A ring laser gyro is a device for measuring rotation in a particular plane. The notable characteristic of the RLG is that it contains no moving parts, unlike early gyroscopic measuring devices which contain a surfeit of them. It works using techniques that are, to me, effing magic; however, they work, and are wicked cool besides, and they allow us to make solid-state INS systems.

A ring laser gyro is a cavity, around the perimeter of which laser beams are induced to travel in opposite directions. The two beams meet at a detector, which measures their frequency with great precision. If the assembly is rotated around an axis normal (perpendicular) to the lasers' plane of travel, then the beam traveling with the direction of rotation will, due to the Doppler Effect, show a slightly increased frequency (a blueshift) whereas the other beam will show a correspondingly decreased frequency (redshift). Careful measurement of this phenomenon allows the user to measure the rotational accelerations placed on the assembly with great precision. From there, math and physics and single vector accelerometers allow the measurement of orientation and translation change on the assembly.

Note that the ring can be active or passive. In the latter case, the cavity is simply a reflective medium, and laser light is fed in from outside the system. In the former case, an excited plasma is placed in the ring, and it lases itself to produce the requisite laser beams.

Large ring laser gyros have been built to perform such tasks as measure the Earth's rotational vector with great precision. These devices, due to their size, allow the observation of their workings with more detail. When the beams pass around the periphery of the cavity, they form a standing wave if the system is not undergoing rotational acceleration. If the system is exposed to such acceleration, the standing wave pattern remains fixed, and the detector will see 'beats' as the standing wave pattern 'moves' past the detector. In fact it isn't moving, but the frequency difference seen by the detector manifests as a slight movement in the standing wave pattern. This is called the Segnac effect.

Backscatter of photons, quantum 'noise' and other effects have a negative impact on the accuracy of the RLG; however, careful engineering and operation can minimize such effects. The most notable is a phenomenon called 'phase lock' in which the standing wave pattern actually does begin to rotate with the surroundings slightly - enough to prevent accurate measurement of the detectors' 'difference' in rotational speed and thus the acceleration.

The mathematics are fairly straightforward. The following is taken from an article in the journal of the International Society for Optical Engineering, in which the builders of a large RLG designed to measure the earth's rotation describe their creation. (For the full article, see: http://www.spie.org/web/oer/september/sep96/gyro.html)

The two counterrotating beams form a standing-wave pattern in inertial space, enclosed and defined by the geometry of the mirrors involved. Imagine an ideal circle of radius R. At a point on the ring D, a detector is placed that looks at the standing-wave pattern. If now the frame F, which is the cavity, is rotated, the standing wave pattern stands still in inertial space (i.e., with respect to the fixed stars), and therefore the detector moves by the pattern, sensing the minima-maxima by producing a beat frequency.

For a rotation angle of (l/2)/R radian, where l is the vacuum wavelength, one beat is recorded. For a constant angular velocity W (radian/second), one sees therefore W/((l/2)/R) beats/second, or Hertz. This beat frequency Df can be written Df = 2RW/l, which, in terms of arbitrary geometries, is:

Df = 2RW/l = 4pR2W/(2pRl) = 4A·W/(Ll)

...where A·W is the scalar product of the area vector and the angular velocity vector; L is the length of the perimeter.

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