Editing Retroreflector (section)

==Types==
There are several ways to obtain retroreflection:<ref name="cpsc" />

===Corner reflector===
[[Image:Corner reflector.svg|right|thumb|Working principle of a corner reflector]]
[[File:Comparison of retroreflectors.svg|thumb|100px|Comparison of the effect of corner (1) and spherical (2) retroreflectors on three light rays. Reflective surfaces are drawn in dark blue.]]
{{Main|Corner reflector}}
A set of three mutually perpendicular reflective surfaces, placed to form the internal corner of a cube, work as a retroreflector. The three corresponding normal vectors of the corner's sides form a basis {{nowrap|(''x'', ''y'', ''z'')}} in which to represent the direction of an arbitrary incoming ray, {{nowrap|[''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 {{nowrap|[''a'', ''b'', ''c'']}} to {{nowrap|[−''a'', ''b'', ''c'']}} to {{nowrap|[−''a'', −''b'', ''c'']}} to {{nowrap|[−''a'', −''b'', −''c'']}} and it leaves the corner with all three components of its direction 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]].

===Cat's eye===
[[Image:Eyeshine-BW-cat.jpg|thumb|right|[[Tapetum lucidum|Eyeshine]] from retroreflectors of the transparent sphere type is clearly visible in this cat's eyes.]]
{{Main|Cat's eye (road)}}
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 [[transparency (optics)|transparent]] sphere and (optionally) a spherical mirror. In the [[paraxial approximation]], this effect can be achieved with lowest divergence with a single [[transparency (optics)|transparent]] sphere when the [[refractive index]] of the material is exactly one plus the refractive index n<sub>i</sub> of the medium from which the radiation is incident (n<sub>i</sub> 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 {{nowrap|''n<sub>i</sub>'' + 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).

The spherical aberration problem with the spherical cat's eye can be solved in various ways, one being a spherically symmetrical index gradient within the sphere, such as in the [[Luneburg lens]] design. Practically, this can be approximated by a concentric sphere system.<ref>{{cite journal|last1=Bernacki|first1=Bruce E.|last2=Anheier|first2=Norman C.|last3=Krishnaswami|first3=Kannan|last4=Cannon|first4=Bret D.|last5=Binkley|first5=K. Brent|title=Design and fabrication of effi cient miniature retroreflectors for the mid-infrared|journal=SPIE Defense & Security Conference 2008, Infrared Technology and Applications|date=2008|volume=XXXIV|issue=30|series=Proc. SPIE 6940}}</ref>

Because the back-side reflection for an uncoated sphere is imperfect, it is fairly common to add a metallic coating to the back half of retroreflective spheres to increase the reflectance, but this implies that the retroreflection only works when the sphere is oriented in a particular direction.

An alternative form of the cat's eye retroreflector uses a normal lens focused onto a curved mirror rather than a transparent sphere, though this type is much more limited in the range of incident angles that it retroreflects.

The term ''cat's eye'' derives from the resemblance of the cat's eye retroreflector to the optical system that produces the well-known phenomenon of "glowing eyes" or [[tapetum lucidum|eyeshine]] in cats and other vertebrates (which are only reflecting light, rather than actually glowing). The combination of the eye's [[lens (anatomy)|lens]] and the [[cornea]] form the refractive converging system, while the [[tapetum lucidum]] behind the [[retina]] forms the spherical concave mirror. Because the function of the eye is to form an image on the retina, an eye focused on a distant object has a focal surface that approximately follows the reflective [[tapetum lucidum]] structure,{{Citation needed|date=June 2008}} which is the condition required to form a good retroreflection.

This type of retroreflector can consist of many small versions of these structures incorporated in a thin sheet or in paint. In the case of paint containing glass beads, the paint adheres the beads to the surface where retroreflection is required and the beads protrude, their diameter being about twice the thickness of the paint.

===Phase-conjugate mirror===
A third, much less common way of producing a retroreflector is to use the [[nonlinear optics|nonlinear optical]] phenomenon of [[phase conjugation]]. This technique is used in advanced [[optics|optical]] systems such as high-power [[laser]]s and [[optical fibre|optical transmission lines]]. Phase-conjugate mirrors<ref>{{cite journal | last= Gower | first= M.C. | title= The Physics of Phase Conjugate Mirrors | journal= Progress in Quantum Electronics | publisher= Elsevier B.V. | issue= 2 | date=1984 | volume= 9 | issn= 0079-6727 | doi = 10.1016/0079-6727(84)90023-5 | pages=101–147| bibcode= 1984PQE.....9..101G }}</ref> reflect an incoming wave so that the reflected wave exactly follows the path it has previously taken, and require a comparatively expensive and complex apparatus, as well as large quantities of power (as nonlinear optical processes can be efficient only at high enough intensities). However, phase-conjugate mirrors have an inherently much greater accuracy in the direction of the retroreflection, which in passive elements is limited by the mechanical accuracy of the construction.