Retroreflector

A retroreflector returns an incoming beam along a path parallel to its incident direction, pointing back toward the source, without needing to be aligned precisely. A flat mirror does this only at normal incidence; a retroreflector does it for any direction within its acceptance cone, which for a corner cube is typically tens of degrees wide. The accuracy is given as the angular deviation of the returned beam from exact antiparallelism: a few arcseconds for precision hollow corner cubes used in metrology, and up to minutes of arc for inexpensive glass ones.

Corner cubes

A corner cube, or cube-corner, has three mutually perpendicular reflecting surfaces meeting at a point. Each reflection reverses one component of the propagation direction, so after the three reflections the direction vector $(k_x, k_y, k_z)$ becomes $(-k_x, -k_y, -k_z)$. The returned beam is also displaced: a ray entering at a distance $h$ from the apex, measured perpendicular to the beam, leaves at the same distance on the opposite side, so the incoming and outgoing rays are separated by $2h$.

Corner cubes are made in two forms, both related to the corner-cube prism.

• Solid corner cubes are glass prisms entered through a flat face. At normal entry the light meets each back face at 54.7°; for N-BK7 the critical angle is 41.2°, so the faces reflect by total internal reflection without a coating. At larger entrance angles TIR fails on some faces, and coated backs (usually silver or aluminum) extend the acceptance.
• Hollow corner cubes are three first-surface mirrors bonded together. They have no glass path, so no dispersion, refraction or ghost from the entrance face, and they are made in large apertures; they are used in precision interferometry and Fourier-transform spectrometers.

TIR at each face imposes a phase difference between s and p components, so an uncoated solid corner cube changes the polarization state of the returned light, and the change varies across the six sectors of the aperture. Metal-coated cubes alter polarization less, which matters in polarization-sensitive interferometers.

Accuracy and diffraction

A deviation $\delta$ from perfect retroreflection moves the returned beam sideways by $\delta z$ at a distance $z$. For $\delta = 1$ arcsecond ($4.85$ µrad) and $z = 100$ m the offset is 0.48 mm. Diffraction sets a further limit: the returned beam spreads with a half-angle of order $\lambda/D$, where $D$ is the aperture, which is 14 µrad for a 38 mm cube at 532 nm.

Cat's-eye retroreflectors

A lens with a mirror at its focal plane also retroreflects: a collimated beam arriving at any angle within the field is focused to a point on the mirror and returned parallel to itself. Glass spheres with a reflective back surface work the same way, and traffic signs and high-visibility clothing use beaded or microprismatic sheeting that combines many small retroreflectors. Their returned beam is deliberately spread slightly, so that a driver, whose eyes sit above the headlights, sees it.

Where retroreflectors are used

• Interferometric displacement measurement. Replacing the moving mirror of a Michelson interferometer with a corner cube makes the return insensitive to tilt of the moving stage, a standard arrangement in laser displacement interferometers and scanning spectrometers.
• Laser trackers and surveying. A spherically mounted corner cube is followed by an instrument that measures its position; surveying total stations measure distance to a prism reflector by time of flight or phase.
• Satellite and lunar ranging. The Apollo 11, 14 and 15 missions left arrays of fused silica corner cubes on the Moon, 3.8 cm across, with 100 cubes in each of the first two arrays and 300 in the third. Pulses sent from Earth return about 2.56 s later at the mean distance of 384 400 km, and the timing gives the Earth-Moon distance to centimeter level or better.
• Alignment and free-space optical links, where a retroreflector at the far end returns a beam to its source for testing or modulated-retroreflector communication.

Pitfalls

The lateral displacement $2h$ means that a beam entering off center returns beside its own path; a beam centered on the apex overlaps itself, and an offset entry is used deliberately to separate the return from the input. Edges between faces, and the apex itself, scatter and diffract light, so the central region and the three seams are poor parts of the aperture.

Common questions

How does a retroreflector differ from a mirror?

A plane mirror reverses only the component of direction normal to its surface, so the return depends on the mirror's orientation. A corner cube reverses all three components and returns light toward the source over a wide range of orientations.

What does the arcsecond specification of a corner cube mean?

It is the maximum angle between the returned beam and the exact reverse of the incident beam. At 100 m, each arcsecond corresponds to about 0.48 mm of lateral offset.

Why do retroreflectors on the Moon still work after decades?

They are passive fused silica prisms with no power or moving parts. Their measured return has decreased over the decades, which studies have attributed to dust and thermal effects, but they remain in use for lunar laser ranging.

References: E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 5; M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 1; J. O. Dickey et al., Science 265, 482 (1994).