Gyroscopes are key components of the navigation systems that keep vehicles on course. In fact, gyroscopes can be found in anti-skid systems in cars, satellites, the Space Shuttle, airplanes, ships, and missiles. The first practical gyroscope instruments were used to create “artificial horizons” for airplanes. The first gyroscope was invented in 1852 by Leon Foucault, however it was Elmer Sperry who made the first practical instruments in 1910 [1]. The first gyroscopes were mechanical, but they’re now made with fiber-optics, ring lasers, and even with solid state MEMS devices [1], [4].
Navigation Systems
Gyroscopes are fundamental building blocks of the navigation systems used to guide airplanes, ships, and spacecraft [1]. A gyroscope is essentially an instrument that measures rotation [1]. By itself, gyroscopes are useful in applications such as measuring the wing angle in aircraft in flight and the roll of ships in heavy seas. However, combined with accelerometers, they are used to create inertial guidance navigation systems [4].
An inertial guidance navigation system is essentially a form of “dead-reckoning”. If the starting position is known, keeping track of the acceleration and rotation that a vehicle undergoes can be used to determine its current position [4]. Such a guidance system is constructed with 3 accelerometers and 3 gyroscopes, each measuring acceleration and rotation in a single axis. Such a system can measure an aircraft’s position, velocity, acceleration, attitude, and heading to a high degree of accuracy [4].
Gyroscopes: Principles of Rotation Measuremens
Before considering photonic solutions to the problem of rotation measurement, it is important to consider previous methods. An important form of gyroscope, still in use today, is the mechanical gyro. The invention of the first mechanical gyroscope is credited to the French experimental physicist Leon Foucault in 1852, who planned to use it to measure the rotation of the earth [2]. As shown in figure 1, a mechanical gyroscope is created by suspending a rapidly spinning rotor inside three frictionless rings, called gimbals.
Figure 1 – [Left] A mechanical gyroscope contains a massive spinning rotor with an angular momentum pointed along the spin axis. If the gyroscope is tilted, [right], the rotor maintains its spin due to conservation of momentum. The tilt of the gimbals gives an indication of the tilt of the instrument [3]
Due to conservation of angular momentum, the spinning rotor maintains its direction in space even if the gyroscope is tilted. Therefore, tilting the gyroscope will cause the gimbals to reorient themselves to maintain the rotating mass in its original spin direction. The angle of rotation of the outer ring about its axis is proportional to the rotation of the gyroscope about its spin axis [3].
Principles of Operation of Fiber-Optic Gyroscopes
Fiber-optic gyroscopes (FOGs) are based on the Sagnac effect. Sagnac interferometers are based on the principle that if the interferometer is rotating, light waves traveling in opposite directions in a loop will acquire a phase difference, resulting in interference. The phase difference is due to the fact that light travels with a constant speed, c, as shown in figure 2. If the interferometer is rotating counter-clockwise (CCW) with an angular velocity, by the time the clockwise (CW) traveling wave (in red) reflects from mirror M1, it will have moved slightly closer to the wave. Likewise, mirror M1 will have moved slightly away from the CCW traveling wave (in blue).
Figure 2 – An illustration of the Sagnac effect. In an interferometer rotating counter-clockwise , the counter-clockwise propagating beam (red) will experience a shorter path length while the clock-wise beam (blue) will experience a longer path length. The difference in path length leads to a phase shift between the two beams and hence interference.
Therefore, the CW traveling wave will have a shorter path length while the CCW wave will have a longer path length. The result will be a net phase difference between the two waves, causing interference.
Interference Fiber-Optic Gyroscopes
The interference fiber-optic gyroscope (IFOG) is based on detecting the phase shift difference that occurs in an interferometer due to the Sagnac effect. Unfortunately, the Sagnac effect is relatively weak, so to overcome this problem kilometers of fiber optic cable are used to increase the path length of the instrument.
An example of the extreme sensitivity needed by gyroscopic instruments is the fact that an inertial guidance system must be capable of detection rotations of 0.01 degrees/hour. Using light with a wavelength of 1 micron, 1 kilometer of fiber and a coil diameter of 30 cm, the resulting phase shift is only 10^-7 rad, which is at the detection limit of current instruments [5].
In order to increase accuracy, a practical IFOG system would measure interference effects at the same port as the input light, such that both lightwaves experience two reflections. This eliminates the extra phase shift from reflection that would otherwise be introduced into the measurement. A polarizer is also placed at the input to eliminate the polarization that is introduced to the light in the fiber. This extra polarization is introduced when light travels through the fibers since optical fibers are birefringent to some degree. Birefringence refers to the fact that light of different polarizations is refracted differently. This occurs in optical fibers most commonly because of small defects in the fibers themselves.
Commercial Examples of FOGs
FOGs are commercially sold by a number of manufacturers, for civilian, military, and space applications. An example of an inertial guidance system is the IMU 200, developed by Northrop Grumman [6]. The IMU 200 contains three gyroscopes and three accelerometers and is designed for high-performance applications, especially for weapons guidance systems. The system can withstand accelerations of 12 g’s, has a long-term stability of 0.5 degrees/hr and misalignment error of 0.1 mRad [6]. A version of this guidance system is currently used in the National Missile Defence interceptor missile [6]. An important point is that in many countries, including the United States, it is illegal to export highly accurate gyroscopes, because of their potential uses in weapons [1].
Future Trends: Photonic-Bandgap Fibers
The prime limitation on the accuracy of FOGs are parasitic effects that occur inside the silica fibers. These include Rayleigh backscattering, the Kerr effect, the Faraday effect, and thermal effects [7]. As mentioned previously, Rayleigh backscattering is caused by impurities in the fiber and leads to large random errors in measurement due to spurious signals. The Faraday effect causes a change in the birefringence of the fiber on the application of a uniform magnetic field. The Kerr effect, meanwhile, is a non-linear optical process that changes the index of refraction of the fiber with small variations of input power of the two beams. This causes a “drift” in the measured rotation rate [5]. Lastly, uneven thermal effects in the fiber can cause unwanted phase change. Air-core photonic-bandgap fibers reduce the thermal effects by a factor of 3-10 and the other effects by a factor of 100-500! [7].
A photonic bandgap material is one in which certain wavelengths of light are unable to propagate. This is very similar to an electronic bandgap, where certain electron energies are not allowed. The photonic bandgap is crated by a periodic microstructure. This effect is also seen in nature, for example in butterfly wings. Butterfly wings contain a fine structure, forming a photonic bandgap. Light with wavelengths in the bandgap region is strongly reflected, forming the bright colours that pattern the wings [8].
A dielectric periodic lattice will exhibit the photonic bandgap effect. For example, as shown in figure 3, this effect is exhibited by a diamond lattice [9]. To create a photonic bandgap fiber, a periodic lattice of airholes is formed in the fiber, creating the photonic bandgap material. A defect center, the central air-core is then introduced. Light propagating in the air core will not be able to leave the fiber because of the photonic bandgap material surrounding it [8]. The structure of a photonic crystal fiber is shown in figure 4.
Figure 3 – [Left] An illustration of a diamond lattice structure. [Right] The resulting bandgap structure [9].
Figure 4 – An illustration of a commercially available photonic bandgap fiber manufactured by Crystal Fibre [8].The accuracy improvements found in air core fibers are mainly due to the advantageous properties of air over silica. The Kerr constant of air is about 800 times smaller than in silica. Likewise, the Faraday effect is about 500 times weaker. Rayleigh scattering is theoretically lower in air. Unfortunately, in current air-core fibers, Rayleigh scattering effects are actually higher than in silica fibers. This is mainly due to small dimensional fluctuations in the wall of the fiber introduced in the manufacturing process [7].
Researchers at Stanford University have created the first air-core photonic bandgap based fiber-optic gyroscope. The FOG was built with 235 m of commercially available fiber manufactured by Crystal Fiber. The minimum sensitivity of the gyroscope was 2.7 degrees/hour and the long term drift was 2 degrees per hour. To compare the performance with regular fiber, the crystal fiber was replaced with 200 m of silica single-mode fiber. The resulting minimum sensitivity was 7 degrees/hour and the long term drift was 3 degrees per hour [7].
The gyroscope created was essentially a proof-of-concept design. Currently, much work is left to be done in the development of photonic bandgap fibers. Current fibers have high loss (~19 dB/km for high quality fiber) and scattering mechanisms. Ultimately, research and development into improved photonic bandgap fibers will lead to FOGs with improved long-term stability, simplified design, lower cost, and higher reliability [7].
References:
[1] Fischetti, M., Gyroscope Guidance: Hidden Guides, Scientific American, Vol. 286, n. 6, June 2002, pp. 96-97
[2] Greenslade, T., Gyroscope, Instruments for Natural Philosophy, 2006
http://physics.kenyon.edu/EarlyApparatus/Mechanics/Gyroscope/Gyroscope.html
[3] Hyperphysics, Gyroscope, Hyperphysics, 2006
http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html
[4] King, A.D., Inertial Navigation – Forty Years of Evolution, GEC Review, Vol. 13, no. 3, 1998. pp. 140-149
[5] Bergh R. et al., An Overview of Fiber-Optic Gyroscopes, Journal of Lightwave Technology, Vol. LT-2, no. 2, 1984. pp. 91-107
[6] Northrop Grumman, IMU 200 Product Brochure, Northrop Grumman Navigation Systems Division, 2000
http://www.nsd.es.northropgrumman.com/Html/IMU200/BrochureIMU-200_Inertial_Measuring_Unit.pdf
[7] Kim H.K. et al., Air-Core Photonic-Bandgap Fiber-Optic Gyroscope, Journal of Lightwave Technology, Vol. 24, no. 8, 2006. pp. 3169-3174
[8] Crystal Fibre, Technology – Air Guiding Fibers, Crystal Fibre, 2005
http://www.crystal-fibre.com/technology/technology_tutorial4.shtm
[9] Johnson, S., Photonic Crystals: Periodic Surprises in Electromagnetism, MIT, 2004
http://ab-initio.mit.edu/photons/tutorial/
[10] Sherman, R., Star Wars Programs, FAS.org, 2006
http://www.fas.org/spp/starwars/program/000708-nmd_ift5_8.jpg
[11] Sensormag, Sensors, Sensormag.com, 2006
http://sensorsmag.com/sensors/data/articlestandard/sensors/142006/318761/0900_101f.gif
[12] Northrop Grumman, Navigation Systems Division Brochure, Northrop Grumman Navigation Division, 2006
http://www.nsd.es.northropgrumman.com
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