Mach bands and airplane shadows cast on dry terrain

Luminous rings are often seen surrounding the shadow of a high-flying airplane. Some of these phenomena are due to water droplets (glories, the Heiligenschein), but a different sort of explanation is required when a luminous ring (sometimes simply a bright spot) is seen while the plane is flying over dry terrain. Demonstrations involving distances and shadows manyfold smaller than those of an airliner's shadow show that Mach bands can produce illusory luminance phenomena that greatly resemble those associated with a plane's shadow over dry terrain. Luminance rings have recently also been observed over dry, sparsely vegetated terrain, around the shadow of an adjacent airplane (i.e., far from the observer's antisolar point), thereby excluding all previous alternative interpretations; Mach bands are thus a likely explanation for at least some instances of dry-terrain luminous rings around airplane shadows.