Retroreflector

A retroreflector is a device or surface that reflects light or other radiation back to its source with minimum scattering. This works at a wide range of angle of incidence, unlike a planar mirror, which does this only if the mirror is exactly perpendicular to the wave front, having a zero angle of incidence. Being directed, the retroflector's reflection is brighter than that of a diffuse reflector. Corner reflectors and cat's eye reflectors are the most used kinds.

Types

There are several ways to obtain retroreflection:

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 in which to represent the direction of an arbitrary incoming ray,. 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 to to to 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

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 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. 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 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 up to around 1.9.
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.
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 eyeshine in cats and other vertebrates. The combination of the eye's 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, 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 optical phenomenon of phase conjugation. This technique is used in advanced optical systems such as high-power lasers and optical transmission lines. Phase-conjugate mirrors 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. 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.

Operation

Retroreflectors are devices that operate by returning light back to the light source along the same light direction. The coefficient of luminous intensity, R_I, is the measure of a reflector performance, which is defined as the ratio of the strength of the reflected light to the amount of light that falls on the reflector. A reflector appears brighter as its R_I value increases.
The R_I value of the reflector is a function of the color, size, and condition of the reflector. Clear or white reflectors are the most efficient, and appear brighter than other colors. The surface area of the reflector is proportional to the R_I value, which increases as the reflective surface increases.
The R_I value is also a function of the spatial geometry between the observer, light source, and reflector. Figures 1 and 2 show the observation angle and entrance angle between the automobile's headlights, bicycle, and driver. The observation angle is the angle formed by the light beam and the driver's line of sight. Observation angle is a function of the distance between the headlights and the driver's eye, and the distance to the reflector. Traffic engineers use an observation angle of 0.2 degrees to simulate a reflector target about 800 feet in front of a passenger automobile. As the observation angle increases, the reflector performance decreases. For example, a truck has a large separation between the headlight and the driver's eye compared to a passenger vehicle. A bicycle reflector appears brighter to the passenger car driver than to the truck driver at the same distance from the vehicle to the reflector.
The light beam and the normal axis of the reflector as shown in Figure 2 form the entrance angle. The entrance angle is a function of the orientation of the reflector to the light source. For example, the entrance angle between an automobile approaching a bicycle at an intersection 90 degrees apart is larger than the entrance angle for a bicycle directly in front of an automobile on a straight road. The reflector appears brightest to the observer when it is directly in line with the light source.
The brightness of a reflector is also a function of the distance between the light source and the reflector. At a given observation angle, as the distance between the light source and the reflector decreases, the light that falls on the reflector increases. This increases the amount of light returned to the observer and the reflector appears brighter.

Applications

On roads

Retroreflection is used on road surfaces, road signs, vehicles, and clothing. When the headlights of a car illuminate a retroreflective surface, the reflected light is directed towards the car and its driver. However, a pedestrian can see retroreflective surfaces in the dark only if there is a light source directly between them and the reflector or directly behind them. "Cat's eyes" are a particular type of retroreflector embedded in the road surface and are used mostly in the UK and parts of the United States.
Corner reflectors are better at sending the light back to the source over long distances, while spheres are better at sending the light to a receiver somewhat off-axis from the source, as when the light from headlights is reflected into the driver's eyes.
Retroreflectors can be embedded in the road, or they can be raised above the road surface. Raised reflectors are visible for very long distances, while sunken reflectors are visible only at very close ranges due to the higher angle required to properly reflect the light. Raised reflectors are generally not used in areas that regularly experience snow during winter, as passing snowplows can tear them off the roadways. Stress on roadways caused by cars running over embedded objects also contributes to accelerated wear and pothole formation.
Retroreflective road paint is thus very popular in Canada and parts of the United States, as it is not affected by the passage of snowplows and does not affect the interior of the roadway. Where weather permits, embedded or raised retroreflectors are preferred as they last much longer than road paint, which is weathered by the elements, can be obscured by sediment or rain, and is ground away by the passage of vehicles.