Shading under Titan's sky

Statistics – Computation

Scientific paper

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Scientific paper

During the descent of the Huygens probe in January 2005, its Descent Imager/Spectral Radiometer (DISR) will take the first images of Titan's surface. The shading imposed by the illumination of a planetary surface contains information on its orography. For the Moon and other planetary bodies without an atmosphere, the light can be assumed to stem from a point source to estimate shape from shading. Even for optically not very thick atmospheres like those of Earth or Mars, this is a reasonably good approximation. For the other extreme of isotropic illumination, ie shading on a cloudy day with completely covered sky, there are also algorithms available to retrieve shape, but they are quite computation expensive because shadowing has to be taken into account. Titan's sky represents an intermediate case here. In the optical the sun is visible from the surface, but the illumination is dominated by the diffuse radiance. However, the diffuse illumination is concentrated in a pronounced solar aureole. In order to investigate the characteristics of shading under Titan's sky and to test algorithms to retrieve shape, a series of simulations has been carried out. Digital terrain models (DTMs) of Earth and Moon and artificial DTMs have been used to simulated images under different types of illumination. The accuracy of different methods to estimate shape form these images is investigated. To the human eye, the simulated shading of a surface under Titan's sky does not appear very different from shading due to a point source. But the nevertheless present deviations cause failing of shape from shading reconstructions assuming a point source. Thus the type of algorithms developed for isotropic illumination has to be extended to handle the non-isotropic illumination by a pronounced solar aureole. It is then required that the sky radiance in dependence on viewing direction is known. This can be reconstructed from measurements by two subintruments of the DISR -- the Solar Aureole Imager and the Up Looking Visible Spectrometer -- with the Titan Inverse Radiation Model (tirm). Shape can be reconstructed from shading under Titan's sky similarly well (and with the same limitations) as for planetary bodies with no or optically thin atmospheres, but with a high computation expense as shadowing has to be taken into account.

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