Exploring the moon in three dimension
There has been a renewed interest in exploration of the moon and in the past four decades the exploration of moon has become a reality . A number of missions have been flown to the moon by many countries. Many of these missions have carried imaging systems that, collectively, have returned an incredible wealth of information on the shape and surface characteristics of the moon. Mapping of moon began in the seventeenth Century by Galileo. Throughout history, maps and charts have played an integral role in the exploration of earth. Their importance holds true for moon exploration as well. Maps of the planets are needed by planners of spaceflights to design missions, including the selection of safe and scientifically fruitful landing sites, and are the framework for recording measurements from a wide variety of spacecraft instruments.
The making of moon maps requires development of new methods and techniques. Most of the commercial mapping software’s support the map making of earth’s surface features based on earth’s projections and datums but the utilization of the same in the current form is not possible for mapping the lunar surface because of the absence of planetary projection and datum in the available software. Many of the basic principles derived from the mapping of the earth have to be reconsidered in the mapping of the moon. Chandrayaan- 1 is India’s first science mission to moon for remote sensing and mapping different aspects of the lunar surface.
Chandrayaan-1 was launched successfully on 22 October 2008 and began operations since November 2008. The primary objective of the mission are to expand the scientific knowledge about the origin and evolution of moon, upgrade India’s technological capabilities and provide challenging opportunities to the young scientists working in planetary sciences. The scientific objectives of this mission are simultaneous geochemical, mineralogical and photo-geological studies and topographical mapping of the moon in visible, near infrared, low and high energy X-rays with high resolution of the whole lunar surface. Apart from technological and scientific gains, this mission provides the thrust to the basic science and research in the country. Chandrayaan-1 carries 11 different types of payloads for mapping and exploration of the moon in many aspects. Out of the eleven payloads five are Indian payloads developed indigenously.
The Indian payloads and their prime objective are :
The six International payloads are:
All the instruments onboard, except forMIP & RADOM are meant for theme specific mapping of the lunar surface.
Stereo image viewing has been the most common method of elevation modelling used by the mapping (or three dimensional exploration), photogrammetry and remote sensing communities. One of the instruments (out of 11) carried by Chandrayaan-1 is Terrain Mapping Camera (TMC), which is a line scanner with three linear arrays of 4K detectors, Fore, Nadir and Aft looking at +26, 0 and -25 degrees respectively for acquiring the stereo imagery of the lunar surface. The swath and resolution of the TMC are 20 km and 5 m respectively. Terrain Mapping Camera provides three images (triplet) of the same object with full overlap. The viewing geometry of TMC is given in figure-1. Table-1 provides the TMC specifications. The aim of TMC is to map topography in both near and far side of the Moon and prepare a 3- dimensional atlas with high spatial and altitude resolution. Such high resolution mapping of complete lunar surface will help us to understand the evolution process and allow detailed study of regions of scientific interests. The digital elevation model (DEM) available from TMC along with the Lunar Laser Ranging Instrument (LLRI) on Chandrayaan-1 will also improve the Moon gravity model. Usage of digital elevation model from TMC in the science analysis of the data from the other instruments can greatly enhance the capability of the deriving the information. In addition the information obtained from chemical, radioactive and mineral mapping has to be superimposed on a topographic map to identify the areas of interest . TMC provides global coverage with the stereo triplets, which can be used for generating Digital elevation Models (DEM) for 3D mapping of the entire moon surface. The definition of Lunar Atlas and the methodology of generation are given in the subsequent sections.
Digital Elevation Model is the most important component (layer) of 3D mapping of any surface and sensor orientation to generate the accurate digital elevation is the key element. To precisely orient the sensor and derive the relation between the image point and object point, we need a mathematical model. The Rational Function Model (RFM) is a general version of the polynomial model that can describe more complex image-to-object point transformations. It is also called Rational Polynomial Coefficients (RPC) model and is used as an alternative solution for the rigorous physical sensor model. It is widely used by Earth Observation Sensors whenever complex sensor model is not provided. The RPC model forms the co-ordinates of the image point as ratios of the cubic polynomials in the co-ordinates of the world or object space or ground point.
A set of images is given to determine the set of polynomial coefficients in the RPC model to minimise the error. RPC model is first time being employed for relating image and object space for lunar mapping. The Chandrayaan-1 data processing team at Space Applications Centre (ISRO) has developed RPC models for the imaging geometry of Chandrayaan-1 TMC. A schematic of the workflow is shown in Figure 2. The production and quality control of stereo DEMs and orthoimages is carried out in LPS general-purpose digital photogrammetric workstation (DPW) environment. Reference for control point is obtained from the available Clementine mosaic of moon along with the ULCN2005 control network [6, 7].
Stereo image matching is performed to generate image conjugate points. Conjugate points are the common points in overlapping areas of two or more images. They connect the images in the block to each other and are necessary input for the triangulation. LPS implements a fast area based stereo-correlation algorithm that determines correspondences between points in two images.
Parallax between corresponding points is then used to determine 3D location. A surface generation step interpolates the calculated 3D points, and resamples the surface on a regular grid to produce the output DEM and corresponding co-registered image.
The DEM is generated using the mass points obtained from automatic matchingprocess. First, we extract the exterior orientation of the two images in a stereo pair from Chandrayaan-1. Intersection calculation is then performed to determine the 3D coordinates of the corresponding matched points. Once the 3D locations of image points have been determined, the 3D points are interpolated using a triangle mesh interpolate. This mesh is then sampled at regular intervals in latitude and longitude. Vertical datum is based on spherical figure of the Moon and a lunar radius of 1737400 m. All elevations thus generated are in meters and represent the true values as the input ULCN points. These calculations are performed under the IAU 2000 Cartesian coordinate system.
|P K Srivastava B Gopala Krishna and Amitabh
|There are four possibilities of stereo image processing for the DEM generation. The combinations are Fore – Aft, Fore- Nadir, Aft – Nadir and Fore-Aft-Nadir images as a pair. Out of many cases, an area in the south polar region acquired on 15-11-2008 is given here as a sample case for DEM generation. The region is a part of the crater Moretus with location -70.6 deg lat and -1.4 deg long.
The DEM generated for all the cases are shown in figure-3. The three camera triplet image (Fore-Aft-Nadir, figure-3e) produced the best matching results with 100 % success in point matching while nearly 87% success in pattern matching.
Due to the relatively large angles between FORE and AFT the matching was poor, which was shown as dark points in the DEM (figure -3c). A colour coding of the DEM is also shown in figure-3f, which clearly show the height range of the crater from -1500m to 4000 m with respect to the mean radial surface of the moon.
A large strip of 1800 km (location: Coulomb C crater) has been divided into 3 individual strips of 600 km and DEMs have been derived for all three strips separately. This break up is done to reduce the processing time in DEM generation. The DEMs and their visualisations are shown in figures-5, 6 and 7.
Lunar Atlas [2, 3] with TMC Data
The high level data products defined for Chandrayaan-1 mission are the Lunar Atlas and maps. The objective of Chnadrayaan-1 lunar atlas and map products are to prepare maps for the entire surface (~37.8 Million Sq. km) of moon and it’s visualisation. Atlas will consist of Terrain Mapping Camera (TMC) and Hyper Spectral (HySI) orthoimage and Image mosaics, Digital elevation model derived from TMC triplets, Contributory themes from each payloads and annotations. Lunar atlas will be in softcopy while in the hardcopy form it will be represented in map catalogue form. Maps of earth’s surface have been produced primarily by piecing together large-scale sketches and diagrams since centuries. Control networks were derived through extensive and laborious ground surveying. By the late nineteenth century, regional maps were produced in this fashion that was relatively accurate. With twentiethcentury technology, the ability to obtain the synoptic view has emerged. Photographs taken from earth-orbiting satellites enabled the rapid production of accurate maps. When combined with well established control networks, these maps have enabled surface features on earth to be located precisely. Planetary explorers, on the other hand, have had the global perspective from the beginning, and they have progressed from global, through regional, to local vantages. The naming of features is as much a part of map making as is the measuring and plotting of their locations. Without names, communication of ideas is impossible. The names applied by explorers on earth often bear their provincial outlook. Ambiguities abound; settles on different parts of the same river often know the river by different names. The tradition that the privilege of naming belongs to the discoverer resulted in hopeless ambiguities, redundancies and inconsistencies. The International Astronomical Union (IAU) has therefore assumed control of the naming process. It’s working groups are composed of planetary scientists from many nations. The main inputs for the planned lunar atlas from Chandrayaan- 1 are the DEM and Orthoimages from TMC and other associated layers from the other payload data along with annotations. The absolute accuracy of the Lunar DEM in turn depends on the basic control used in the modelling the imaging geometry. As the initial results show, it is possible to derive relatively accurate DEMs from Chandrayaan-1 TMC imagery, which is the prime input for DEM generation towards Lunar Atlas preparation. Three CCD imagery in the triplet form, when compared to stereo pair leads to a good DEM in terms of detail due to the better point and pattern matching accuracies. The DEMs at 25 m grid interval depicts a very good representation of the terrain, which can be a prime input to the science analysis, when used along with the other payload data sets from Chandrayaan-1, in addition to its usage in the 3D mapping of moon.
Figure-5: Orthoimage, DEM with colour coding and Visualisation of Image draped over DEM (Coulomb C Crater)
Figure-6: Part of Mare Orientale (a) Orthoimage (b) colour coded DEM (20 km x 65 km long) (c)
1. A quest for moon, Narendra Bhandari, Current Science, Vol. 83, No.4, 25 August 2002
2. Lunar Cartographic Dossier Vol-1, Lawrence A. Schimerman, NASA , 1973
3. Planetary Mapping, Ronald Greeley and Raymond M. Batson; Cambridge University Press 1991
4. Scientific Challenges of Chandrayaan- 1:The Indian Lunar polar orbiter mission, Narendra Bhandari, Vol. 86, No. 11, 10 June 2004
5. ISRO page: http://www.isro.gov.in
7. webgis.wr.usgs.gov/download/ ClementineUVVIS ULCN2005.warp
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