To correct geometric distortions introduced by electrostatic and magnetic focusing systems the two Mariner 10 cameras each had a grid of 111 metallic reseaux deposited on the inside surface of the vidicon. The position of each reseau on the vidicon was recorded to within 0.001 mm [Benesh and Morrill, 1973]. Utilizing these pre-launch measurements and our subsequent measurements of the locations of the reseaux found in the images of Mercury, the Mariner 10 frames can be geometrically rectified. The positions of the reseaux in the Mercury images vary from frame-to-frame due to changes in scene brightness and exposure level. Areas of high contrast, such as a bright limb against the space background, often show the worst reseau position discrepancies from the nominal locations. Additionally, we found that the location of the reseaux changed by more than 5 pixels from the first encounter (March 29, 1974) to the second encounter (September 21, 1974) for portions of each vidicon. This may be due to the fact that the onboard camera heater failed for the second encounter, thus the vidicons were at a lower temperature [Murray and Burgess, 1977]. Utilizing close approach images of Mercury that were transmitted with a low data rate [Danielson et al., 1975], thus relatively high signal-to-noise-ratio, we derived nominal reseau positions for each camera for each encounter (total of six nominal position files). Utilizing the FINDRX program (an autocorrelation program) within the ISIS software package [USGS, 1998], and adjusting parameters specifically for Mariner 10, the reseau locations were automatically found in each image utilizing the nominal locations as the correlation starting point. The majority of Mariner 10 high resolution images were sent back in real time (117.6 Kbits/s) with an attendant increase in bit errors during transmission [Danielson et al., 1975; Soha et al., 1975]. This resulted in severe salt and pepper random noise [Soha et al., 1975] that hampers the automatic identification of reseaux, especially in areas with low signal such as terminator regions and space. Due to the generally noisy nature of the data [Danielson et al., 1975; Soha et al., 1975] tolerances were set high (0.90 correlation) to help avoid spurious reseau identifications. Failure to find an actual reseau at a given position resulted in default to the nominal position for a given camera/encounter combination.

From the original control point measurements [Davies et al., 1976] and the new reseau positions (for each image) an initial run of the analytical triangulation revealed that some control points had large residuals relative to the average. Inspection of suspect points showed that some of the original measurements contained crater misidentifications, and these points were thrown out. We also noted that some images had a high percentage of bad points, and it was found that reseau misidentification had occurred. These problem images were inspected and the reseau locations were measured manually. A second iteration of the analytical triangulation resulted in improved residuals. Again, bad points were deleted and reseaux were located manually on problem images in preparation for a third run.

The final analytical triangulation contains 10,704 measurements of 2306 points from 811 images acquired during the three Mariner 10 encounters. The overdetermination in the new control net is 3.04, and was calculated according to the following equation.

Where N is the number of measurements, M is the number of images, and N is the number of points. The standard measurement error is 0.00844 mm (0.6 pixels). Mercury’s radius was assumed to be 2439 km except where occultation data and radar measurements give more precise values. As part of the analytical triangulation new values for the focal length of each camera were derived (Camera A 1493.6 mm, camera B 1500.1 mm).

The control network of Mercury is computed using the J2000 coordinate system that is defined by the FK5 star catalog and has the standard epoch of J2000 January 1.5 (JD 2451545.0), TDB. The spin axis of Mercury is normal to its orbital plane and its rotation is 3/2 synchronous with the Sun [Pettengill and Dyce, 1965; Klaasen, 1975]. The direction of the north pole is specified by the value of its right ascension (µ ₀) and declination (d ₀). The location of the prime meridian is specified by the angle W that is measured along Mercury’s equator in an easternly direction with respect to its north pole from the node of Mercury’s equator on the standard equator, to the point where the prime meridian crosses Mercury’s equator [Davies et al., 1996]. The IAU/IAG/COSPAR Working Group on Cartographic Coordinates and Rotational Elements of the Planets and Satellites [Davies et al., 1996a] publishes a report every three years updating tables that give definitions of the current best estimates of the directions of the north poles and equations that define the prime meridians of the planets and satellites. Thus, the new equation for W is

where the constant term (W₀) ensures that the longitude of the crater Hun Kal is at 20 longitude in the control network [Davies et al., 1996b]. The positions of both the north and south poles are shifted approximately 1° in latitude from that shown in previous maps (Davies et al., 1978).