A fiber-optic gyroscope is a measurement device for measuring an angular velocity by utilizing the principle that the phase difference between two light waves which have propagated clockwise and counterclockwise in a fiber coil is in proportion to the angular velocity of the fiber coil. "Phase modulation" means that the phase of the light waves propagating in the optical fiber is modulated by expanding and shrinking a part of the optical fiber near an end of the fiber coil. The two lights-- clockwise light and counterclockwise light-- interfere with each other at an input surface of a photodetector. The modulation angular frequency is denoted by .OMEGA.. The intensity of the interference light which is detected by the photodetector includes an infinite series of a fundamental signal of a first order of modulation and harmonics of higher orders of modulation having oscillating parts of the frequency of n.OMEGA. (n:integer) and coefficients of Bessel functions.
Thus, the fundamental signal or arbitrary order of harmonics will be obtained by phase-sensitively detecting the output signal of the photodetector using carrier signals of the modulation frequency or of the modulation frequency multiplied by an integer. The amplitude of the odd number order harmonic components (including the basic signal) in the photodetector signal is written by EQU 2 E.sub.1 E.sub.2 J.sub.2m+1 (.xi.) sin .DELTA..theta. (1)
where E.sub.1 and E.sub.2 are amplitudes of the clockwise light and the counterclockwise light, J.sub.2m+1 (.xi.) is a Bessel function of the (2m+1) order, and .DELTA..theta. is the phase difference between the clockwise propagating light and the counterclockwise propagating light. ".xi." which designates the intensity of modulation is given by, EQU .xi.=2b sin (.OMEGA.Ln/2c) (2)
where b is the amplitude of the phase of modulation, .OMEGA. is the angular frequency of modulation, L is the length of the fiber coil, n is a refractive index of the optical fiber and c is a velocity of light in vacuum.
The amplitude of the second order harmonic component is written by, EQU 2 E.sub.1 E.sub.2 J.sub.2n (.xi.) cos .DELTA..theta. (3)
where J.sub.2n (.xi.) is a Bessel function of the 2n-th order. All harmonics include the phase difference .DELTA..theta.. The harmonics of even number order include cos .DELTA..theta., while the harmonics of odd number order include sin .DELTA..theta.. If the amplitude of the light and the strength of modulation are stable enough, the phase difference .DELTA..theta. will be obtained from the fundamental wave component alone.
In order to keep the modulation strength .xi. a constant value, the driving circuit for the phase modulator should be controlled so as to keep the amplitude of pertinent odd number harmonic component to be zero. Thus, .xi. is fixed to the zero point .xi..quadrature., if the 2n-th order of Bessel function; J.sub.2n (.xi..quadrature.)=0. If the modulation strength .xi. is constant, all the Bessel functions included in the series of the output signal are constant, known values.
If the amplitudes of the clockwise or counterclockwise propagating lights vary with time, the phase difference .DELTA..theta. will be obtained as a tangential form tan .DELTA..theta. by dividing the fundamental component by the fourth harmonic component or another even number harmonic component. Since the amplitudes of the lights have cancelled away by the division, the result includes no component varying with time.
Then the accurate phase difference .DELTA..theta. can be obtained by the three components; the basic wave component, the second order harmonic component and the fourth order harmonic component. Such phase modulated fiber-optic gyroscopes have been proposed by Japanese Patent Applications No. 1-57634, No. 1-57635, No. 1-57636, No. 1-57637, No. 1-291628, No. 1-291629, No. 1-291630, No. 1-291631, No. 1-295500, No. 2-3809, and No. 2-10055.
Since a fiber-optic gyroscope measures an angular velocity from the phase difference .DELTA..theta. between the clockwise propagating light and the counterclockwise propagating light by having them interfere, the polarization planes of the two lights must be the same. Here, a "polarization plane" is defined as a plane which includes the polarization vectors of light waves. Thus, the polarization plane is in parallel with both the direction of electric field and the direction of propagation of light.
If the polarization planes were different, the intensity of the interference light would decrease in proportion to cosine of the angle held by the two polarization planes. Furthermore, if the polarization planes met at a right angle, the two lights could not interfere at all.
Thus, the polarization planes of the clockwise propagating light and the counterclockwise propagating light must be coincident in order to obtain the intensity signal of the interference light. Since a single-mode optical fiber permits two degenerate lights with different polarization planes to propagate with the same phase constant therethrough, the polarization planes are likely to rotate spontaneously. If the polarization planes varied in a fiber coil made from a single mode optical fiber, the intensity of interference light would irregularly change in proportion to cosine of the angle between the polarization planes of the two lights. A single mode fiber cannot forbid the polarization planes of light from rotating spontaneously. "Single mode" means that the fiber permits a light of a certain phase constant to propagate therethrough. But polarization of light is another physical property of light. The lights with the same phase constant include two different lights with different polarization planes. The diameter of the core of an optical fiber determines the number of lights which can propagate through it by restricting the phase constants of the lights. This "single mode" surely means a single light regarding the phase constant. But as a single mode fiber has a small, rotationally symmetric core, two lights with different polarization planes can propagate through it with the same phase constant. Since the two lights have the same phase constant, the two lights would mix together in a single mode fiber, if the polarization plane of a light rotated spontaneously.
Instead of the single mode fiber, a polarization maintaining single mode optical fiber which has recently been manufactured can also keep a polarization plane of light, because the degeneracy regarding the polarization is solved in the fiber. It is a kind of single mode fiber. Briefly, it is called a polarization maintaining fiber. The core of the polarization maintaining fiber has anisotropy around the optical axis. The diameters or the stresses of the core are different in two directions vertical to the center axis. The two directions are called here optical principal axes. Thus, if a light is introduced in a polarization maintaining fiber, the phase constant will split into two values according to the direction of the polarization planes. The polarization plane of a light is kept to be either of the two optical principal axes in the fiber because of the induced difference of the phase constants.
Thus, such an improvement of fiber-optic gyroscopes would be proposed that almost all optical paths should be constructed by polarization maintaining fibers instead of single mode fibers and the light should be converted into a linearly-polarized light by a polarizer before it was splitted into two partial lights by a beam splitter. Since the polarization planes of the partial lights would be maintained in coincidence with two vertical principal optical axes and no rotation of the polarization planes would occur, the clockwise propagating light or the counterclockwise propagating light would completely interfere because of the coincidence of the polarization planes. Thus, the fiber-optic gyroscope using the polarization maintaining fibers would be an excellent improvement.
However, such an improved fiber-optic gyroscope has never produced yet in spite of the theoretical advantages. It would be far expensive because a polarization maintaining fiber is still more expensive than a simple single mode fiber.
After all, a fiber coil and most other optical paths should preferably be constituted by simple single mode fibers. However, single mode fibers have some difficulties which have been partially described.
Although it is called a single mode fiber, it means that one mode only about the phase constant stands in the fiber. In practice, there are two modes of light with different polarization planes. Two modes of light with different polarization planes would be independent in an ideal case. However, two modes of light are likely to mix together, when the polarization planes rotate by some reason, because two modes have the same phase constant in macroscopic scale.
Furthermore, two modes with different polarization planes have not the same effective length of light paths, even when two modes have propagated by the same length, because the microscopic fluctuations of the light paths are different.
Thus, if two modes with different polarization planes were allowed to propagate in a fiber coil, the clockwise transmitted light and the counterclockwise transmitted light which have different effective lengths of light paths would interface together. Then, the interference light would include an offset deriving from the difference of the effective lengths. Here, an "offset" means a deviation of the phase difference .DELTA..theta. from 0 when the angular velocity .OMEGA..sub.o of a fiber coil is 0. It is a matter of course that two modes bear the offset, because of the effective differences of the optical paths.
The clockwise propagating light and the counterclockwise propagating light must experience entirely the same optical path for suppressing the offset. For this purpose, it would be preferable that the polarization plane of the light should be fixed to a certain direction by propagating through a polarizer before the light is divided by a beam splitter or an optical fiber coupler. If the polarization plane is fixed, only one mode with the determined polarization plane will propagate in a single mode fiber of a fiber coil. Then, the effective length of the optical paths will be rigorously the same. The situation is similar to the case of the mentioned polarization maintaining fiber up to here.
However, since the polarization plane of light is likely to rotate in a single mode optical fiber, the fixation of the polarization by a polarizer is not sufficient to obtain a maximum output without fluctuation of amplitude of light.
The light linearly-polarized by a polarizer is splitted into two lights by a beam splitter. The two lights propagate clockwise or counterclockwise through the fiber coil. Then, two lights meet together at the beam splitter or at the fiber coupler and pass through the polarizer in the inverse direction. At the moment, the polarization planes of the two clockwise and counterclockwise propagating lights do not necessarily coincide with the principal axis of the polarizer owing to probable rotation of the polarization planes in the single mode fiber of the fiber coil.
A deviation angle between the principal axis of the polarizer and the polarization plane of a light is denoted by .phi.. If .phi. is not 0, the amplitude of the light penetrating through the polarizer decreases in proportion to cos .phi.. The angles .phi. for the clockwise light and for the counterclockwise light are not the same. Furthermore, the deviation angles .phi. will change with temperature. Thus, the amplitudes of the clockwise light and the counterclockwise light (for simplicity, "propagating" will be often omitted in the clockwise or counterclockwise propagating light) would vary at a photodetector. Thus, the output of the photodetector would also fluctuate owing to the rotation of the polarization planes of the lights.
Therefore, it was found that a depolarizer should be used in addition to the polarizer, if the fiber coil was constituted by a single mode optical fiber. A depolarizer is an optical device which converts a linearly-polarized light into a non-polarized light. Here, a non-polarized light means ensemble of partial lights with polarization planes distributed uniformly in all directions. Namely, although all the partial lights have different polarization planes, the vector sum of the polarization planes is always zero. Thus, the light has no effective polarization plane as a whole. The action of the depolarizer is reverse to that of the polarizer.
Such a fiber-optic gyroscope equipped with a depolarizer was proposed by,
K. Boehm et al.: "Low-Drift Fiber Gyro Using a Superluminescent Diode, ELECTRONICS LETTERS, vol. 17, No. 10, p352 (1981).
FIG. 2 shows the schematical view of the fiber-optic gyroscope proposed by K. Boehm.
The light emitted from a light emitting device (1) passes through a lens (21), a beam splitter (22), a polarizer (23) and a lens (24) and enters one end of an optical fiber (25). The lenses (21) and (24) make the light enter the narrow core of the optical fiber (25) by converging the light emitted with a wide solid angle from the light emitting device (1). Since the polarizer (23) is positioned between the lenses (21) and (24), the light entering the optical fiber (25) is linearly polarized. Namely, a single mode of light with one polarization plane enters the optical fiber (25). The linearly-polarized light propagates all the optical devices in the gyroscope. The optical fiber (25) couples with another optical fiber (27) by an optical fiber coupler (26). The optical fiber coupler (26) divides the incident linearly polarized light into two lights which will propagate clockwise or counterclockwise through a fiber coil (4). The clockwise light once goes out in the air, passes through a lens (28), a depolarizer (29) and another lens (30). The depolarized light is converged by the lens (30) at one end of a single mode fiber of the fiber coil (4). The light entering the optical fiber propagates clockwise through the fiber coil (4) and passes through a phase modulator (5).
On the other hand, the counterclockwise light enters another optical fiber (27), passes through the phase modulator (5) and propagates counterclockwise through the fiber coil (4). Then, the counterclockwise light passes through the depolarizer (29). The depolarizer (29) converts a linearly-polarized light into a non-polarized light to the contrary of the action of a polarizer. The depolarizer is called a Lyot depolarizer which has two transparent birefringent crystals with rectangular optical axes for ordinary and extraordinary rays that are glued together so as to settle the angle between two optical axes of the transparent crystals to be 45 degrees. The thicknesses of the optical crystals are in a ratio of 1:2.
Both of two crystals have so large thickness that the difference of the optical paths between the ordinary ray and the extraordinary ray is longer than the coherent length of the light emitting device (1). Thus, a thinner depolarizer requires such a light emitting device with a shorter coherent length of light. Here, some terms are briefly explained. Coherent light is an ideal light which should have the waves with a common phase relation extending unlimitedly in space and in time. Two lights with a common phase can interfere together. Thus, two lights which are coherent together can interfere. In general, gas lasers have good coherency. Coherent length is the maximum length within which the waves of a light have a common phase relation. Birefringence means that the refractive index depends on the polarization plane of light. A uniaxial birefringence crystal has two principal axes which are perpendicular together. A ray with a polarization plane parallel with one of the principal axes is called an extraordinary ray. The other ray with a polarization plane parallel with the other of the principal axes is called an ordinary ray. The refractive index is different for the ordinary ray and the extraordinary ray. Since an optical path is defined as the product of the refractive index and the path length, the difference of the optical paths is the product of the path length (thickness of crystal) and the difference of the refractive indexes.
The fiber-optic gyroscope shown in FIG. 2 which had a fiber coil constituted by a single mode fiber had solved the problem of the drift of the output power caused by the spontaneous rotation of the polarization plane by using a polarizer and a depolarizer.
Boehm et al. proposed another fiber-optic gyroscope shown in FIG. 3. The light emitted from a light emitting device (1) passes through a cylindrical lens (33), a lens (34) and another lens (35), and convergently enters an optical fiber (36). Another fiber (32) communicating with a photodetector (6) is coupled with the optical fiber (36) by a coupler (37). The light going out from the optical fiber (36) passes a lens (38), a polarizer (39) and a lens (40). The light is now linearly polarized. The polarized light convergently enters another fiber (41). The light is divided by a coupler (42) into two partial lights; clockwise, counterclockwise propagating lights.
The clockwise light goes out in the air from the fiber (43). The light passes through a lens (45), a crystal depolarizer (Lyot depolarizer) and a lens (47). The light is now depolarized.
The depolarized light convergently enters a single mode fiber and propagates through a fiber coil (4) clockwise. The clockwise propagating light is then phase-modulated by a phase modulator (5). The modulated clockwise light passes through the coupler (42) and the polarizer (39) in a reverse direction. Then, the light passes through the coupler (37) and enters the photodetector (6).
The counterclockwise light passes through the fiber coupler (42) and the phase modulator (5). The modulated counterclockwise light propagates through the fiber coil (4) counterclockwise. The light passes through the depolarizer (46), the fiber coupler (42), the polarizer (39) and the coupler (37). The light enters the photodetector (6). Thus, the clockwise light and the counterclockwise light interfere on the surface of the photodetector. The intensity of the interference light is detected.
Both the fiber-optic gyroscopes shown in FIG. 2 and in FIG. 3 fix the polarization plane to a unique plane at first, divide the light into two lights and depolarize the light. Since the clockwise light and the counterclockwise light are phase-modulated at different times, the effect of the phase-modulation is not cancelled and is included in the output signal of the photodetector. The output signal will be phase-sensitively detected by a lock-in-amplifier with the modulation signal. The method for modulation and demodulation of the signal is similar to the conventional phase modulated fiber-optic gyroscopes without depolarizer.
In these improvements, the lights once polarized are depolarized by a depolarizer and then polarized again. As mentioned before, the amplitude of the light passing through a polarizer is in proportion to cosine of the deviation angle held between the principal axis of the polarizer and the polarization plane of the light. Even if the polarization planes of partial lights spontaneously or inducedly rotated in the fiber coil, half of the partial light energy could pass through the polarizer, because the rotation of the polarization planes would happen to all the partial lights with the same probability and the partial lights would have the polarization planes distributed in all directions with the same probability.
Therefore, the problem of the drift or the decrease of the output signal owing to the probable rotation of the polarization planes was solved by the improvements.
However, the gyroscopes shown in FIG. 2 and FIG. 3 had another difficulty. They were not practical, compact devices but unpractical, bulky devices elaborately built up in a laboratory. The gyroscopes included discrete, bulky optical parts for depolarizers and polarizers which were constituted by optically active single crystals. The polarizers and depolarizers were far larger than optical fibers. Furthermore, bulky lenses must be positioned in front of and behind the polarizers or depolarizers, because the lights must pass through them as plane waves. These discrete optical parts made the gyroscopes very bulky and large.
For practical use, fiber-optic gyroscopes must be small, weightless devices. In order to make such a practical, small, weightless fiber-optic gyroscope, it is strongly desired that a depolarizer and polarizer should be made only of optical fibers.
It is well-known that a depolarizer and a polarizer can be made of optical fibers. A practical fiber-optic gyroscope would not be obtained before the optical parts could be made only of optical fibers. Besides the depolarizer and polarizer, such a beam splitter with a prism is similarly undesirable for a compact gyroscope. The bulky beam splitter should be replaced by an optical fiber coupler.
The replacement of the beam splitter by an optical fiber coupler leads to the version shown in FIG. 3. Would it be enough to replace the bulky, discrete optical components, depolarizer (46) and polarizer (39), by the equivalent parts constituted by optical fibers for obtaining a practical, compact fiber-optic gyroscope? It is not sufficient. Perhaps the reason why such a simple replacement would be insufficient has been noticed by this inventors for the first time. The reason will now be explained.
Although the light just emitted from the light emitting device (1) is linearly polarized in a certain direction determined by the geometric shape of the light emitting device (1), the polarization plane may rotate spontaneously or inducedly in a single mode optical fiber before the polarizer. Although the intermediate fiber (36) is short, it is difficult to harmonize the polarization plane of the light emitted from the light emitting device (1) with the principal axis of the polarizer. If the polarization plane did not coincide with the principal axis of the polarizer, the amplitude of the light which can pass through the polarizer would decrease.
In the case of using a discrete polarizer of a bulk crystal as shown in FIG. 2 or FIG. 3, it is possible to adjust the direction of the polarizer by rotating it so as to maximize the output power of the photodetector. However, in the case of using a fiber type polarizer, it is impossible to adjust the principal axis of a fiber type polarizer, because a light can be transmitted through the fiber type polarizer after it has been coupled with the single mode fibers. The coupling between the fiber type polarizer and the other fiber is done by melting and fitting their ends. If the fiber type polarizer is connected to the other fibers, the relative rotation therebetween is strictly forbidden.
Rotation of the light emitting device (1) may enable us to harmonize the polarization plane with the principal axis of the fiber type polarizer. If so, the polarization plane sometimes would rotate in a single mode fibers in front of and behind the fiber type polarizer spontaneously or inducedly by the change of temperature, the stress or the magnetic field. Such rotation would reduce the light power passing through the polarizer and would change the scale factor which is a ratio between an input variable and an output signal.
As described before, the problem of the rotation of the polarization plane of light in the single mode fibers between the fiber type polarizer and the fiber coil has successfully been solved by inserting a depolarizer at a point in the vicinity of the fiber coil. However, the inventors think another problem of the rotation of the polarization plane in the single mode fibers between the light emitting device and the polarizer has never been anticipated nor solved yet.
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