The designer of a stealthy military vehicle aims to make its metal surface retro-reflect the minimum possible radar energy. Well known retro-reflecting (RR) concave structures such as mutually orthogonal plates, involving two and three successive reflections (edge and corner reflectors) respectively, are avoided . They are examples of persistent features because their retro-reflection occurs over a wide range of directions.

Geometrical Algebra (GA) is used to derive expressions for the two and three reflections of an entry ray vector x. The exit ray vectors are shown to be RxR^† and -PxP^† respectively where R and P are rotors. Interpreting the expressions leads to quite fundamental laws of reflection from two and three flat reflectors from which new RR structures are predicted. The GA expression for two and three successive reflections is easily generalized to arbitrary number of reflections. All reflectors are assumed to be one-sided, i.e. the continuous reflecting surface encloses a volume inaccessible to radiation. In practice an exit ray is deemed retro-reflective if the ``spread'' angle, between the entry ray reversed (ERR) and the exit ray, is less than a small spread tolerance. The corresponding ``entry'' angle, the angle between the retro-reflective direction and the ERR, is suggested as a measure of the persistence of the multiple reflection. Expressions for intermediate values for persistence are derived for the two and three reflecting configurations in general.

MFDEROME@dera.gov.uk