COHERENT SURFACE GAUSSIANS FOR A SPECULAR SYNTHETIC APERTURE

Millimeter-wave radar sees through packaging, fabric and clutter, which makes it an attractive sense for robots, but its images are not shapes. We trace the reason to the optics of a synthetic aperture: each position is a co-located source and detector that receives glints only from surface points whose normals point back at it. Each sub-aperture therefore observes its own band of normals, back-projection images a convex surface behind its front, at a depth we predict in closed form, and the phase history determines a glint's center of curvature and its radius minus the radar's range offset, but not the two separately. We represent the scene by coherent surface Gaussians, curved primitives whose near-field echo has a closed form under a quadratic range approximation and whose angular response follows from their size and curvature. The closed form matches quadrature over the same primitives to within 1.4%, while flat Gaussians err by 24–98%. The same optics predicts that holding out a sub-aperture, a natural analogue of novel-view synthesis, is a weak learning signal, because the other sub-apertures see different normals; in a ten-seed physical-optics study it removes phantoms only by stopping early and losing surface, whereas generic cross-validation selects models reliably. Multipath ghosts seen by all sub-apertures are virtual glints and cannot be rejected by any hold-out. An encoder trained in simulation reduces the phantom rate of back-projection by an order of magnitude on unseen shapes, and a measured 77–81 GHz scan follows the predicted streak geometry.