavelength. In order to smooth the responsivity curve, the slopes were fit with an inverse hyperbolic tangent in energy space (Fig. 9). Additionally, this function was used to interpolate or extrapolate (as appropriate) the slope of the dependence of responsivity on temperature for the three WAC filters that were used only for targeted imaging (A, H, and K, Fig. 9), because there were not enough data acquired through these filters to derive the relationship directly. The temperature dependence of the responsivity of the NAC was found to be identical within error to that of WAC filter G, and thus the same coefficients were used for both. In all cases, the orbital linear approximations agreed well with the colder ground calibration data; however, as all plots were normalized to the $-30.3~^{\circ}\mbox{C}$ ground calibration data point and as the second cold ground calibration data point was close in temperature ($-34.2~^{\circ}\mbox{C}$), this agreement is unremarkable. The room-temperature ground calibration data point ($25.9~^{\circ}\mbox{C}$) was not fit well by any of the orbital linear fits.

Fig. 8

$I/F$ (normalized to 1.0 at a temperature of $-30.3~^{\circ}\mbox{C}$, equivalent to 1060 DN) versus raw CCD temperature for the F, G, and I filters. The median of each image used in this analysis was plotted, with the color scale indicating the density of points (low density blue; high density red). The linear fit to ground calibration data (pink line; Hawkins et al. 2007), quadratic fit to ground and cruise data (teal line; Hawkins et al. 2009), and linear fits to commissioning (black line) and orbital data (orange line) are shown. Additionally, the linear fit after smoothing the correction slopes by fitting an inverse hyperbolic tangent are shown (dashed blue line). There is typically little difference between the linear fit to the orbital data and the smoothed coefficients; the largest difference is found for the G filter

Fig. 9

Comparison of the slopes of the linear fits to temperature versus responsivity derived from the ground calibration, commissioning phase, and orbital data. The blue line and circles show the inverse hyperbolic tangent fit to the orbital data points in energy space

The application of the final linear correction is

$$ R_{f,T,b} = R_{f,-30.3~^{\circ}\text{C},b} \bigl( \mathit{correction} \_\mathit{offset}_{f} + T_{CCD} [ \mathrm{DN} ] \times \mathit{correction}\_\mathit{slope}_{f} \bigr) $$

(2)

where $R_{f,T,b}$ is responsivity in filter $f$ at CCD temperature $T_{CCD}$ in units of DN, and $b$ is the binning mode. $R_{f,-30.3~^{\circ}\text{C},b}$ is responsivity at filter $f$ for a temperature of $-30.3~^{\circ}\mbox{C}$ (1060 DN), and $\mathit{correction}\_\mathit{slope}_{f}$ and $\mathit{correction}\_\mathit{offset}_{f}$ are the slope and offset of the linear relationship between temperature and responsivity for each filter (Table 3).

Table 3 Responsivity coefficients derived from orbital data; the WAC B filter (clear) is included for completeness, but its responsivity was not reanalyzed

The derived relationship provides a suitable correction for data acquired under nominal MDIS thermal conditions. However, for periods when the MDIS wax pack was fully melted and temperatures rose above $-7~^{\circ}\mbox{C}$ (see Sect. 3), the correction at these hot temperatures does not appear to be adequate for color data and results in images with anomalously high signals at longer wavelengths. The number of affected images is relatively small, but this also means that the dataset was insufficient to further refine the high-temperature correction using the methodology described here. One other note of caution is that the WAC B filter (clear) was not typically used for Mercury imaging, apart from several NAC–WAC calibration sequences (Table 2) and imaging of permanently shadowed interiors of polar impact craters. No updates have been made to its responsivity since the ground calibration, and thus reflectance or radiance values calculated for data acquired through the clear filter may be in error by several tens of percent.

4.5 Changes in WAC Responsivity During the Mission

An initial in-flight calibration was performed during cruise (Hawkins et al. 2009). However, during the orbital phase of the MESSENGER mission, variations in apparent responsivity of the WAC system were observed that far exceeded the $\pm5\%$ typical accuracy attainable in imager radiometric calibration. Responsivity appeared to vary in time over periods as short as days (Fig. 10), and by filter, such that the basic assumption of responsivity varying only with detector temperature was seen to be inadequate and yielded smooth spectra at some times and spurious spectra with artifacts of $\pm15\%$ at other times.

Fig. 10

Repeat imaging of the same portion of Mercury’s surface ($\sim60^{\circ}\mbox{S}$, 200°E) shown with the 1000, 750, and 430 nm filters displayed in red, green, and blue, respectively. Each image mosaic from the dates indicated has been photometrically standardized (and all were acquired under similar illumination and viewing conditions). The same contrast stretch has been applied in order to highlight the rapid changes in apparent responsivity that occurred over a period of days, resulting in marked color differences

The causes of these variations in responsivity were the subject of extensive investigation. After completion of regular eight-color mapping acquired for the global color base map, a series of color images was obtained covering a broad expanse of the southern hemisphere for the purpose of monitoring changes in responsivity. This campaign resulted in 323 total image sets acquired, on average, twice each week from 5 June 2012 until color mapping was complete near the end of the mission in March 2015. Initially each image set consisted of the eight colors used for global mapping; when eleven-color targeted imaging began, the calibration monitoring campaign was updated to include the additional three filters. A quick method for evaluating changes in responsivity during this campaign was to measure the deviation of the G filter, which appeared to have the largest variation relative to filters around it. While not a perfect measure, as other filters showed variations as well, this simple metric is essentially a 750-nm band depth, calculated by interpolating 750 nm reflectance from values at 630 and 830 nm, and comparing this reflectance to the measured value as a percent difference. We searched for correlations between this “band depth” and other variables for which we had measurements (e.g., filter position to explore any possible light leaks, dark current level as measured in the masked pixels, CCD temperature, WAC telescope temperature, spacecraft temperature, spacecraft altitude, exposure time, incidence angle, angle between the orbital plane of the spacecraft and the vector to the Sun), and we could find no relationship except for clear variability with time (Fig. 11).

Fig. 11

Results from the southern hemisphere calibration monitoring campaign. (a) For each color set in the calibration monitoring campaign, a 750-nm “band depth” was calculated by interpolating 750-nm reflectance from reflectance at 630 and 830 nm and computing the percent difference between this value and the measured value. The value plotted is the median for the entire scene. The expected value is approximately zero, given Mercury’s lack of visible to near-infrared absorption bands. The colors in panel (a) correspond to the median spectra from each time period shown in (b), where spectra are offset by 0.02 for clarity. The transition from eight-color observations to eleven-color observations occurred between the spectra shown in orange and light green, and the light green dashed line shows the equivalent eight-color spectrum for comparison. At dates shown in blues and grays, substantial deviations were also observed in the 830-nm filter, which resulted in wide variations in the “band depths” shown in (a)

What could cause such time-dependent changes in responsivity? Degradation of the filters by radiation damage is unlikely, because such a change would not be reversible, and it appears that some filters recovered some of their response after previous decreases in performance. Contamination is also unlikely, as it is hard to understand how a contaminant could affect some filters at certain times, and others later on. We searched for some pattern with the order of filters on the filter wheel, to see if adjacent filters could have been affected by some process while non-adjacent filters were not. Although there are some similarities in the changes in response over time, no obvious pattern was found (e.g., the 900-nm and 1000-nm filters are adjacent on the filter wheel and show similar changes in response, but the 430 and 630 nm filters are also adjacent to each other but do not). We examined the total accumulated time each filter spent in the “active” position of the filter wheel, and we made an operational change to position the wheel at the 700-nm position when no imaging was occurring, rather than the 750-nm position, but this change appeared to have no obvious effect on the subsequent performance of either filter. Stray light was considered (Sect. 4.6), and we searched for any possible correlation with spacecraft orientation relative to the Sun, but none was found. All ground software was examined and exonerated to the best of our knowledge. Thus as of now, the causes of these variations in responsivity remain a mystery. Speculation centers on transient radiation effects on the detector or electronics (analog-to-digital conversion?), incorrect recording of exposure time (considered unlikely but not impossible), or periodic deposition and burnoff of a contaminant on some filters.

With no definitive explanation for why the variation in responsivity occurred, an empirical solution is the only remedy. An initial empirical correction for images acquired in the first year of operations was developed (Keller et al. 2013). Here we describe development of the correction that spans the full duration of MESSENGER’s orbital operations and was applied to individual WAC images and final mosaics delivered to the PDS.

To derive this responsivity correction, we took advantage of the availability of repeat imaging of Mercury’s surface. Parts of the southern hemisphere were imaged over 50 times in each spot in each filter, whereas areas in the north were typically imaged $>4$ times in each filter (the difference is due in part to the large eccentricity of the orbit, which results in large image footprints in the south and small footprints in the north). To avoid spurious results in areas of low overlap in the north, and because the timescale for changes appeared to be on the order of days (Fig. 10), we derived responsivity correction factors for each Earth day (2 or 3 orbits depending on mission phase). For each day, we selected all image data with a pixel scale $>50~\mbox{m}$ and incidence angle (measured at the center pixel) $<80^{\circ}$. The images were calibrated to reflectance using the standard calibration with the updates described in the preceding sections. Images were then photometrically normalized to an incidence angle of 30° and emission angle of 0° (Domingue et al. 2016; see Sect. 6), trimmed to exclude any portions of the scene with incidence angle $>70^{\circ}$ or emission angle $>30^{\circ}$, and mapped to an equal-area (sinusoidal) projection at 4 km/pixel. All images acquired on each day were mosaicked for each filter, typically resulting in a fairly narrow north–south strip that had substantial overlap with surrounding days.

With this dataset, multiplicative correction factors for each day were calculated through a weighted least-squares optimization that minimized the discrepancy between the median values for all spatial overlaps. The optimization was performed in two steps. First, a mosaic of data acquired before 22 May 2011 was held as a constant reference, because this dataset was seen to be largely self-consistent. However, these data covered only a fraction of the planet, so a mosaic with greater coverage was created from images that were corrected in this first iteration and exhibited low residual values. In the second step, all data were allowed to vary in the simultaneous optimization, with the mosaic from the first step held as reference. The resulting multiplicative correction factors are shown in Fig. 12. Correction factors were derived for days on which no data were included in our optimization process by interpolating between adjacent days. The three filters not used in global or regional mapping campaigns (700, 950, and 1020 nm) did not have enough overlap to derive correction factors with this method. Instead, the empirical correction was derived by comparing them with a synthetic global mosaic created by linear interpolation from images acquired with adjacent filters. The correction is applied by determining the correction factor relevant to the date of acquisition of a given image and a given filter and multiplying Eq. (1) by this factor.

Fig. 12

Multiplicative correction factors derived for WAC filters; each is offset by 0.4 (black horizontal line indicates the location of 1.0 for each filter). The points are empirical correction factors derived from image data; blue lines show segments interpolated from surrounding days

The correction factors show a large degree of variability over short time periods (Fig. 12). These timescales are consistent with the types of changes observed visually (e.g., Fig. 10), so no attempt to smooth or filter the correction factors was made. However, it is likely that these empirical correction factors also include any residual photometric differences that remain after photometric normalization, rather than changes in responsivity alone.

The final WAC CDRs included in this procedure were archived in the PDS imaging node both with and without the empirical correction applied as a multiplicative factor. A table of the empirical correction factors can be found in the MDIS CDR calibration directory in the PDS (https://pdsimage2.wr.usgs.gov/archive/mess-e_v_h-mdis-4-cdr-caldata-v1.0/MSGRMDS_2001/CALIB/). Final mosaics archived in the PDS (see Sect. 8) were created using the updated correction, and an analysis of overlap among individual images shows that residual differences (which include errors from calibration, scattered light, and possible incomplete correction of photometric variation) average 1.8–2.3% (depending on the filter). No comprehensive analysis to search for changes in response for the NAC was performed.

This empirical calibration is not ideal in several ways, a situation that prompts caution and yet promises potential future avenues to pursue improved corrections. Although the correction resulted in great improvements to the global and regional multispectral mosaics (Fig. 13), there are several reasons why the empirical correction process may be insufficient for analysis of individual color sets. First, WAC data acquired on days with no data that met our selection criteria (i.e., all images on that day were $<50~\mbox{m/pixel}$, or did not include any pixels where the incidence angle was $<70^{\circ}$ and the emission angle was $<30^{\circ}$) have a high likelihood of larger residual errors, given that the correction factors on those days were interpolated, and there is clearly high-temporal-frequency variation that may not be captured with this methodology (Fig. 12). Fortunately, there are relatively few color data meeting these conditions. Second, correction factors were derived individually for each filter, with no regard to other filters in a color set (no effort was made to ensure that the spectra for each color set were smoothly varying). This decision was made because, as described above, the changes in responsivity varied by filter with time. We have high confidence in spectra from global and regional mosaics, as each pixel in the mosaic is a median of all overlapping data at that point and the standard deviation for each pixel in each filter is provided (see Sect. 9). However, individual color image sets should be used with caution and are more likely to contain spurious spectral features. Whenever possible, spectra from individual color sets should be validated through comparison with other images and/or mosaics that cover the same terrain. All of the evidence suggests, however, that spectral artifacts are constant within a given multispectral image set. Therefore, one approach to spectral analysis of individual image sets can be to ratio the data to “typical” terrain present in the scene, e.g., intermediate plains, to look for departures from the bland spectra of such materials.

Fig. 13

MDIS 8-color mosaic shown with the 1000, 750, and 430 nm filters in red, green, and blue, respectively. (Top) With no correction for time-varying responsivity. (Bottom) After application of the empirical correction factors shown in Fig. 12. Sinusoidal projection centered at 180°E. The same contrast stretch is applied to both mosaics

Future improvements to the calibration of the WAC dataset could be made to derive corrections directly for all dates, to inspect for and correct spurious spectral features on some days, and to ensure continuity with images from MESSENGER’s three Mercury flybys prior to orbit. In addition, the choice of one Earth day as the time period for which images were binned and then corrected may not be ideal; the optimal time period may be shorter or longer (or variable). Also, although all of the mosaics showed improvement with application of the empirical calibration, the low-phase five-color mosaic was acquired under special illumination and viewing conditions (Sect. 8), and refinement of the calibration with a focus on this dataset could result in further improvement. An initial examination of the five-color mosaic calibration showed that further improvements may require a methodology that was different from the one described here in terms of the baseline image mosaic held as constant and the range of incidence angles included when deriving the correction.

4.6 Scattered Light Characterization

Early in the MESSENGER mission it became evident that the MDIS WAC was susceptible to scattered light. The initial scattered-light correction concept was based on the approach to the mitigation of image blurring seen in the NEAR multispectral imager that resulted from thruster burn products that plated out on the foreoptic. This approach entailed the empirical determination of the in-flight point spread function (PSF) and the recovery of deblurred images through Fourier-transform spectral domain PSF deconvolution (Li et al. 2002).

The PSF deconvolution approach is numerically and procedurally elegant, but its applicability is dependent on a number of assumed instrument characteristics. Two of the key prerequisites are that the scatter pattern is not strongly dependent on the position of the source in the FOV and that there is no significant scatter either from outside the FOV onto the detector (excess signal) or from within the FOV off of the detector (signal deficit). Exploratory investigation of the in-flight scattered light characteristics demonstrated that for the WAC neither of these simplifying assumptions held. A comparison of empirically derived (Braden et al. 2011) and model optical PSFs for the center of the FOV and modeled optical PSFs for distal portions of the FOV demonstrated that there was a strong field-angle dependence to the structural details of the optical PSF. Evaluation of Mercury flyby observations acquired with the illuminated portion of the target just outside the FOV and optical modeling of similar observational circumstances demonstrated that the WAC was susceptible to out-of-field scatter onto the detector with a source azimuth dependence. These complicating instrument characteristics motivated the pursuit of a less elegant but more robust approach to the correction of WAC scattered and stray light. This approach used the instrument optical model to estimate the in-field and out-of-field light contributions to any given pixel within a WAC image.

In support of this effort, a comprehensive model of the WAC was created using FRED (not an acronym), ray-tracking and optical engineering software from Photon Engineering (Harvey et al. 2015). The WAC model includes all of the relevant hardware components and instrument characteristics, and the assembly of this model required the specification of the spectral scattering behavior of every internal instrument surface that could be directly or indirectly illuminated in the instrument. The FRED modeling system was used to generate a suite of spatially resolved signal contribution maps for a $50 \times 50^{\circ}$ area encompassing the $10.5 \times 10.5^{\circ}$ WAC FOV as well as enough of the surrounding angular space to capture all significant out-of-field sources. Within the FRED model, a $32 \times 32$ raster of elements across the $1024 \times 1024$ element detector was serially illuminated, with rays propagating “backwards” through the MDIS-WAC optical model and recorded on a sampling grid in object space (Fig. 14). Reciprocity allows the recorded intensity on the source-space sampling grid to be recast as a source probability map for the illuminated detector element. The aggregate of all $32 \times 32$ contribution maps is shown in Fig. 15 and represents the probability that an out-of-field source will end up on the detector by scattering off a particular element within the camera. This presentation of the FRED modeling results illustrates the key WAC hardware components that direct out-of-field light onto the detector—the baffle, detector pins, and an exposed gold strip adjacent to the detector—as well as the corresponding locations of these components in object space where there is a significant unintended ray path.

Fig. 14

Visualization of the FRED optical engineering software model of the WAC. Rays (yellow) are traced from an illuminated detector element, though the WAC instrument model (red and blue), onto a sampling grid in object space (green)

Fig. 15

Aggregate of $32 \times 32$ contribution maps calculated with the FRED modeling system. The intensity of light is shown on a $\log_{10}$ scale to highlight both the intended in-field ray paths, which fall on the detector raster, and the dominant out-of-field contributions, which come from the baffle and hardware elements physically adjacent to the active area of the detector—pins and a gold strip

The quantitative application of the FRED optical modeling results to a given WAC image requires the radiance both within and surrounding the FOV at the time of acquisition to be determined (Fig. 16). Using attitude information for the MESSENGER spacecraft and a custom instrument kernel that encodes the oversized FOV geometric information, a customized derived data record (DDR) containing latitude, longitude, incidence angle, emission angle, and phase angle information for every pixel in a synthetic oversized FOV for the acquisition circumstances of a given source observation is generated, and the latitude and longitude are used to sample a reference WAC mosaic (Fig. 16b). The custom DDR illumination and viewing information is used to calculate model bidirectional reflectance for each pixel in the synthetic oversized FOV using a photometric model and the reference mosaic. The solar distance of Mercury at the time of the source observation acquisition and the solar flux for the filter under consideration are then used to transform the pixel-scale $I/F$ in the sampled image to radiance (Fig. 16c). By using the FRED model to determine the locations and radiance of out-of-field scattered light (Fig. 16d), it is clear that the scattered light in a particular image will depend on the illumination conditions and the geological features, such as high-reflectance crater ejecta, that are outside the WAC FOV.

Fig. 16

The processing steps used to calculate the radiance of a synthetic oversized FOV image and then model the contributions of out-of-field scattered light to the image. (a) Example image CW0249466927G. (b) Synthetic extended FOV image sampled from an MDIS WAC G-filter mosaic, with the actual FOV of image CW0249466927G outlined in blue. (c) Model radiance image for the synthetic oversized FOV. The reference reflectance data from the WAC mosaic, the pixel-specific photometric model, and the solar spectral irradiance information appropriate to conditions at the time image CW0249466927G was acquired were all combined to produce a spatially resolved model of the radiance field over the extended FOV. Pixels that correspond to unpopulated areas of the mosaic used in this case are filled by the photometric model. (d) Aggregate FRED out-of-field contribution map shown at 33% transparency over the model extended FOV radiance image. This panel highlights how variations in illumination and geology (e.g., high-reflectance craters outside the FOV) can affect the amount of scattered light within a particular image

The scoring of a given WAC observation for expected excess (out-of-field) signal consists of spatially reconciling the FRED ray-tracing model contribution maps and the synthetic oversized FOV model radiance image, along with the sampling of the model out-of-field radiance by the FRED ray-tracing results, to determine the magnitude of the excess signal present in the calibrated CDR (Fig. 16d). To establish a basis for comparison, an empirical approach to scoring individual images for radiometric discrepancy was also established. The empirical radiometric discrepancy score was calculated as the weighted average of the cumulative distribution function discrepancies (after photometric correction) between the image under consideration and all the common-filter images that intersect, with the weighting set by the intersection area. There was a positive but weak correlation between the FRED scores and image discrepancy scores for the WAC image sets under consideration, but the FRED score distribution was unexpectedly compact and lacked the long tail expected for a relatively small number of images that appeared to be severely impacted by out-of-field scatter.

In addition to the scalar scores, both the optical model and empirical approaches to the evaluation of out-of-field radiometric contribution and data set radiometric inconsistency also allow for the derivation of spatially resolved correction and/or residual images. The spatially resolved presentation of the modeling and calculation results demonstrated that the out-of-field scatter was not the only significant component of the observed data set radiometric inconsistency, and that a portion of the spatially resolved residual structure isolated for a subset of the MDIS-WAC filters was consistent with a flat-field calibration residual.

Following the completion of the “final” WAC radiometric calibration, described in the preceding sections, the approach to isolating a spatially resolved radiometric residual pattern for a set of overlapping observations was repurposed to improve the radiometric consistency of high-science-priority regional multispectral image mosaics. One such mosaic, of the region surrounding the “b30” basin (Fassett et al. 2012) (Sect. 9.3), consists of 142 three-color image sets and 1748 binary intersections per filter (Fig. 17). The overlap area statistics and spatial sampling of the constituent observations for each overlap were interrogated and the radiometric discrepancy recorded as a function of detector position. The accumulation of discrepancy summary statistics resulted in a data-set-specific residual pattern (Fig. 18). In the simplest implementation, both the accumulation and application of the residual pattern are multiplicative, in which case the residual pattern can be interpreted as a mosaic-specific refinement to the flat field that to first order compensates for scattered light. An illustration of the improved radiometric consistency across the b30 mosaic with the empirical radiometric residual correction is shown in Fig. 19. The same method was also used to derive the mosaic-specific residual for the Caloris targeted mosaic (Sect. 9.3).

Fig. 17

A count map showing the number of times a given spatial location is covered by images in the b30 mosaic. The map is shown in a Lambert azimuthal equal-area projection with spatial dimensions given in reference to a unit sphere. The coverage density ranges from a single image (light blue) to 21 observations that overlap a common spatial location (dark blue)

Fig. 18

Multiplicative radiometric residual pattern for the b30 mosaic. The residuals for the 1000-, 750-, and 430-nm filters are displayed in red, green, and blue, respectively. A linear stretch from 0.96 to 1.04 has been applied to each band

Fig. 19

Examples showing the effects of applying the multiplicative residual pattern shown in Fig. 18 to images from the b30 mosaic. (a) One three-color image set highlighting the gradients in color across the scene. (b) The same image set after correction shows a more uniform color. (c) A portion of the b30 mosaic, created by overlaying images in the order in which they were acquired. Numerous image boundaries show mismatches in color, several of which are indicated by arrows. (d) The same portion of the b30 mosaic after correction. The mismatches in color along image boundaries are greatly reduced. In each panel, the 1000-, 750-, and 430-nm filters are displayed in red, green, and blue respectively

5 In-flight Geometric Calibration

Knowledge of the pointing of each pixel in an MDIS image relative to Mercury is required for cartography and photogrammetry, in particular to construct mosaics and topographic models of Mercury’s surface, and to coregister multispectral images from individual frames taken through different WAC filters. The goal for precision of pointing knowledge before application of control using feature identification in Mercury images is 150 μrad (6 NAC pixels) image to image (Hawkins et al. 2007). Four major factors contributing to precision and accuracy of pointing knowledge are knowledge of the WAC and NAC focal lengths and radial distortions, knowledge of their relative pointing as they pivot together as a fixed assembly, knowledge of pointing of the cameras within the pivot plane as the pivot moves, and knowledge of the pointing of the fixed base of the pivot. Each of these elements in MDIS pointing knowledge was characterized in detail during flight, in each case markedly improving the knowledge attained during ground calibrations, as described by Hawkins et al. (2007).

This knowledge is recorded using the Spacecraft, Planet, Instrument, Camera pointing, and Events (SPICE) software package, as a series of matrices or “kernels” that provide the relationship of pixel pointing to the surface of Mercury. The key elements in the “chain” of kernels that provide this connectivity are shown in Fig. 20. Static relative orientations are included in the frames kernel (fk) and dynamic and time-variable orientations in c-kernels ($\mbox{ck}n$). Angular relations within the NAC or WAC FOV are included in the instrument kernel (ik).

Fig. 20

Hierarchical representation of the chain of static and dynamic angular and positional relationships between WAC and NAC pixels and the surface of Mercury

In the discussion below we ignore the planetary constants kernel (pck) describing Mercury and the spacecraft c-kernel (ck1) describing the position and orientation of the spacecraft structure on which MDIS is mounted. We do note, however, that orientation of the spacecraft in the latter kernel is an interpretation; what is actually represented is a transformation of the attitude reported by the star camera that is propagated over times without valid star camera data by the inertial measurement unit (Leary et al. 2007). Working from the CCD outward (“up” the chain), we describe inflight characterization of the WAC and NAC FOV including effects of focal length and distortion as represented in the ik (Sect. 5.1), the relative alignments of the WAC and NAC to the MDIS pivot represented in the fk (Sect. 5.2), the time variable-pointing of the pivot (ck2), including accurate calibration of pivot position (Sect. 5.3), as well as temporal creep in the attitude of the instrument base holding the pivot (Sect. 5.4). For these discussions, cognizance of the spacecraft and instrument coordinate systems is relevant; these are shown in Fig. 21 on NAC and WAC images.

Fig. 21

Spacecraft and image coordinate systems shown on WAC and NAC images taken nearly simultaneously after the first Mercury flyby. Note that the two camera coordinate systems are rotated approximately 180° from each other: with the spacecraft sunshade-surface normal ($-y$ axis) pointed at the Sun, the Sun appears to the right in WAC images and to the left in WAC images with the image shown properly with the origin at upper left. The spacecraft $+z$ axis is pointed outward nearly along the camera boresights when the pivot is pointed orthogonal to the $x$ axis

5.1 Focal Lengths and Distortions

The WAC is a four-element refractive telescope with unpowered filters in the filter wheel mounted between the last lens element and the CCD detector. The thickness of each filter is tailored to minimize chromatic aberrations over the bandpass of the given filter (Table 4). The differences in filter thickness result in the focal length being wavelength-dependent. Hawkins et al. (2007) reported static, temperature-independent nominal focal lengths of the telescope through each filter from the instrument design, which together with the 14-μm pixel pitch of the detector predict the WAC’s $\sim179\mbox{-}\upmu \mbox{rad}$ instantaneous field of view (IFOV). WAC multispectral images from the first Mercury flyby, which contained abrupt brightness boundaries at all scales, yielded registration artifacts that demonstrated the design focal lengths to be slightly different from the as-built focal lengths.

Table 4 MDIS designed and flight-calibrated focal lengths as functions of temperature

The focal length of the WAC was recalibrated in flight as a function of temperature, using two data sets that accumulated over the course of the mission. One data set consisted of star images taken through the WAC clear filter at different pivot positions (“pivot calibrations” and “thermal calibrations” from Table 2); these hundreds of images sampled the full operational range of the WAC telescope from orbit about Mercury (Fig. 22). To derive the fits, for each image, stars were centroided and their distances compared with known angular separations using a star catalog. Focal length was solved for each image using the relation of pixel distance to angle derived with a root-mean-squared (RMS) fit as a function of temperature, assuming as a known the 14-μm pitch of the CCD pixels. The solutions at many temperatures were fit to a polynomial of the form

$$ F ( T ) =A0+A1\times T +\cdots + An\times T^{n} $$

(3)

where $F(T)$ is focal length as a function of temperature, $T$ is telescope temperature in degrees Celsius, $A0$ is the reference value at $0~^{\circ}\mbox{C}$, and $A1$ through $An$ are polynomial coefficients. Only a first-order, linear expression was required, and the change in scale over the operational temperature range is equivalent to a pixel over the $1024\times1024$ pixel FOV.

Fig. 22

Measurement of WAC focal length from clear-filter star field images, acquired over the operational temperature range of the WAC telescope. The green line is the fit used to derive the clear filter parameters listed in Table 4. This temperature is distinct from and warmer than the CCD temperature discussed in Sect. 4

The other data set is the set of WAC multispectral and NAC images of Mercury collected through all filters with Mercury filling the field-of-view (including dedicated “coalignment calibrations” in Table 2, as well as selected image sets taken during color mapping campaigns). The focal lengths of other filters were determined, as part of the process of stereophotoclinometric modeling (Gaskell et al. 2008) of Mercury’s shape. The temperature dependence of the WAC focal length was assumed to apply to all of the other images. Resulting temperature-dependent WAC focal lengths for all filters are listed in Table 4.

NAC focal length was determined using similar procedures. However, the NAC bandpass filter (designed to preclude saturation in Mercury images acquired at low phase angle near perihelion) resulted in relatively few stars being detectable across the NAC FOV. To yield sufficient detections, the star fields used were open clusters rich in relatively bright stars, such as the Pleiades imaged through the NAC and WAC clear filter as part of these “coalignment calibrations.” Sixteen WAC–NAC co-aligned sets with a total of 544 images were acquired at temperatures ranging from $-30~^{\circ}\mbox{C}$ to $20~^{\circ}\mbox{C}$. Focal length was fit as a function of temperature as for the WAC; values are given in Table 4.

The results of the above calibrations yield for the WAC clear filter a full FOV of 10.54° and an IFOV of 179.6 μrad, and for the NAC a full FOV of 1.493° and an IFOV of 25.44 μrad. However, neither FOV is perfectly square, due to optical distortions. The same calibrations described above were used to fit distortion models simultaneously with focal length.

The optical distortion for both cameras was modeled using a combination of three transformations that convert a three-dimensional (3-D) vector in instrument coordinates into pixel coordinates, i.e., pixel lines and samples. The first of these is the simple pinhole camera transformation that projects a 3-D vector in instrument coordinates ($x,y,z$) into ideal camera coordinates ($x _{i},y _{i}$):

$$ \binom{x_{i}}{y_{i}} = \frac{F ( T )}{z} \binom{x}{y} $$

(4)

where $F(T)$ is the temperature-dependent focal length in millimeters. The next transformation accounts for optical distortion from the ideal camera coordinates ($x _{i},y _{i}$) to the distorted coordinates ($x _{d},y_{d}$) via a translation of deviation terms $\Delta x$ and $\Delta y$.

$$ \binom{x_{d}}{y_{d}} = \binom{x_{i} +\Delta x}{y_{i} +\Delta y} $$

(5)

The final transformation takes the distorted coordinates ($x _{d},y_{d}$) in units of millimeters and converts them into pixel lines and samples ($s,l$) that have units of pixels:

$$ \binom{s}{l} = \left ( \textstyle\begin{array}{c@{\quad}c} K_{x} & K_{xy}\\ K_{yx} & K_{y} \end{array}\displaystyle \right ) \binom{x_{d}}{y_{d}} + \binom{s_{0}}{l_{0}} $$

(6)

where ($s_{0},l _{0}$) is defined to be the center of the detector, 512.0 pixels. The diagonal terms $K _{x}$ and $K _{y}$ scale into units of pixels while the off-diagonal terms $K _{xy}$ and $K _{yx}$ introduce shearing.

The WAC distortion transformation is modeled as an on-axis reflector with slight “barrel” and “keystone” distortions. From an origin at the center of the image, this distorted pixel position is modeled with the expression

$$ \binom{\Delta x}{\Delta y}_{WAC} = \left ( \textstyle\begin{array}{c@{\quad}c@{\quad}c@{\quad}c@{\quad}c@{\quad}c} - y_{i} r_{i} & x_{i} r_{i}^{2} & - y_{i} r_{i}^{3} & x_{i} r_{i}^{4} & x_{i} y_{i} & x_{i}^{2}\\ x_{i} r_{i} & y_{i} r_{i}^{2} & x_{i} r_{i}^{3} & y_{i} r_{i}^{4} & y_{i}^{2} & x_{i} y_{i} \end{array}\displaystyle \right ) \left ( \textstyle\begin{array}{c} e_{1}\\ e_{2}\\ e_{3}\\ e_{4}\\ e_{5}\\ e_{6} \end{array}\displaystyle \right ) $$

(7)

where $r_{i} ^{2}=x _{i} ^{2}+ y _{i} ^{2}$. $e _{1}$ and $e _{3}$ are tangential distortions, $e _{2}$ and $e _{4}$ are radial, and $e _{5}$ and $e _{6}$ are keystone. In the best-fit solution using the temperature-dependent focal length, only radial and keystone distortions are present; the same model is applicable to all filters:

$$\begin{aligned} e _{1} =& 0.0\quad (\mbox{fixed}) \\ e_{2} =& 5.509\times10^{-6} \\ e _{3} =& 0.0\quad (\mbox{fixed}) \\ e _{4} =& 0.0\quad (\mbox{fixed}) \\ e_{5} =& 3.600\times10^{-6} \\ e_{6} =& -7.721\times10^{-5} \\ k _{x} =& 71.429\quad (\mbox{fixed}) \\ k_{y} =& 71.440 \\ k _{xy} =& 0.0\quad (\mbox{fixed}) \\ k_{yx} =& -6.761\times10^{-4} \end{aligned}$$

The NAC is an off-axis reflector with an optic axis well outside its FOV. This geometry, shown in Fig. 23, proved difficult to model. The chosen model is based on that of Seidl et al. (2010). The expression used to represent that model is:

$$ \binom{\Delta x}{\Delta y}_{NAC} = \binom{Rx_{i} r_{i}^{2} +2 Kx_{i} y_{i} +A x_{i}}{Ry_{i} r_{i}^{2} +B r_{i}^{2} +2S y_{i}^{2}} $$

(8)

The best fit solution yielded

$$\begin{aligned} R =& 1.004\times10^{-5} \\ K =& -2.547\times10^{-4} \\ A =& 1.854\times10^{-3} \\ B =& 9.060\times10^{-4} \\ S =& -2.743\times10^{-4} \\ k _{x} =& 71.429\quad (\mbox{fixed}) \\ k _{y} =& 71.429\quad (\mbox{fixed}) \\ k _{xy} =& 0.0\quad (\mbox{fixed}) \\ k _{yx} =& 0.0\quad (\mbox{fixed}) \end{aligned}$$

Fig. 23

Ray-trace analysis of the angular relations of corners of $64\times64$ pixel boxes for the NAC projected to infinity, compared with the pixel locations on the CCD. The square grid represents the locations of the corners of the pixel boxes, and the “×” symbol shows their projected locations. The distortion of the projected locations has been exaggerated by a factor of 20 for clarity; the actual maximum distortion is 0.7%

Focal length and distortion of both cameras are recorded in the MDIS instrument kernel (Stephens and Turner 2015).

5.2 NAC–WAC Alignment

Because of its extensive characterization, the WAC clear (B) filter has been used as the reference for the alignment of other WAC filters and the NAC. By default, the other WAC filters are assigned the same boresight; however, FOVs vary as described in Sect. 5.1.

Relative alignment of the NAC and WAC was an additional outcome of the co-alignment calibrations. As is barely evident from inspection of Fig. 21 (after accounting for the flipped image orientation), the NAC is offset about 1.3 μrad from the WAC in the sunward (spacecraft $-y$) direction and slightly twisted. The translation and rotation from the WAC to NAC reference frame is given by Nguyen and Turner (2013) in the MESSENGER frames kernel:

$$\begin{aligned} \left ( \textstyle\begin{array}{c@{\quad}c@{\quad}c} -9.9982 \times10^{-1}& 1.8816 \times10^{-2}&1.6808 \times10^{-3}\\ -1.8816 \times10^{-2}& -9.9982 \times10^{-1}&3.8964 \times10^{-5}\\ 1.6812 \times10^{-3} & 7.3317 \times10^{-6}& 1.0000 \end{array}\displaystyle \right ) \end{aligned}$$

5.3 Pivot Angle Calibration

NAC image mosaics acquired during the first flyby of Mercury, in January 2008, exhibited significant misalignment between rows of image frames, which were acquired at different pivot positions as the Sun-Mercury-spacecraft (phase) angle changed rapidly around the time of closest approach. To measure the systematic errors in pointing knowledge, NAC mosaics were overlaid on WAC images projected onto a sphere and rendered from the NAC’s viewing geometry. This comparison demonstrated errors in converting telemetered pivot position to pivot angle larger by more than a factor of 3 (to $>20~\mbox{NAC}$ pixels; Fig. 24, black symbols) than the $\sim150~\upmu \mbox{rad}$ goal (6 NAC pixels) for precision of pointing knowledge (Hawkins et al. 2007). This error was traceable to usage of telemetry from the pivot. There are two possible approaches to measuring pivot position, using the position resolver included in the instrument, or dead reckoning using counted motor steps (Hawkins et al. 2007). During instrument integration and testing, excessive noise in data from the pivot position resolver was introduced by test equipment, invalidating resolver calibration; the noise led to a mistaken interpretation that the resolver was unreliable. A linear transformation of the raw count of pivot motor steps was used instead to estimate angular position within the pivot plane, for the first three and a half years of the mission through the first Mercury flyby. This approach ignored nonlinearity in the relation between pivot step count and pivot angle. Inspection of specifications of the pivot system suggested that the harmonic drive gear would result in a non-linear relationship that could be modeled.

Fig. 24

Errors in pivot position resulting from the original linear transformation of motor step counts (black plus symbols), the non-linear conversion of pivot step counts that models behavior of the harmonic drive (green diamonds), and the resolver as calibrated in flight (red triangles). Each NAC pixel is 25 μrad, and each telemetry count of pivot position is 95 μrad

To quantify the non-linear relation between pivot step count and pivot angle, a series of inflight WAC clear-filter star images was designed to characterize the relation in detail at the center and the lower and upper bounds of the range of angles expected to be most used during Mercury orbital imaging, the 0°, $-8^{\circ}$, and 28° positions, respectively. A single star was imaged near each of the three positions, and two sets of images were obtained at the 0° and $-8^{\circ}$ positions. In order to sample the entire harmonic drive response at each location, several dozen images were obtained within a 3° range centered at each position.

In an initial correction to reduce systematic errors in pivot pointing knowledge, a model for the harmonic drive was created through Fourier spectral analysis of the test data, which proved consistent with that expected from the harmonic drive design. Ground software was updated with a harmonic drive model that minimized the RMS difference between the star location within the image and the modeled location. The result improved the RMS error from 12.6 NAC pixels for the linear model to 6.8 NAC pixels for the non-linear harmonic drive model (Fig. 24, green symbols).

Two effects dominated residuals from the harmonic drive model. The first was a so-called “turn-around effect.” The star imaging was completed in such a manner that the pivot changed directions halfway through the sequence; residuals exhibit relatively consistent sign and magnitude in each of the “forward” versus “backward” directions. The second effect is power cycling of the instrument data processing unit (DPU), which required “homing” the MDIS pivot to regain positional knowledge, by backing it up against a hard stop at a known position. However at each homing, between 0 and 4 150-μrad motor steps could be skipped, introducing new and accumulating error from dead reckoning. Overcoming this effect would require inflight star calibrations—and segmentation of the harmonic drive model—at each homing, a burdensome procedure that would also require bookkeeping of homing events (not recorded in instrument telemetry) from the command history.

Instead, a second update to the pivot position measurement approach was made by calibrating the resolver in flight and using it as designed. Contrary to expectations from ground testing, the resolver fully functioned in flight, and at the locations of the star calibrations the RMS precision error was within 1 NAC pixel regardless of the direction of pivot. To leverage the motor-step-to-angle model in calibrating the position resolver, what was missing was a resolver-to-motor-step relation. Away from changes in direction, the forward and backward harmonic drive models are offset by a constant value. Therefore, a test was designed that would scan the entire pivot plane in order to obtain a resolver-to-motor-step relation from telemetry. This scan was completed in both directions to provide two samples of the curve, and the data were downlinked in the form of telemetry attached to “throwaway” images to which the maximum possible pixel binning and lossy compression were applied. Each curve formed from the returned data was line-subtracted and adjusted to have zero mean so that the forward and backward data could be combined. A Fourier analysis of these data was completed to obtain a “predicted” resolver-to-motor-step positional offset as a function of pivot position, and the angle was obtained by combining that with the harmonic drive model. Two sets of WAC clear-filter star images were obtained at the 0° and $-22.9^{\circ}$ positions to validate the model and to verify absence of the noise in the resolver values observed in ground data. The result of these flight tests and analyses is a pivot position resolver calibration that is unaffected by DPU power cycling, directional dependencies, or changes in the direction of pivot motion. The RMS error of 1.2 NAC pixels (Fig. 24, red symbols) is smaller than uncertainties in reported spacecraft attitude (about 3 NAC pixels).

The calibrated pivot position as a function of time is stored as the MDIS pivot c-kernel, which is available online at https://naif.jpl.nasa.gov/pub/naif/pds/data/mess-e_v_h-spice-6-v1.0/messsp_1000/data/ck/msgr_mdis_gm040819_150430v1.lbl.

5.4 Pivot Base Calibration

During the cruise and orbital mission phases, numerous calibrations of the orientation of the pivot base were conducted (pivot and thermal calibrations, Table 2). At each such calibration, WAC clear-filter images were used to create five vectors representing WAC pointing at five different pivot positions, thus defining a plane. The pointing of the pivot base was defined as the closest vector in that plane to the spacecraft $+z$ axis, i.e., with the pivot nearly normal to the spacecraft instrument deck. It was originally envisioned that pivot orientation calibrations would measure two separate effects, the reference orientation of the pivot base (pivot calibrations), and the elastic perturbation of that orientation by transient heating of the MDIS instrument structure near periapsis during orbit (thermal calibrations). This expectation was based on the orientation history of the Near Earth Asteroid Rendezvous multispectral imager, which was highly correlated with temperature of the spacecraft structure (Murchie et al. 2002). The actual behavior proved more complicated, which led to a continued regimen of pivot calibrations throughout the orbital phase.

One behavior that occurred was change in the pivot orientation on a timescale of less than weeks. A change of about 400 μrad occurred at or near the time of Mercury orbit insertion when the spacecraft main engine executed its largest burn and the spacecraft thermal environment underwent a marked change (Fig. 25). Another change about half as large occurred in summer 2012, then reversed itself, at a time when the spacecraft experienced a seasonal temperature peak.

Fig. 25

Individual measurements of the orientation of the MDIS pivot base during cruise (blue) and in the months following Mercury orbit insertion (red)

More gradual changes occurred throughout the orbital phase of the mission. From orbit insertion through summer 2013, with the exception of the excursion in summer 2012, the pivot orientation slowly changed along a trend that can be modeled linearly as a function of time (Fig. 26). That gradual change ceased in summer 2013, and pivot orientation remained relatively stable for the remainder of the MESSENGER mission.

Fig. 26

Individual measurements of the orientation of the MDIS pivot base in the post-orbit-insertion reference frame, fit with a trend line for the period March 2011 through July 2013 (exclusive of the anomaly in summer 2012)

It is not known whether these apparent changes in orientation of the pivot base reflected actual physical movement of MDIS within tolerances of its mounting bolts, similar movement of the star camera, or deformation of the intervening spacecraft structure. For simplicity, these changes are incorporated into the MDIS pivot c-kernel described in Sect. 5.3.

6 Control Networks and Digital Elevation Models

The quality of mapping products, such as digital elevation models (DEMs), greatly depends on the accurate determination of the image position and pointing parameters. Initial estimates for these parameters were provided by the MESSENGER navigation team in the form of spacecraft position and attitude data collected from the navigation system on the spacecraft during image acquisition. These data are provided in the form of the Spacecraft and Planet kernels (SPK) and Spacecraft (attitude/pointing) kernels (CK) that are attributed to every image at the precise time they are acquired. The uncertainty in these data—described above typically to be on the order of 100 μrad after application of inflight calibrations—leads to registration errors between images that directly impact the quality and integrity of cartographic map and topographic DEM products.

To correct for these errors, a control process was applied using the Integrated Software for Imagers and Spectrometers (ISIS; Anderson et al. 2004) system. This process consists of two major steps: (1) creation of a control network (Becker et al. 2017a) that consists of measurements of common features found in overlapping images, and (2) minimization of registration offsets through a photogrammetric technique known as a least squared bundle adjustment (Edmundson et al. 2012). The bundle adjustment process solves for the local planetary radius at each control point (comprised of common measurements) in the network that are then used to produce a DEM using interpolation. The process also updates the individual pointing attitude of each image to minimize the overlapping image co-registration errors. Products derived from this process were a DEM (Becker et al. 2016) and smithed CK kernels, which contain the corrected pointing for each image. These products were used to process MDIS images (Sect. 8) to create the final orthorectified cartographic map products (Sect. 9). The creation of the control networks and DEM are summarized below; full details can be found in the DEM Software Interface Specification document (Becker et al. 2017b).

6.1 Creation of Control Networks

Control networks are a critical input element to the bundle adjustment process. A minimally acceptable network for purposes of control identifies at least three well-distributed measures per image in all overlapping images that contain the same feature. However, to create an interpolated DEM from the control network, a high density of well-distributed control points is required. In addition, constraints on individual image observation parameters must be applied when creating a DEM from the control point network.

6.1.1 DEM Control Network

A subset of MDIS NAC and WAC-G filter images were selected that were constrained by resolution and observation geometry. Table 5 shows the constraints applied to the all MDIS images acquired during the orbital phase of the MESSENGER mission at Mercury. These parameters were chosen so that a DEM could be created at better than 1 km/pixel sampling. Note that the geometry constraints were essentially eliminated at Mercury’s poles since there are areas where the Sun never illuminates the surface.

Table 5 Resolution and geometry constraints applied to MDIS NAC and WAC-G images for control

Of 176,352 NAC and WAC-G images evaluated, 101,177 met the constraints in Table 5. Individual image-based control networks were created that consisted of a reference image and all images that had at least 3.5% of common overlap. Common features were then identified in overlapping regions of the images using Open Source Computer Vision (OpenCV) feature-based image matching algorithms to detect, extract, and match common features in images. We chose the Features from Accelerated Segment Test (FAST; Rosten and Drummond 2005) detector, Scale Invariant Features Transform (SIFT; Lowe 2004) extractor, and BruteForce matcher algorithms to successfully match 100,432 of the images (99.2%).

All 100,432 image-based networks were then combined into a single global network. This process involved the creation of a k-dimensional binary tree structure (kd-tree) of control points from all image-based control networks in order to perform efficient range or nearest-neighbor searches, which was then queried to find all control points with common measures that are less than or equal to an average of 1 pixel from one another (i.e., control points of the same surface feature). The final step prior to bundle adjustment is to combine these points of the same feature into a single control point, which increases the number of images in each control point.

A bundle adjustment was then run on the global control whereby the pointing angles were constrained to $\pm0.2^{\circ}$ and points to $\pm10~\mbox{km}$ radius. After adjustment, the average RMS error in sample and line was 0.85 pixels. From this resulting network, the DEM was created. The smithed CK kernels associated with this DEM control network are archived at the PDS Navigation Node as msgr_mdis_sc20<yy>_usgs_v<d>, where yy is the year and d is the version number.

6.1.2 Color Control Network

Because of the constraints applied to image resolution and geometry parameters, not all WAC G-filter images were included in the DEM network. This meant that many of the images that were part of the regional and global color mosaics would not have had updated pointing, and because those products were created as averages of all overlapping images (Sect. 9), this omission resulted in reduced spatial resolution (Fig. 27). Thus, a second control network was created that included all G-filter images identified in those mosaics (an additional 2,190 images).

Fig. 27

A portion of the three-color mosaic showing the Rachmaninoff basin (306 km diameter, centered at 27.7°N, 57.4°E) in enhanced color created from a principal component (PC) analysis with PC2 and PC1 displayed in red and green, and the ratio of the 430- to 1000-nm filters displayed in blue. (a) The mosaic created from images and standard SPICE kernels without updated pointing; all images from this campaign with each filter were averaged to increase signal-to-noise ratio and to minimize calibration and/or scattered light artifacts, but this process led to “blurring” from misregistration. (b) The same mosaic created with updated pointing from the control network, which results in a marked improvement in resolution

The processing for this network was different from that for the initial DEM network. The pointing to all of the DEM NAC and WAC images was updated, and the DEM was used to orthorectify the point geometry for subsequent processing. All control point measures were co-registered to the sub-pixel level. All overlapping images for each of the additional 2,190 images were identified, and new image-based control point networks were created. The control measures were registered to the sub-pixel level and combined with the DEM network by merging these control points with points in the global network. A bundle adjustment was then run on this network with the same constraints as those applied in the DEM bundle adjustment, and all image pointing was updated. Note that this result was biased toward the DEM control and provides continuity with those images and the DEM for orthorectification of the color map products. The smithed CK kernels associated with this color control network are archived at the PDS Navigation Node as msgr_mdis_sc20<yy>_wacg_usgs_v<d>.bc, with the same naming convention as described above.

For each color set, all other WAC filters were coregistered to the controlled WAC G-filter image and processed as described in Sect. 8 to produce the final products.

6.2 DEM Creation

A global DEM of Mercury was created with ISIS by interpolating the local radius values at each control point from the bundle-adjusted control network. Statistics at each output DEM map pixel were produced to aid in the assessment of the resulting topographic map produced in standard cartographic projections.

A kd-tree was constructed from all the control points in the network, and queries were issued to select a set of the 11 closest points nearest to the center of each output map coordinate. From this set of points, a one-standard-deviation filter centered about the median radius was applied to eliminate outliers. The median of the remaining point radius values was selected and used to create the DEM in a global equirectangular map projection at 665 m/pixel. A series of boxcar smoothing filters was applied to the output map, and the final DEM product (Fig. 28) is available in the PDS. Comparisons with a DEM created with data from MESSENGER’s Mercury Laser Altimeter in Mercury’s northern hemisphere and from radio occultations in the southern hemisphere show general agreement, but the mean radius from the MDIS DEM is 75 m larger, with $\sim5\%$ smaller values for oblateness and elongation (Neumann et al. 2016).

Fig. 28

A colorized shaded-relief map of the final 665 m/pixel Mercury global DEM (Becker et al. 2016) in a Robinson projection centered at 180°E. Elevations relative to Mercury’s average radius are given in meters

7 Photometric Standardization

Photometric standardization (also called photometric correction or normalization) is used to standardize the calibrated value of reflectance in images obtained at a variety of illumination and viewing geometries to a common geometry, for the construction of mosaics and maps and for comparison with spectral measurements acquired in the laboratory. For the MDIS suite of images a comparison was made between the Hapke model (Hapke 1981, 1984, 1986, 1993, 2002, 2008, 2012) and the Kaasalainen-Shkuratov model (Kaasalainen et al. 2001; Shkuratov et al. 2011; Schröder et al. 2013) for providing the best algorithm for photometric standardization. The Kaasalainen-Shkuratov model was determined to provide the better solution for creating near-seamless mosaics for the illumination and viewing conditions under which the images in MDIS regional to global mapping campaigns were acquired (Domingue et al. 2016).

The form of the Kaasalainen-Shkuratov model used is given by

$$ \frac{I}{F} = A_{N} e^{-\alpha\mu} \biggl[ c_{l} \biggl( \frac{2\cos i}{ \cos i+\cos e} \biggr) + ( 1- c_{l} ) \cos i \biggr] $$

(9)

where $i$, $e$, $\alpha$ are the incidence, emission, and phase angles, respectively, $A _{N}$ is the normal albedo, $\mu$ is the phase function parameter associated with surface roughness, and $c _{l}$ is the disk-function partition parameter between Lommel-Seeliger-like (proportional to $\frac{2\cos i}{\cos i+\cos e}$) and Lambert-like (proportional to $\cos i$) scattering (Shkuratov et al. 2011). This equation was applied to 8-color observations acquired for the purpose of examining Mercury’s photometric properties, as described by Domingue et al. (2015, 2016), and then extrapolated to the remaining three narrow-band filters using procedures analogous to those described in Sect. 4.5 (Domingue et al. 2017).

The photometric measurements acquired with the 8-color photometric observations (Domingue et al. 2015, 2016) were modeled using a least-squares grid search that minimized $\chi^{2}$, defined as

$$ \chi^{2} = {\sum_{i=1}^{N} \sqrt{ ( r_{measured} - r_{model} )^{2}}} / {N} $$

(10)

where $N$ is the number of measurements, $r_{measured}$ is the measured reflectance, and $r_{model}$ is the modeled reflectance. All parameters were varied simultaneously. The resulting parameter values were then fit as a function of wavelength with a polynomial function (Domingue et al. 2016). The resulting polynomial provides parameter values that are smooth as a function of wavelength to avoid introducing spectral artifacts from round-off errors in the parameter values and to enable extrapolations to the filter wavelengths not sampled in the photometric observations (Domingue et al. 2017). The resulting model parameter values are listed in Table 6; the WAC G filter parameters are also used for the NAC.

Table 6 Photometric parameter values for the Kaasalainen-Shkuratov model, Eq. (9), for each MDIS filter (Domingue et al. 2016, 2017)

Images can be photometrically standardized to any set of incidence, emission, and phase angle values using the Kaasalainen-Shkuratov model. The image data used in mosaics delivered to the PDS have all been standardized to incidence, emission, and phase angles of 30°, 0°, and 30°, respectively. The multiplicative correction factor to these standardization angles is given by $C$, where

$$ C= \frac{{I}/{F} (i=30,e=0,\alpha=30)}{{I} / {F} ( i_{m}, e_{m}, \alpha_{m} )} $$

(11)

and where $i _{m}$ is the incidence angle of the observation, $e _{m}$ is the emission angle of the observation, $\alpha _{m}$ is the phase angle of the observation, and $I/F$ is calculated using Eq. (9) and the parameter values from Table 6.

8 Image Processing

The radiometric calibration (CDR), georeferencing (DDR), and photometric correction (Sect. 7) of MDIS images used to produce the advanced products delivered to the PDS (Sect. 9) was performed with the ISIS image processing system (Anderson et al. 2004). After images were imported as engineering data records (EDRs) and the appropriate spice kernels attached, the images were calibrated using the updates described in Sect. 4 (CDR version 5), orthorectified with the global Mercury DEM (Sect. 6), and photometrically standardized using the model of Kaasalainen-Shkuratov (Sect. 7). For the photometric standardization, photometric angles were calculated relative to a sphere because the DEM is typically of substantially lower resolution than the individual images. The assembly of the seven large-scale maps and the regional targeted mosaics was performed with the ACT Mshell system.

For color products, smithed kernels were available only for the G filter, and thus all other filters in a color set were co-registered to the G filter in sensor space. To adjust each image in a color set to the G filter image, a set of match points was first found with the Speeded Up Robust Features (SURF) methodology (Bay et al. 2008). The matched point set was filtered to remove outlier errors and then used to warp each image into the G-filter sensor frame. The warping approach used the homography (planar projective transformation) implementation in the OpenCV library. This implementation includes an additional match-point filtering pass completed with the RANdom SAmple Consensus (RANSAC) method provided in OpenCV. Then the images for each filter were map projected using only the corresponding G filter georeference information (DDR). The overlapping area for each color set could then be averaged into one of the color map products (Sect. 9.2).

9 Final Project Products

In total, seven large-scale mosaics of Mercury’s surface were produced from MDIS images, along with numerous local mosaics of areas targeted as of special interest to science throughout the mission and a set of DEM products that range in scale from global to local (Table 7). Each of the large-scale mosaics was created from all images that best met the desired characteristics, regardless of the orbital campaign (Table 2) in which the image was originally acquired. All of the MDIS final project products listed in Table 7 are archived in the PDS, and each of the image mosaic products has been photometrically standardized to a solar incidence angle of 30°, an emission angle of 0°, and a phase angle of 30° (Sect. 7). These products form a complementary and extensive set of mosaic products that enable Mercury’s surface to be investigated from a diverse set of viewing, lighting, imaging, multispectral, and resolution conditions. The DEM products complement the image mosaic products and enable topographic studies. All of these products also facilitate comparisons with surface measurements from other MESSENGER instruments. Additional details follow for the four main categories of products: monochrome global maps, multispectral global and regional maps, regional targeted mosaics, and MDIS DEM products.

Table 7 MDIS final advanced products available in the PDS

9.1 Monochrome Global Maps

Four global monochrome maps (Table 7) were produced from MDIS orbital images and are available in the PDS: the Basemap Reduced Data Record (BDR), the Low-Incidence-Angle Basemap Reduced Data Record (LOI), the High-Incidence-Angle Basemap Illuminated from the East Reduced Data Record (HIE), and the High-Incidence-Angle Basemap Illuminated from the West Reduced Data Record (HIW). In the PDS, these maps are available through a series of files, with each of Mercury’s non-polar quadrangles (Davies et al. 1978) divided into four tiles (corresponding to the northwestern, northeastern, southwestern, and southeastern potions of each quadrangle) and one tile for each of the north and south polar quadrangles. Combining these 54 components produces a map with global coverage. These four monochrome maps provide complementary views of Mercury’s surface under a range of lighting conditions, as shown in the example region in Fig. 29.

Fig. 29

The region near Villa-Lobos crater (67 km diameter, centered at 5.24°N, 6.93°E, simple cylindrical projection) illustrates the complementary views provided by the four final monochrome global map products: (a) moderate-incidence-angle view in the BDR basemap, (b) high-incidence-angle view with illumination from the west (HIW), (c) high-incidence-angle view with illumination from the east (HIE), and (d) low-incidence-angle (LOI) view

The four monochrome global maps were produced as “stacked” mosaic products, meaning that images were sequentially overlain on top of each other, with the “best” being visible on the “top” of the mosaic. “Best” was defined for each mosaic using a stacking metric optimized for the purpose of each map. The PDS files provide the detailed stacking metric approach that was applied to each map; early MDIS monochrome map products used stacking metrics that were often based on one or two equations or requirements, but further effort showed that improved results were achieved through greater manual inspection and control of the stacking process, especially at higher latitudes near the polar regions. Additionally, manual inspection of the products, aided by use of the ACT REACT software, led to the production of lists of images specifically excluded from the final products, in order to further refine the images that appear on the “top” of each stacked mosaic product.

In general, all NAC and WAC G (750 nm) images with pixel scales $> 50~\mbox{m}$ were considered for the initial creation of each of the four monochrome global map products, with multiple subsequent iterations leading to the final products. For example, 97,597 images were considered in creating the final BDR product. The MDIS-derived global DEM was used to orthorectify images in the final monochrome global mosaics, and the large majority of NAC and WAC G images in the monochrome mosaic products used the DEM control network (Sect. 6.1.1), resulting in improved registration between images. The monochrome global mosaic products in the PDS include six bands: the photometrically corrected surface reflectance value and backplanes that give the Observation ID value and stacking metric value for each image that is shown in the mosaic, and the solar incidence, emission, and phase angles (Fig. 30).

Fig. 30

Final monochrome global map products archived in the PDS contain six planes of data: (a) reflectance; (b) the Observation ID of each image shown in the mosaic; (c) solar incidence angle; (d) emission angle; (e) phase angle; and stacking metric value for each image (not shown in this figure). The examples shown in this figure are for the final BDR product in simple cylindrical projection centered at 0° longitude

9.2 Multispectral Global and Regional Maps

Three large-scale global and regional multispectral color products are included in the final MDIS products (Table 7) archived in NASA’s PDS: the 8-Color Multispectral Reduced Data Record (MDR), the 3-Color Multispectral Reduced Data Record (MD3), and the 5-Color Multispectral Reduced Data Record (MP5). In the PDS, these maps are available as a set of files that use the same tile scheme as the monochrome products. In contrast to the monochrome global maps, these multispectral products are created as average rather than stacked mosaics. The PDS documentation for each multispectral mosaic product provides the detailed criteria used to decide which images were included or excluded from each average mosaic product. In general, the images acquired for the MDR and MD3 were designed to minimize the solar incidence angle and the emission angle, whereas the images acquired to support the MP5 were designed to minimize the phase and incidence angles (and thus required higher emission angles at high latitudes).

Mosaics were produced by taking the average value of all images covering a geographic location (pixel) to determine the surface reflectance value in each filter. This process increased the signal-to-noise ratio and minimized artifacts due to residual calibration errors, scattered light, or incomplete correction for variations in illumination and viewing conditions. In addition to the reflectance bands, the multispectral mosaic products contain a band that gives the total count of WAC filter sets that contributed to the average. In total, the MDR consists of the average of 4992 WAC eight-color sets, the MD3 uses 7139 WAC three-color sets, and the MP5 was produced from 1121 WAC five-color sets. All of these multispectral mosaic products also have bands that give the standard deviation calculated along with the average value for each WAC filter, as shown in the example in Fig. 31. The MDIS-derived global DEM was used to orthorectify the images included in the final multispectral mosaic products, and all WAC G images in the multispectral products use the color control network (Sect. 6.1.2); the other WAC filters were registered to the corresponding WAC G image prior to generating the mosaic products (Sect. 8).

Fig. 31

(a) MDR multispectral mosaic product, shown with the 1000-nm, 750-nm, and 430-nm reflectance bands in red, green, and blue, respectively, in simple cylindrical projection centered on 0°E. In addition to the reflectance bands, the final multispectral global and regional map products archived in the PDS contain bands that provide (b) the total number of all WAC image sets that contribute to the average product at each pixel and (c) the calculated standard deviation from the average, with a separate band for each WAC filter (standard deviation band for the WAC 630-nm filter shown as the example)

The eight-color MDR provides near-global coverage through eight of the WAC narrow-band filters. In addition, the eight-color MDR archived in the PDS includes two types of alternate tiles. First, the archived MDR has two alternate south polar tiles. One version of the south polar tile limits the resolution to include only images with pixel scales $<2000~\mbox{m}$, consistent with the rest of the mosaic; the alternate version includes images with lower resolution up to 2700 m/pixel to increase the coverage of the south polar region. Second, the MDR has five alternate tiles covering portions of quadrangles H01 and H03 (region shown in purple in Fig. 32) that include only images with pixel scales $<500~\mbox{m}$. These H01 and H03 alternate tiles are provided at a scale of 128 pixels per degree, rather than the 64 pixels per degree available for the full MDR map. These regions of the mosaic are available at higher resolution because during the periods of time when these images were acquired, data volume constraints allowed these images to be downlinked without additional onboard pixel binning in the spacecraft’s main processor.

Fig. 32

The location and coverage of the final global and large-scale regional multispectral products in Table 7. The map is in simple cylindrical projection, centered at 0°E

Because of MESSENGER’s highly eccentric orbit, images of the northern hemisphere generally have higher spatial resolution than those for the southern hemisphere (when no pixel binning was used), and the three-color MDR is composed of images acquired at higher resolution than the eight-color MDR. Consequently, the three-color MD3 does not have global coverage but instead is limited largely to the northern hemisphere. Additionally, for the higher-resolution MD3 product, only three narrow-band WAC filters were used, because of considerations both of the total data volume and of the footprint overlap between the first and last WAC filter in a color set. When the spacecraft was closer to the planet in the north, its rapid motion relative to the ground resulted in only small amounts of overlap between all eight filters if the images were not binned (binning reduced the minimum interval between successive images from 4 s to 1 s). The five-color MP5 covers latitudes north of 60°N at a comparable resolution to the threecolor MD3, and the images for this mosaic were acquired at lower phase angles to minimize shadows. The regions covered in each of the multispectral mosaics are shown in Fig. 32, including the locations of the alternate MDR tiles, and the Caloris and b30 mosaics, which are described further in Sect. 9.3.

9.3 Regional Targeted Mosaics

In addition to the global and regional monochrome and multispectral mosaic products, a large number of local-area mosaics are also archived in the PDS as MDIS final products. These additional mosaics are termed “Regional Targeted Mosaics” (RTMs) because, as the name implies, the images that comprise these mosaics were acquired as purposefully targeted images, and each was acquired over a short time duration of the mission. This situation contrasts with the global and regional products described in Sects. 9.1 and 9.2, which are composed of images acquired over substantial durations of time, some spanning the entire orbital mission.

In total, 2541 final NAC RTMs (N01) are archived in the PDS (Table 7, Fig. 33A). The NAC RTMs are strips of NAC images acquired over a short period of time during individual MESSENGER orbits. These targets were selected through the use of the ACT REACT software by the MESSENGER science team, and generally the purpose was to acquire the highest-resolution imagery possible of a feature of special scientific interest, often under prescribed illumination conditions. Once a target was selected and entered in the target database via REACT, it was assigned a unique Site ID number, which was used to track it through selection, acquisition, processing, and ultimately archiving in the PDS. The target database produced is archived in the PDS with the RTMs and provides a description field relating the original scientific motivation associated with each Site ID. The NAC RTMs are in orthographic projection centered at the local latitude and longitude, at the minimum resolution of images acquired for that target, with the first image acquired stacked on the bottom of mosaic. The five bands of the NAC RTMs are the same as those of the monochrome global map products but without the stacking metric band: reflectance, image Observation ID, and incidence, emission, and phase angles.

Fig. 33

The locations of RTMs from the (a) NAC and (b) WAC, shown over the BDR monochrome mosaic in simple cylindrical projection, centered at 0°E. The WAC RTMs exclude the locations and extent of the Caloris and b30 RMTs, which are shown in Fig. 32

The large majority of the final WAC RTMs, 715 in total (Table 7, Fig. 33B), are composed of a single image set of WAC filters having a pixel scale $< 1000~\mbox{m}$. The three-color (containing “W03” in the file name) and eight-color (W08) WAC RTMs were acquired to provide multispectral views of the surface that are complementary to those of the global and regional multispectral products, such as higher in spatial resolution or imaged under different viewing or lighting conditions. The eleven-color WAC (W11) RTMs were acquired during the final half of MESSENGER’s orbital mission, providing the only color sets since MESSENGER’s flybys of Mercury that include all of the WAC’s eleven narrow-band filters. WAC RTMs were targeted using REACT, just as was done for the NAC RTMs, and each also has a corresponding Site ID, linking it to the PDS-archived target database. Along with a reflectance band for each of the WAC filters present in a given RTM, WAC RTMs have bands for incidence, emission, and phase angles. Numerous WAC image sets were also acquired as targeted observations to support the photometry campaign (Sect. 7), but these images generally had low spatial resolution ($>1000~\mbox{m/pixel}$) and hence are not included in the WAC RTMs; the photometric target images acquired are in the PDS, tagged as “Photometry” for the Observation Type (Table 2).

Finally, two three-color WAC RTMs are distinct from those detailed above and require specific description: Caloris and b30. In many ways, these two RTMs resemble regional versions of the three-color multispectral map product (MD3), in that each is an average product with the same bands as present in the MD3 mosaic product. Additionally, unlike the other WAC RTMs, the Caloris and b30 mosaics are not single WAC color sets but rather cover an extended region, as shown in Fig. 32. The Caloris RTM covers the Caloris basin and the b30 RTM covers an ancient basin, referred to as “b30” by Fassett et al. (2012). However, in contrast to the MD3 map, the Caloris and b30 RTMs were targeted for acquisition over a relatively short period (a few weeks each), making them similar to targeted observations. The short time period of image acquisition was chosen to minimize any changes in lighting or temporal variation in WAC responsivity (Sect. 4.5) across the targeted mosaics. It also allowed an additional correction to be derived for these two mosaics by using overlapping regions between the images in each set to determine an empirical, flat-field-like correction (Sect. 4.6). This empirical correction is thought to first order to compensate for scattered light in the scene, although it was applied as a multiplicative correction to the images that compose the Caloris and b30 RTMs. Application of this empirical correction, which is archived in the PDS in the RTM Extras directory, resulted in smaller discrepancies in surface reflectance values within overlapping areas. The Caloris and b30 RTMs are archived in simple cylindrical projection at resolutions determined from the acquired images for each mosaic product.

9.4 MDIS Digital Elevation Models

In addition to the global and regional monochrome and multispectral mosaic products, a number of DEM products were created from MDIS images, ranging from a global product to regional products that cover Mercury quadrangles, to high-resolution DEMs derived from targeted imaging to cover features of high scientific interest. Table 7 details the MDIS DEM products archived in the PDS. In addition to the MDIS-derived DEM products, Mercury Laser Altimeter (MLA) DEM products are also archived separately. Comparisons of the various DEM products and their relative accuracies have been described by Becker et al. (2017b).

Each of the three main types of MDIS DEM products was produced independently, all utilizing MDIS images but also with each using slightly different methods and procedures. (1) The global DEM product was derived from a global control network of images, described in more detail in Sect. 6 (Becker et al. 2016). (2) DEMs of Mercury quadrangles were produced using photogrammetry methods led by a MESSENGER Participating Scientist at the German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt, DLR) and are described in a series of publications by Oberst et al. (2017), Preusker et al. (2017a, 2017b), and Stark et al. (2017). (3) Regional DEMs were produced largely from targeted high-resolution NAC images that provided stereo pairs covering features of special interest; these regional DEMs also used MLA profiles and WAC images to serve as geodetic reference. Production of the regional DEMs was led by MESSENGER team members at Arizona State University using SOCET SET and has been described by Manheim et al. (2017). In addition to the DEM files, the regional DEM products have a number of additional files archived along with the DEM files and in the EXTRAS directory at the PDS, including confidence maps, color shaded-relief maps, slope maps, terrain shaded-relief maps, orthorectified images, and legends and documentation of the file types.

10 Future Directions

Although the image calibrations and products described here represent the “final” results from the MESSENGER project, no such data set is ever truly final, and here we note several paths that could be pursued for further improvements to the data set. Depending on the particular scientific investigation, some of these possible refinements could be of little consequence, whereas in other cases they could be substantially important.

Particularly for investigations that make use of images with low signal or images of astronomical targets (Table 2), reductions in noise could be gained by developing a dark correction method that uses a scalable dark frame, or a series of dark frames at different temperatures for both the NAC and WAC, not-binned and binned. The current model (Hawkins et al. 2007), as examined in Sect. 4.1, includes a modeled gradient across the scene, rather than a true pixel-dependent correction, so that anomalous or “hot” pixels are not optimally adjusted. To account for this situation, most astronomical imaging was accompanied by a series of three images of space acquired both before and after the imaging sequence, which can be combined by taking the median value at each pixel and then subtracted from the scene in lieu of using the dark model. However, there are cases where this method is not possible, and an alternate dark correction scheme could result in further improvements.

A further reexamination of flat fields, especially that of WAC filter F, may also be warranted. As described in Sect. 4.3, the final flat fields are a merged product that uses the low-frequency portion of the flat fields acquired during pre-launch calibrations and the high-frequency portion determined from orbital images. When creating the scene-dependent corrections for the b30 and Caloris mosaics (Sect. 4.6), it was apparent that the correction for filter F was larger than expected on the basis of scattered light alone, and the correction factor resembled the low-frequency portion of the flat field determined from orbital images (this was not the case for the G and I filters). This outcome suggests that for filter F, and possibly other filters that were not part of the analysis in Sect. 4.6, the pre-launch calibration may not accurately represent the low-frequency gradient, and flat fields derived from orbital imaging only may be preferable.

Scattered light also proved to be a challenging issue (Sect. 4.6). The MDIS multispectral mosaics took advantage of repeat coverage by averaging all image data in each filter that covered each pixel in the mosaic, thus smoothing the effects of scene-dependent scattered light. However, further work to model and subtract scattered light from each image would likely result in improvements, particularly when examining the spectral properties of small, high-contrast features within a scene.

Alternate methods to correct for the temporal variations observed in MDIS responsivity (Sect. 4.5) would also yield improved consistency from image to image. One possible avenue to explore would be to redo the empirical correction model using the same method, but to reduce the time interval from which the correction factors are calculated from one Earth day to a smaller interval, possibly down to the image-to-image timescale. Ideally this calculation would be performed after scattered light correction. The current correction is likely adequate for anyone using the multispectral mosaics in the PDS; however, further refinement for spectral studies (e.g., spectral shape, absolute reflectance) that make use of individual WAC color sets, including targeted images, would be of high priority.

Additionally, no examination of the NAC or WAC B (clear) filter responsivity data has been performed using flight data; studies that use either of these data sets, and for which absolute reflectance is important, may benefit from further appraisal of their radiometric accuracy.