 IMPROVED PHOTOCLINOMETRY METHOD: TOPOGRAPHY OF LARGE-SCALE POLYGONS AT THE PHOENIX LANDING SITE FROM A SET OF IMAGES.  N. V. Bondarenko, I. A. Dulova and Yu. V. Kornienko, Institute of Radiophysics and Electronics, NAS of Ukraine, 12 Ak.Proskury, Kharkov, 61085, Ukraine (nbondar@ucsc.edu).  Introduction:  Polygonally patterned ground is widely observed on high latitudes of Mars. Polygons at the Phoenix landing site are ~4 m across, their slopes are gentle (a few degrees), their typical topography amplitude is a few tens of centimeters, and they are superimposed on other geologic landforms, including larger 20-25 m polygons [1]. Morphology and sizes of polygons vary widely over high-latitude terrains on Mars; their morphology has a strong latitudinal zonality, but regional variations are also observed [2, 3]. Details of the polygon formation and evolution are highly controversial and are a subject of debates [1, 4 and references therein]. Their understanding is a key for deciphering recent climate change on Mars. Detailed morphometry of the polygons can give important constraints on the mechanism of their formation and evolution. The polygons are much smaller than the resolution of laser altimeter MOLA; their topographic amplitude of a few tens of centimeters is at the principal margin of relative vertical accuracy of photogrammetric topography reconstruction with HiRISE stereopairs [5]. The only class of methods useful for quantitative morphometry of small polygons with available remote sensing data is photoclinometry with HiRISE images. In the present work we show examples of relief reconstruction for the part of polygonally patterned surface in the vicinity of Phoenix landed site based on improved photoclinometry from images taken by HiRISE camera onboard MRO spacecraft.. Improved photoclinometry:  The method of improved photoclinometry [6] is based on the accurate mathematical formulation of the problem in the frame of statistical approach. The method allows calculation of the most probable surface height variations based on available images. The height accuracy depends on the noise level of image registration.  The method uses known dependence of the surface facet brightness on its orientation and includes as a first step calculation of topography slope fields from available images. After that [6] the problem solution leads to the Poisson equation with the boundary conditions stated that at the area boundary the normal component of calculated heights gradient should to be equal to the normal component of slopes derived from initial image (Von Neumann condition).   The improved photoclinometry is the most mathematically rigorous. It gives the most probable surface relief in contrast to widely used approach firstly proposed by Van Diggelen [7] (for example, [8]),which in its formulation (as shown in [6]) is a mathematically incorrectly posed problem.  Fig. 1. Surface area located 640 m eastward from the Phoenix lander; (a) portion of PSP_008591_2485; 5.5-65 m - scale topography obtained from two source images (b) and a single source image (c). Topography reconstruction:  We used areas having 190×190 m in size from MRO HiRISE images PSP_008591_2485 and PSP_008855_2485 of Martian surface. Sampling of these images is ~25 cm per pixel, their resolution (the minimal distance between resolvable objects) is about 1 m. They have been obtained at the following incidence (illumination azimuth) angles: 48.80° (261.01°) and 51.18° (272.57°), respectively. The difference in illumination azimuth angles is equal to 11.56°. Examples of areas under study are shown in Fig. 1 and 2. One of two source images used for relief reconstruction is presented in Fig.1a and 2a, direction of surface illumination is marked with yellow arrows.  For calculations of surface heights gradient we adopted Lambert law as an a priori known photometric function of the surface. The surface albedo was considered to be constant over the surface and equal to 0.185. To get rid of spurious global tilts and noise and focus on larger-scale topographic features, we applied a band-pass filter defined as 5.5 m - 65 m wavelength window in spatial frequency domain. The resulting larger-scale topography of areas under study calculated from two source images is presented in Fig. 1b and 2b. Troughs are shown with thin arrows. Topography amplitude of large polygons (60 - 90 m in diameters) marked in Fig. 1b with "X" reaches ~45 cm. Topography in Fig. 2b does not exhibit polygonal structure. Height of hills (marked with "X") varies from 35 to 52 cm, their diameters are ~50-60 m.  Large-scale topography of the same areas calculated like ones presented in Fig. 1b and 2b but from a single source image is shown in Fig. 1c and 2c. Generally, many topography details are similar in Fig. 1b and 1c, and in Fig. 2b and 2c (see feature marked with thick arrow in Fig. 1 and features marked with "X" in Fig. 1 and 2). However, many differences are also seen, for example, features inside blue circles in Fig. 1 and 2 appeared to be better reconstructed, if two source images were used.  Conclusions:  The improved photoclinometry method for relief reconstruction from images allows calculation of the most probable surface topography based on available images. The use of several source images of the surface taken at different illumination azimuths is preferable for obtaining reasonable topographic information.  References:  [1] Mellon M. T. et al. (2009), JGR, 114, doi:10.1029/2009JE003418. [2] Mangold, N. (2005) Icarus, 174, 336-359. [3] Levy J. et al. (2009) JGR, 114, E01007. [4] Levy J. S. et al. (2010) Icarus, 206, 229-252. [5] Kirk R. L. et al. (2007) 7th Int. Conf. on Mars. [6] Dulova I. A. et al. (2008) Telecom. Rad. Eng., 67, 1605-1620. [7] Van Diggelen J. (1951) Neth. Astron. Inst. Bull., 11, 283-289. [8] Lohse V. et al. (2006) P&SS, 54, 661-674.  Fig. 2. Surface area located eastward from the Phoenix lander at distance of 860 m. (a) portion of PSP_008591_2485; 5.5-65 m - scale topography obtained from two source images (b) and one source image (c). 
