A radar measures range purely from round-trip time-of-flight, R = c·t/2, and bearing from the direction the returning wavefront arrives from. It has no way to know whether a pulse travelled straight to the target or bounced off terrain, a building or water on the way. When it bounces once off a flat reflecting surface before (and after) reaching the target, the extra path length gets misread as extra range, and the arrival angle points toward the reflection point — not the real target. The radar plots a second, entirely fictitious "phantom" blip at that false range/bearing. This is the leading real-world explanation for a large share of radar-tracked UFO reports.
R = c·t / 2 (time-of-flight range)
T' = mirror(target, reflector line) (image-source method)
R_phantom = |O → T'| (one-way path O→P→target)
θ_phantom = bearing(O → T') (angle of arrival ≈ bearing to reflection point P)
valid only if segment O→T' crosses the finite reflector
- Target range/bearing — the true, direct-path aircraft or object being tracked.
- Reflector range/bearing — where a flat reflecting surface (ridge, building face, water edge) sits relative to the radar.
- Reflector height (RCS) — a taller, more solid reflector returns more energy, making the ghost easier to detect.
- Radar sensitivity — lower detection threshold picks up weaker (smaller/farther/lower-RCS) multipath returns, so more phantoms appear.
- Ray path — toggle to trace the bent radar → reflector → target path versus the straight line the radar mistakenly reports.
Real-world relevance: multipath and ground-clutter ghosting is a routine radar-engineering headache near coastlines, mountains and cities, and it is the mechanism behind many "unidentified radar contact" reports before they are correctly identified and discarded.