Retroreflectors

Retroreflector

A gold corner cube retroreflector
Uses	Distance measurement by optical delay line

A retroreflector (sometimes called a retroflector or cataphote) is a device or surface that reflects light back to its source with a minimum of scattering. In a retroreflector an electromagnetic wavefront is reflected back along a vector that is parallel to but opposite in direction from the wave's source. The angle of incidence at which the device or surface reflects light in this way is greater than zero, unlike a planar mirror, which does this only if the mirror is exactly perpendicular to the wave front, having a zero angle of incidence.

There are several ways to obtain retroreflection:

A set of three mutually perpendicular reflective surfaces, placed to form the corner of a cube, work as a retroreflector. The three corresponding normal vectors of the corner's sides form a basis (x, y, z) in which to represent the direction of an arbitrary incoming ray, [a, b, c]. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to -a while the y and z components are unchanged. Therefore, as the ray reflects first from side x then side y and finally from side z the ray direction goes from [a,b,c] to [-a,b,c] to [-a,-b,c] to [-a,-b,-c] and it leaves the corner with all three components of motions exactly reversed.

Corner reflectors occur in two varieties. In the more common form, the corner is literally the truncated corner of a cube of transparent material such as conventional optical glass. In this structure, the reflection is achieved either by total internal reflection or silvering of the outer cube surfaces. The second form uses mutually perpendicular flat mirrors bracketing an air space. These two types have similar optical properties.

A large relatively thin retroreflector can be formed by combining many small corner reflectors, using the standard hexagonal tiling.

Another common type of retroreflector consists of refracting optical elements with a reflective surface, arranged so that the focal surface of the refractive element coincides with the reflective surface, typically a transparent sphere and (optionally) a spherical mirror. In the paraxial approximation, this effect can be achieved with lowest divergence with a single transparent sphere when the refractive index of the material is exactly one plus the refractive index n_i of the medium from which the radiation is incident (n_i is around 1 for air). In that case, the sphere surface behaves as a concave spherical mirror with the required curvature for retroreflection. In practice, the optimal index of refraction may be lower than n_i+1≅2 due to several factors. For one, it is sometimes preferable to have an imperfect, slightly divergent retroreflection, as in the case of road signs, where the illumination and observation angles are different. Due to spherical aberration, there also exists a radius from the centerline at which incident rays are focused at the center of the rear surface of the sphere. Finally, high index materials have higher Fresnel reflection coefficients, so the efficiency of coupling of the light from the ambient into the sphere decreases as the index becomes higher. Commercial retroreflective beads thus vary in index from around 1.5 (common forms of glass) up to around 1.9 (commonly barium titanate glass).