Modeling orthorectification and PSF distortions on a HEALPix grid

The quality of analysis-ready Earth Observation (EO) products strongly depends on the ability of the processing chain to accurately model the mapping from the Earth’s surface to the detector geometry. This mapping involves a convolution with the instrumental Point Spread Function (PSF) and an orthorectification step that corrects for terrain-induced geometric distortions using a Digital Elevation Model (DEM).

These distortions are challenging, as they can lead to spatially varying PSF deformations. Even worse, some areas with strong topographic gradients lead to an effective PSF with multiple modes and may cause the failure of standard operational orthorectification algorithms.

To anticipate these failures, we introduce critical incidence maps. For a given point on a DEM, such a map provides the maximum sensor incidence angle at which this point remains visible, i.e. not occluded by surrounding terrain in any azimuthal direction. We show that, for moderate incidence angles (typically below ~20°), rugged areas responsible for orthorectification failures cover only a very small fraction of Earth’s surface, leaving therefore ample room for more robust algorithms to tackle these thorny points.

For smooth regions, we introduce and compare various semi-analytical orthorectification schemes that achieve appealing trade-offs between computational cost and geometric precision. We then combine two distinct orthorectification strategies, tailored respectively to smooth and rugged terrain, and express the overall ground-to-detector mapping as a sparse linear operator.

This formulation yields an efficient forward model that accurately captures terrain-induced PSF distortions, including multimodality. Finally, we apply this model to invert the data projection, from the detector to the Earth’s surface, in the context of a HEALPix discrete grid.