CA2211992A1 - Optimum coupler configuration for fiber optic rate gyroscope using 3x3 coupler - Google Patents
Optimum coupler configuration for fiber optic rate gyroscope using 3x3 couplerInfo
- Publication number
- CA2211992A1 CA2211992A1 CA002211992A CA2211992A CA2211992A1 CA 2211992 A1 CA2211992 A1 CA 2211992A1 CA 002211992 A CA002211992 A CA 002211992A CA 2211992 A CA2211992 A CA 2211992A CA 2211992 A1 CA2211992 A1 CA 2211992A1
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- optical
- waveguides
- sensing loop
- optical waveguides
- fiber
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C19/00—Gyroscopes; Turn-sensitive devices using vibrating masses; Turn-sensitive devices without moving masses; Measuring angular rate using gyroscopic effects
- G01C19/58—Turn-sensitive devices without moving masses
- G01C19/64—Gyrometers using the Sagnac effect, i.e. rotation-induced shifts between counter-rotating electromagnetic beams
- G01C19/72—Gyrometers using the Sagnac effect, i.e. rotation-induced shifts between counter-rotating electromagnetic beams with counter-rotating light beams in a passive ring, e.g. fibre laser gyrometers
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
- G02B6/24—Coupling light guides
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- Optics & Photonics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Electromagnetism (AREA)
- Power Engineering (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Gyroscopes (AREA)
Abstract
A fiber optic rotation sensor includes a 3 x 3 optical coupler formed of first, second and third optical waveguides. The first, second and third optical waveguides are formed such that the fractions of light coupled from anyone of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of thermally-induced changes in the interaction length. An optical signal source provides an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides. The optical fiber in which the sensing loop is formed has ends that are coupled to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in a fiber optic sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
Description
OPrlMUM CONFIGURA'llON OF A 3 X 3 COUPLER FOR A PrBER OPI'IC GYROSCOPE
BACKGROUND OF T~E INVENTION
This invention relates generally to Sagnac effect rotation sensors S and particularly to fiber optic rotation sensors that guide counterpropagating light waves in a sensing loop to measure rotations about a sensing axis perpendicular to the plane of the sensing loop. $till more particularly, this invention relates to fiber optic rotation sensors that use 3x3 couplers to ~upply optical signals to the sensing loop and to guide 10 the optical output signals from the sensing loop to electrical apparatus that processes the optical output signals to determine the rotation rate.
Piber optic rotation sensors are well-known in the art. Previous fiber optic rotation sensors included evanescent field couplers to couple light between two lengths of optical fiber. Subsequently, fiber optic 15 rotation sensors using 3x3 coupler were developed. The primary advantage of using a 3x3 coupler in a fiber optic rotation sensor is the ease with which such devices are interfaced with electronics.
United States Patents 4,440,498 and 4,479,715 to Sheem disclose two fiber optic rotation sensors that include 3x3 couplers. United States 20 Patent 4,440,498 is clirected to a fiber optic rotation sensor that includes a fiber optic sensing lloop and an input fiber. A 3x3 fiber optic coupler divides light between the input fiber and the two legs of the fiber optic sensing loop.
United States Patent 4,479,715 discloses a Sagnac effect rotation 25 sensor in which the e:nds of a fiber optic sensing loop are coupled to a pairof optical waveguides. Light is input to a central input waveguide that is between the optica] waveguides that are coupled to the ends of the sensing loop fiber. The three optical waveguides are arranged to fo~n a 3x3 optical coupler. The input light is coupled from the central input waveguide to the optical waveguides that are connected to the optical fiber coil to produce the counterpropagating waves in the fiber optic sensing loop. The waves traverse the sensing coil and combine in the 5 coupler. The combined waves are detected, and the resulting electrical signals are processed to deterrnine the rotation rate.
United States Patent 4,944,590 to Poisel et al. discloses an optical fiber gyroscope that uses a 3x3 coupler to couple optical signals into and out of a fiber optic sensing loop. Poisel et al. discloses a photodetector 10 arranged to detect the light that has been input the 3x3 coupler that is not coupled into the fiber optic sensing loop. The electrical signal resulting from detecting this light is used in signal processing circuitry to make ad~ustments for variations in the input light intensity.
Such fiber optic rotation sensors may be operated in phase 15 quadrature, which provides maximum sensitivity at zero rotation rate.
Unfortunately, previous fiber optic rotation sensors that include 3x3 optical couplers are sensitive to temperature changes. The coupling ratios of the 3x3 fiber optic couplers are temperature-sensitive such that bias errors of 1000~ per hour are typically observed. Errors of such m~nit~ e~0 are unacceptable for most applications of rotation sensors.
~UMMARY OF THE INVENTION
The present invention is an improved fiber optic rotation sensor using 3x3 couplers with optimized coupling ratios. The coupling ratios are selected to prevent changes in the amount of light coupled into the two 25 counterpropagating waves caused by temperature changes and other mechanical factors. The selected coupling ratios also m~ximi7e the optical power output that is delivered to the rate photodetectors.
A fiber optic rotation sensor according to the present invention comprises a 3x3 optical coupler that includes first, second and third optical waveguides arranged to have an interaction length in which light couples between the first, se'cond and third optical waveguides, the first, second S and third optical walveguides being formed such that the fractions of lightcoupled from any one of the first, second and third optical waveguides to the other two opticall waveguides are constant, independent of thermally-induced changes in the interaction length. An optical signal source is arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides. The optical fiber in which the sensing loop is formed has ends that ~re coupled to the second and third optical waveguides to receive optical signals that form cou~ ,o~g~ting optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
The optical coupler is forrned such that first, second and third optical waveguides being formed such that the optical splitting ratios between the first, second and thirld optical waveguides are 0.4108: 0.1783: 0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterprop~g~tin~ waves is 0.4108A2 and the optical intensity output by the first optical waveguide is 0.1783A2.
An appreciation of the objectives of the present invention and a more complete understanding of its structure and method of operation may be had by stndying the following description of the preferred embodiment and by referring to the accompanying drawings.
CA 022ll992 l997-07-3l WO 97/~1981 PCT/US95/16178 BRIEF DESCR~TION OF THE DRAVVIN~S
FI~. 1 illustrates a fiber optic rotation sensor that includes a 3x3 evanescent field optical coupler;
FIG. 2 schematically illustrates a 3x3 coupler; and FIG. 3 illustrates the derivative with respect to coupling length of the intensity of the signal output by the fiber optic rotation sensor of FIG.
1.
DESCRIPTION OF TH~ PR~FERRED EMBODIMENT
Referring to FIG. 1, a fiber optic rotation sensor 10 includes a 3x3 optical coupler 12 and a length of optical fiber 13 arranged to form a fiber optic sensing coil 14. The optical coupler 12 includes optical waveguides 1-3 formed on a substrate 15. The optical fiber 13 has ends 16 and 18. The fiber ends 16 and 18 are butt-coupled to ends 20 and 22 of the corresponding optical waveguides 1 and 2, respectively.
A pair of output optical fibers 30 and 32 are connected to ends 34 and 36 of the optical waveguides 2 and 3, respectively. The output optical fiber 30 directs a light beam to first photodetector 38, which produces an electrical signal S l that is indicative of the intensity of the optical signal transmitted thereto by the output optical fiber 30. Similarly, the output optical fiber 32 directs a beam of light to a second photodetector 40, which produces an electrical signal S2 that is indicative of the intensity of the optical signal tr~n~mitte-l thereto by the output optical fiber 32.
The optical waveguide l is formed in the substrate 15 between the optical waveguides 2 and 3. The optical waveguides 1-3 are arranged to form the 3x3 coupler 12. The 3x3 coupler 12 is preferably an evanescent field coupler.
An input optical fiber 46 has an end 48 that receives light from a light source 50. The other end 52 of the input optical fiber 46 is butt-WO 97/21981 PCTIUS95/~6I78 coupled to an end 54 of the optical waveguide 1. An output optical fiber 56 has one end S~ butt-coupled to an end 60 of the central optical waveguide 3. The other end 62 of the output optical fiber 56 directs a beam of light to a third detector 64, which produces an electrical signal S3 5 that is indicative of the intensity of the optical signal tran~mitt~d thereto by the output optical fiber 56.
The 3x3 coupler 12 is preferably an evanescent field coupler that couples optical sigl~als between the optical waveguide 1 and the optical waveguides 2 and :3. A portion of the light input to the 3x3 fiber optic 10 coupler 12 remains in the optical waveguide l.
Referring to FIG. 3, the 3x3 coupler has a coupling length L in which the evanesce~t fields of light waves guided by the waveguides 1-3 interact so that lighl: couples between them. The intensity of light coupled between the waveguides 1-3 is a function of the coupling length L. As 15 the temperature of the coupler 12 fluctuates, the light intensity coupled between the wavegllides 1- 3 also fluctuates.
In an ideal environment the three coupling ratios of the 3x3 optical coupler 12 are all equal to 1/3. When the coupling ratios are all equal to 1/3, the light intensities output from the three optical waveguides 1-3 are 20 equal. However, because of temperature sensitivity mentioned above, if the coupling ratios of the 3x3 optical coupler 12 are all 1/3 at a particular desired operating temperature, then unacceptably large errors result because of unavoidiable temperature fluctuations that cause the coupling ratios to change. l[he present invention comprises a fiber optic rotation 25 sensor using a 3x3 coupler that have coupling ratios selected to minimi7e the bias errors to the order of 10~ to 100~ per hour and which is insensitive to temperature changes. It has been found that there is a set of coupling ratios for which the fraction of light coupled into any selected one of the CA 022ll992 l997-07-3l optical waveguides 1-3 remains constant as the coupling length L changes in response to temperature changes.
The optimum configuration for the 3x3 optical coupler 12 is insensitive to temperature changes while providing a lar~er rate 5 discriminant than has been obtained with previous designs. Referring to Figs. 2 and 3, the 3x3 ~1ber optic coupler 20 may be described by the linear differential equations da d J + ikj j+laj+l + ikj j+2aj+2 = 0 (1) where:
j=1,2,3 j=j+3 aj is the light amplitude in waveguide j; and k is the coupling ratio between any two of the three fibers 1-3.
For example, k,2 is the coupling ratio between waveguides 1 and 2;
k23 is the coupling ratio between waveguides 2 and 3, and k3l is the coupling ratio between waveguides 3 and 1. The coupler 12 is preferably formed so that the coupling constants are kl2 = k23 = k3l - k so that the solution to equation (1) is aj(z)=cjeikZ+de~i2kZ with the condition that ~,cj=1, (2) j=l 20 where c and d are constants. If the power input to the fiber optic rotation sensor 10 by the input optical fiber 46 to the 3x3 coupler 12 is A~, then the amplitude of the light in the waveguides at the input end where z = 0 is given by:
al(0)=A,and ~3~
a2(0)=a3(0)=o- (4) Using Eqs. ('3) and (4) in Eq. (1) gives information that may be used to find expressions for the constants c and d in terms of A, for which a numerical value can easily be ascerlained.
A = cleik~ + de-i2kz A=cl+d. (6) cl = A--d. (7) ~ = C2eik~ + dlo--i2kO (8) c2 =--d. (9) O = c3eik~ + de-i2kO (10) c3 =-d. (11) From Eqs. (7), (9) and (11), it is found that cl+c2+c3=~o. (12) A--d--d--d =- 0. (13) Therefore, the constants c~, C2, C3 and d are given by:
d= 3; (14) c _ A and (15) cl =--A. (16) At the other end of the coupler where the distance z = L, the solution equation for optical waveguide 1 becomes:
al(L) =--Aeik:L + 1 Ae-i2kL (17) S~uaring the amplitude to obtain the intensity of the light in optical waveguide 1 gives:
q ¦al(L3¦ = ¦--A~ikL + 1 Ae~i2kL¦ (18) ¦al(L)¦2 = ~ eikL + e-i2kL¦2 (19) ¦al~L)¦2 =--l2coskL+i2sinkL+cos2kL-isin2kLI2. (20) W O97/21981 PCT~US95/16178 lal (L)¦2 =--¦2cos kL + cos2kL + i(2sin kL - sin2kL)¦2 . (21) ¦al(L)¦2 = 9 (4cos~ kL+4coskLcos2kL+cos22kL+
4 sin2 kL - 4 sin kL sin 2kL + sin2 2kL) . (22) ¦al(L)¦~= g (5+4cos3kL). (23) S At the other end of the coupler where the distance z = L, the solution equation for optical waveguide 2 becomes:
la2(L)1 = ¦--1 AeikL + 1 Ae~i2kL¦ (24) ¦a2(L)¦2=--¦-coskL-isinkL+cos2kL-isin2kL¦2. (25) ¦a2(L)¦2 = 9 I(-coskL + cos2kL) - i(coskL + sin2kL)I2. (26) ¦a2(L)¦ = g (cos2 kL - 2 cos kL cos 2kL + cos2 2kL) +sin2 kL t 2sinkLsin2kL + sin2 2kL). (27) ¦a2(L)¦2 = 9 (2-2(coskLcos2kL-sinkLsin2kL). (28) ¦a2(L)¦2 = 9 (1-cos3kL). (29) Because a2 = a3, where the distance z = L, the solution equation for optical waveguide 3 is:
¦a3(L)¦2 =¦A2(L)¦2 = 9 (1-cos3kL). (30) The optical intensity in the optical waveguides 2 and 3 is the optical intensity input to the fiber optic sensing coil 14 at the ends 16 and 18 of the optical fiber 12. Therefore the input to the legs of the fiber optic gyroscope are ¦a2(L)¦2 and ¦a3(L)¦2 given by Eqs. (29) and (30). These inputs to the fiber optic sensing coil 14 have a definite phase relationship.
After traversing the fiber optic sensing coil 14, there is a phase shift ~
between the counterpropagating waves. The return inputs to the coupler wo 97nl981 PCT/US9S/16178 12 after the counterprop~g~ting waves traverse the fiber optic sensin_ coil 14 are given by:
al(O)= :p; (31) - A2 -5 i~
a2(0)= 2 9 (1-cos3kL e2; and (32) - 2 -.5 i~
a3(0) = 2 9 (1- cos3kL e 2 . (33 Loop loss in the optical fiber 12 is ignored. The angle ~ is the Sagnac phase shift angle between the beams caused by rotation of the sensing loop at angular velocity Q about the sensing axis, which is perpendicular to the plane of the fiber optic sensing coil 14. The phase 10 angle ~ and the ~angular velocity Q are related by the Sagnac equation:
q, 2~eD Q
where ~ is the length of the fiber in the sensing coil 14, D is the diameter of the sensing coil 14, ~ is the wavelength of the optical signals and c is the speed of light.
After propag;ating through the coupler 12 through the coupling len~th, L, the optica:L signals that have been output from the output of the fiber optic sensing coil are given by:
a~ ,L)= 3 --9 (1--cos3kL) [cos2+i3sin--]e 2 2A~9(1-cos3kL) cos~e~i2kL.
a~ ,L) = 3 --9 (1--cos3kL) [cos 2 + i3sin 2]e + 2coS q) e-i2kL (36) ¦a~ ,L)¦ = 9 9 (1-cos3kl,) *
¦[(cos~2 +i3sin~P)(cos(kL)+isinkL) ~2cosq)(cos(2kL) - isin2kL)]¦ . (37) L)I2-- 8 l ( 1 - cos 3kL)[cos ~ cos kL - 3 sin ~2~ sin kL
+2cos~coskL + i(3sin ~ (coskL) ~
cossinkL(2cos~psin2kL)12. (38) S ¦a~ ,L)¦ = 81 (1- cos3kL(7 + 2cos3kL - 2cos~(1- cos3kL) +6sin~sin3kL. (39) Define a quantity Sl by the following equation:
Sl =¦al(L)¦ = 4 (5+4cos3kL). (40) Define S2 and S3 by 0 S2 3 = la,~ ((p,L)l ~ (41) Referring to Eq. (39), S2 and S3 are given by S2 3 = 8 1 (1 - cos 3kL)(7 + 2 cos 3kL--2 cos~(l - cos3kL
+6sinq)sin3kL). (42) In Eq. (42) the - sign applies to S2 and the + sign applies to S3 .
The signal output of the fiber optic rotation sensor 10 may be written in terms of Sl, S2 and S3:
S3-S2 2A2 9 (1-cos3kL)(12sinOsin3kL) Sl 81 A2 5 + 4cos3kL
S3 - S2 8 . ~ (1- cos3kL~sin3kL) Sl 3 5 + 4cos3kL
What is desired is to find the m~xim~ and minim~ in the relationship 20 of Eq. (44) with respect to the argument (31~L) of the trigonometric functions in Eq. (44) to determine whether there is an optimum set of coupling ratios that do not change as the coupling length L changes Therefore, taking the derivative of Eq. (44) with respect to (3kL) gives:
BACKGROUND OF T~E INVENTION
This invention relates generally to Sagnac effect rotation sensors S and particularly to fiber optic rotation sensors that guide counterpropagating light waves in a sensing loop to measure rotations about a sensing axis perpendicular to the plane of the sensing loop. $till more particularly, this invention relates to fiber optic rotation sensors that use 3x3 couplers to ~upply optical signals to the sensing loop and to guide 10 the optical output signals from the sensing loop to electrical apparatus that processes the optical output signals to determine the rotation rate.
Piber optic rotation sensors are well-known in the art. Previous fiber optic rotation sensors included evanescent field couplers to couple light between two lengths of optical fiber. Subsequently, fiber optic 15 rotation sensors using 3x3 coupler were developed. The primary advantage of using a 3x3 coupler in a fiber optic rotation sensor is the ease with which such devices are interfaced with electronics.
United States Patents 4,440,498 and 4,479,715 to Sheem disclose two fiber optic rotation sensors that include 3x3 couplers. United States 20 Patent 4,440,498 is clirected to a fiber optic rotation sensor that includes a fiber optic sensing lloop and an input fiber. A 3x3 fiber optic coupler divides light between the input fiber and the two legs of the fiber optic sensing loop.
United States Patent 4,479,715 discloses a Sagnac effect rotation 25 sensor in which the e:nds of a fiber optic sensing loop are coupled to a pairof optical waveguides. Light is input to a central input waveguide that is between the optica] waveguides that are coupled to the ends of the sensing loop fiber. The three optical waveguides are arranged to fo~n a 3x3 optical coupler. The input light is coupled from the central input waveguide to the optical waveguides that are connected to the optical fiber coil to produce the counterpropagating waves in the fiber optic sensing loop. The waves traverse the sensing coil and combine in the 5 coupler. The combined waves are detected, and the resulting electrical signals are processed to deterrnine the rotation rate.
United States Patent 4,944,590 to Poisel et al. discloses an optical fiber gyroscope that uses a 3x3 coupler to couple optical signals into and out of a fiber optic sensing loop. Poisel et al. discloses a photodetector 10 arranged to detect the light that has been input the 3x3 coupler that is not coupled into the fiber optic sensing loop. The electrical signal resulting from detecting this light is used in signal processing circuitry to make ad~ustments for variations in the input light intensity.
Such fiber optic rotation sensors may be operated in phase 15 quadrature, which provides maximum sensitivity at zero rotation rate.
Unfortunately, previous fiber optic rotation sensors that include 3x3 optical couplers are sensitive to temperature changes. The coupling ratios of the 3x3 fiber optic couplers are temperature-sensitive such that bias errors of 1000~ per hour are typically observed. Errors of such m~nit~ e~0 are unacceptable for most applications of rotation sensors.
~UMMARY OF THE INVENTION
The present invention is an improved fiber optic rotation sensor using 3x3 couplers with optimized coupling ratios. The coupling ratios are selected to prevent changes in the amount of light coupled into the two 25 counterpropagating waves caused by temperature changes and other mechanical factors. The selected coupling ratios also m~ximi7e the optical power output that is delivered to the rate photodetectors.
A fiber optic rotation sensor according to the present invention comprises a 3x3 optical coupler that includes first, second and third optical waveguides arranged to have an interaction length in which light couples between the first, se'cond and third optical waveguides, the first, second S and third optical walveguides being formed such that the fractions of lightcoupled from any one of the first, second and third optical waveguides to the other two opticall waveguides are constant, independent of thermally-induced changes in the interaction length. An optical signal source is arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides. The optical fiber in which the sensing loop is formed has ends that ~re coupled to the second and third optical waveguides to receive optical signals that form cou~ ,o~g~ting optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
The optical coupler is forrned such that first, second and third optical waveguides being formed such that the optical splitting ratios between the first, second and thirld optical waveguides are 0.4108: 0.1783: 0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterprop~g~tin~ waves is 0.4108A2 and the optical intensity output by the first optical waveguide is 0.1783A2.
An appreciation of the objectives of the present invention and a more complete understanding of its structure and method of operation may be had by stndying the following description of the preferred embodiment and by referring to the accompanying drawings.
CA 022ll992 l997-07-3l WO 97/~1981 PCT/US95/16178 BRIEF DESCR~TION OF THE DRAVVIN~S
FI~. 1 illustrates a fiber optic rotation sensor that includes a 3x3 evanescent field optical coupler;
FIG. 2 schematically illustrates a 3x3 coupler; and FIG. 3 illustrates the derivative with respect to coupling length of the intensity of the signal output by the fiber optic rotation sensor of FIG.
1.
DESCRIPTION OF TH~ PR~FERRED EMBODIMENT
Referring to FIG. 1, a fiber optic rotation sensor 10 includes a 3x3 optical coupler 12 and a length of optical fiber 13 arranged to form a fiber optic sensing coil 14. The optical coupler 12 includes optical waveguides 1-3 formed on a substrate 15. The optical fiber 13 has ends 16 and 18. The fiber ends 16 and 18 are butt-coupled to ends 20 and 22 of the corresponding optical waveguides 1 and 2, respectively.
A pair of output optical fibers 30 and 32 are connected to ends 34 and 36 of the optical waveguides 2 and 3, respectively. The output optical fiber 30 directs a light beam to first photodetector 38, which produces an electrical signal S l that is indicative of the intensity of the optical signal transmitted thereto by the output optical fiber 30. Similarly, the output optical fiber 32 directs a beam of light to a second photodetector 40, which produces an electrical signal S2 that is indicative of the intensity of the optical signal tr~n~mitte-l thereto by the output optical fiber 32.
The optical waveguide l is formed in the substrate 15 between the optical waveguides 2 and 3. The optical waveguides 1-3 are arranged to form the 3x3 coupler 12. The 3x3 coupler 12 is preferably an evanescent field coupler.
An input optical fiber 46 has an end 48 that receives light from a light source 50. The other end 52 of the input optical fiber 46 is butt-WO 97/21981 PCTIUS95/~6I78 coupled to an end 54 of the optical waveguide 1. An output optical fiber 56 has one end S~ butt-coupled to an end 60 of the central optical waveguide 3. The other end 62 of the output optical fiber 56 directs a beam of light to a third detector 64, which produces an electrical signal S3 5 that is indicative of the intensity of the optical signal tran~mitt~d thereto by the output optical fiber 56.
The 3x3 coupler 12 is preferably an evanescent field coupler that couples optical sigl~als between the optical waveguide 1 and the optical waveguides 2 and :3. A portion of the light input to the 3x3 fiber optic 10 coupler 12 remains in the optical waveguide l.
Referring to FIG. 3, the 3x3 coupler has a coupling length L in which the evanesce~t fields of light waves guided by the waveguides 1-3 interact so that lighl: couples between them. The intensity of light coupled between the waveguides 1-3 is a function of the coupling length L. As 15 the temperature of the coupler 12 fluctuates, the light intensity coupled between the wavegllides 1- 3 also fluctuates.
In an ideal environment the three coupling ratios of the 3x3 optical coupler 12 are all equal to 1/3. When the coupling ratios are all equal to 1/3, the light intensities output from the three optical waveguides 1-3 are 20 equal. However, because of temperature sensitivity mentioned above, if the coupling ratios of the 3x3 optical coupler 12 are all 1/3 at a particular desired operating temperature, then unacceptably large errors result because of unavoidiable temperature fluctuations that cause the coupling ratios to change. l[he present invention comprises a fiber optic rotation 25 sensor using a 3x3 coupler that have coupling ratios selected to minimi7e the bias errors to the order of 10~ to 100~ per hour and which is insensitive to temperature changes. It has been found that there is a set of coupling ratios for which the fraction of light coupled into any selected one of the CA 022ll992 l997-07-3l optical waveguides 1-3 remains constant as the coupling length L changes in response to temperature changes.
The optimum configuration for the 3x3 optical coupler 12 is insensitive to temperature changes while providing a lar~er rate 5 discriminant than has been obtained with previous designs. Referring to Figs. 2 and 3, the 3x3 ~1ber optic coupler 20 may be described by the linear differential equations da d J + ikj j+laj+l + ikj j+2aj+2 = 0 (1) where:
j=1,2,3 j=j+3 aj is the light amplitude in waveguide j; and k is the coupling ratio between any two of the three fibers 1-3.
For example, k,2 is the coupling ratio between waveguides 1 and 2;
k23 is the coupling ratio between waveguides 2 and 3, and k3l is the coupling ratio between waveguides 3 and 1. The coupler 12 is preferably formed so that the coupling constants are kl2 = k23 = k3l - k so that the solution to equation (1) is aj(z)=cjeikZ+de~i2kZ with the condition that ~,cj=1, (2) j=l 20 where c and d are constants. If the power input to the fiber optic rotation sensor 10 by the input optical fiber 46 to the 3x3 coupler 12 is A~, then the amplitude of the light in the waveguides at the input end where z = 0 is given by:
al(0)=A,and ~3~
a2(0)=a3(0)=o- (4) Using Eqs. ('3) and (4) in Eq. (1) gives information that may be used to find expressions for the constants c and d in terms of A, for which a numerical value can easily be ascerlained.
A = cleik~ + de-i2kz A=cl+d. (6) cl = A--d. (7) ~ = C2eik~ + dlo--i2kO (8) c2 =--d. (9) O = c3eik~ + de-i2kO (10) c3 =-d. (11) From Eqs. (7), (9) and (11), it is found that cl+c2+c3=~o. (12) A--d--d--d =- 0. (13) Therefore, the constants c~, C2, C3 and d are given by:
d= 3; (14) c _ A and (15) cl =--A. (16) At the other end of the coupler where the distance z = L, the solution equation for optical waveguide 1 becomes:
al(L) =--Aeik:L + 1 Ae-i2kL (17) S~uaring the amplitude to obtain the intensity of the light in optical waveguide 1 gives:
q ¦al(L3¦ = ¦--A~ikL + 1 Ae~i2kL¦ (18) ¦al(L)¦2 = ~ eikL + e-i2kL¦2 (19) ¦al~L)¦2 =--l2coskL+i2sinkL+cos2kL-isin2kLI2. (20) W O97/21981 PCT~US95/16178 lal (L)¦2 =--¦2cos kL + cos2kL + i(2sin kL - sin2kL)¦2 . (21) ¦al(L)¦2 = 9 (4cos~ kL+4coskLcos2kL+cos22kL+
4 sin2 kL - 4 sin kL sin 2kL + sin2 2kL) . (22) ¦al(L)¦~= g (5+4cos3kL). (23) S At the other end of the coupler where the distance z = L, the solution equation for optical waveguide 2 becomes:
la2(L)1 = ¦--1 AeikL + 1 Ae~i2kL¦ (24) ¦a2(L)¦2=--¦-coskL-isinkL+cos2kL-isin2kL¦2. (25) ¦a2(L)¦2 = 9 I(-coskL + cos2kL) - i(coskL + sin2kL)I2. (26) ¦a2(L)¦ = g (cos2 kL - 2 cos kL cos 2kL + cos2 2kL) +sin2 kL t 2sinkLsin2kL + sin2 2kL). (27) ¦a2(L)¦2 = 9 (2-2(coskLcos2kL-sinkLsin2kL). (28) ¦a2(L)¦2 = 9 (1-cos3kL). (29) Because a2 = a3, where the distance z = L, the solution equation for optical waveguide 3 is:
¦a3(L)¦2 =¦A2(L)¦2 = 9 (1-cos3kL). (30) The optical intensity in the optical waveguides 2 and 3 is the optical intensity input to the fiber optic sensing coil 14 at the ends 16 and 18 of the optical fiber 12. Therefore the input to the legs of the fiber optic gyroscope are ¦a2(L)¦2 and ¦a3(L)¦2 given by Eqs. (29) and (30). These inputs to the fiber optic sensing coil 14 have a definite phase relationship.
After traversing the fiber optic sensing coil 14, there is a phase shift ~
between the counterpropagating waves. The return inputs to the coupler wo 97nl981 PCT/US9S/16178 12 after the counterprop~g~ting waves traverse the fiber optic sensin_ coil 14 are given by:
al(O)= :p; (31) - A2 -5 i~
a2(0)= 2 9 (1-cos3kL e2; and (32) - 2 -.5 i~
a3(0) = 2 9 (1- cos3kL e 2 . (33 Loop loss in the optical fiber 12 is ignored. The angle ~ is the Sagnac phase shift angle between the beams caused by rotation of the sensing loop at angular velocity Q about the sensing axis, which is perpendicular to the plane of the fiber optic sensing coil 14. The phase 10 angle ~ and the ~angular velocity Q are related by the Sagnac equation:
q, 2~eD Q
where ~ is the length of the fiber in the sensing coil 14, D is the diameter of the sensing coil 14, ~ is the wavelength of the optical signals and c is the speed of light.
After propag;ating through the coupler 12 through the coupling len~th, L, the optica:L signals that have been output from the output of the fiber optic sensing coil are given by:
a~ ,L)= 3 --9 (1--cos3kL) [cos2+i3sin--]e 2 2A~9(1-cos3kL) cos~e~i2kL.
a~ ,L) = 3 --9 (1--cos3kL) [cos 2 + i3sin 2]e + 2coS q) e-i2kL (36) ¦a~ ,L)¦ = 9 9 (1-cos3kl,) *
¦[(cos~2 +i3sin~P)(cos(kL)+isinkL) ~2cosq)(cos(2kL) - isin2kL)]¦ . (37) L)I2-- 8 l ( 1 - cos 3kL)[cos ~ cos kL - 3 sin ~2~ sin kL
+2cos~coskL + i(3sin ~ (coskL) ~
cossinkL(2cos~psin2kL)12. (38) S ¦a~ ,L)¦ = 81 (1- cos3kL(7 + 2cos3kL - 2cos~(1- cos3kL) +6sin~sin3kL. (39) Define a quantity Sl by the following equation:
Sl =¦al(L)¦ = 4 (5+4cos3kL). (40) Define S2 and S3 by 0 S2 3 = la,~ ((p,L)l ~ (41) Referring to Eq. (39), S2 and S3 are given by S2 3 = 8 1 (1 - cos 3kL)(7 + 2 cos 3kL--2 cos~(l - cos3kL
+6sinq)sin3kL). (42) In Eq. (42) the - sign applies to S2 and the + sign applies to S3 .
The signal output of the fiber optic rotation sensor 10 may be written in terms of Sl, S2 and S3:
S3-S2 2A2 9 (1-cos3kL)(12sinOsin3kL) Sl 81 A2 5 + 4cos3kL
S3 - S2 8 . ~ (1- cos3kL~sin3kL) Sl 3 5 + 4cos3kL
What is desired is to find the m~xim~ and minim~ in the relationship 20 of Eq. (44) with respect to the argument (31~L) of the trigonometric functions in Eq. (44) to determine whether there is an optimum set of coupling ratios that do not change as the coupling length L changes Therefore, taking the derivative of Eq. (44) with respect to (3kL) gives:
3 2 = 8 sin~ [(sin23kL+(l-cos3kL)cos3kLsin3kL*
d(3kL) Sl 3 (5 ~ 4cos3kL) + 4(1- cos3kL)sin2 3kL](5 + 4cos3kL)-2. (45) At the maxima and minim~ of the expression of Eq. (45) has zero slope. Tlherefore, near the maxima and minim~ of Eq. (45), the coupler 12 5 has minimum sensitivity to temperature changes. To find mAxirr~ and minim~ in Eq. (45) the derivative is set to equal zero, which gives:
0 = -4cos3 3kL - lOcos2 3kL + 5cos3kL + 9. (46) Solving Eq. (46) ~or 3kL gives 3kL = 148.061 rad. (47) Therefore the quantity kL is kL = 49.354 rad. (48) Looking at the graph of FIG. 2, it is seen that the output has a m~ximl~m value when 3kL = 148.061 rad. Using the value of kL from Eq.
(48) in Eq., (44), it is found ~hat the signal output of the fiber optic rotation 15 sensor 10 is S3S ~2 = l.~j24sin~. (49) Returning to Eqs. (22), (29) and (30), we than find that ¦al(L)¦2 = Ag (5+4cos3kL) = 9 ~5+4cos(148.061)). (50) ¦al(L)¦2 =--(5~cos(148.061)) (51) ¦¦al(L)¦2 = 0.l783A ¦ (52) ¦a2(L)¦ = g ~ cos3kL) = g (1- cos(l48.061)) = 0.4108A
¦¦a2(L)2 = 0-4108A2¦ (54) ¦~a3(L) = ¦a2(L)¦2 = 0.4108A2.¦ (55) Therefore, the coupler splitting ratio is 0.4108:0.1783:0.4108.
Referring to Eq. 34, the solution equation fQr the fiber optic rotation sensor lS
Output = 1.624 sinq~ = 1.624 s~n( ~ Q) (56) For this particular set of coupling ratios, the coupler 12 is insensitive to variations in coupling length that typically occur over time and temperature. The signals on the output legs are higher ~or this set of coupling ratios than for other coupling ratios.
The structures and methods disclosed herein illustrate ~he principles of the present invention. The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects as exemplary and illustrative rather than restrictive. Therefore, the appended claims rather than the foregoing description define the scope of the invention. All modifications to the embodiments described herein that corne within the meaning and range of equivalence of the claims are embraced within the scope of the invention.
d(3kL) Sl 3 (5 ~ 4cos3kL) + 4(1- cos3kL)sin2 3kL](5 + 4cos3kL)-2. (45) At the maxima and minim~ of the expression of Eq. (45) has zero slope. Tlherefore, near the maxima and minim~ of Eq. (45), the coupler 12 5 has minimum sensitivity to temperature changes. To find mAxirr~ and minim~ in Eq. (45) the derivative is set to equal zero, which gives:
0 = -4cos3 3kL - lOcos2 3kL + 5cos3kL + 9. (46) Solving Eq. (46) ~or 3kL gives 3kL = 148.061 rad. (47) Therefore the quantity kL is kL = 49.354 rad. (48) Looking at the graph of FIG. 2, it is seen that the output has a m~ximl~m value when 3kL = 148.061 rad. Using the value of kL from Eq.
(48) in Eq., (44), it is found ~hat the signal output of the fiber optic rotation 15 sensor 10 is S3S ~2 = l.~j24sin~. (49) Returning to Eqs. (22), (29) and (30), we than find that ¦al(L)¦2 = Ag (5+4cos3kL) = 9 ~5+4cos(148.061)). (50) ¦al(L)¦2 =--(5~cos(148.061)) (51) ¦¦al(L)¦2 = 0.l783A ¦ (52) ¦a2(L)¦ = g ~ cos3kL) = g (1- cos(l48.061)) = 0.4108A
¦¦a2(L)2 = 0-4108A2¦ (54) ¦~a3(L) = ¦a2(L)¦2 = 0.4108A2.¦ (55) Therefore, the coupler splitting ratio is 0.4108:0.1783:0.4108.
Referring to Eq. 34, the solution equation fQr the fiber optic rotation sensor lS
Output = 1.624 sinq~ = 1.624 s~n( ~ Q) (56) For this particular set of coupling ratios, the coupler 12 is insensitive to variations in coupling length that typically occur over time and temperature. The signals on the output legs are higher ~or this set of coupling ratios than for other coupling ratios.
The structures and methods disclosed herein illustrate ~he principles of the present invention. The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects as exemplary and illustrative rather than restrictive. Therefore, the appended claims rather than the foregoing description define the scope of the invention. All modifications to the embodiments described herein that corne within the meaning and range of equivalence of the claims are embraced within the scope of the invention.
Claims (4)
1. A fiber optic rotation sensor for sensing rotation of a sensing loop of optical fiber about a sensing axis perpendicular to the plane of the sensing loop, comprising:
a 3 x 3 optical coupler that includes first, second and third optical waveguides formed in a substrate and arranged to have couping ratios such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of temperature changes in the 3x3 optical coupler;
an optical signal source arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and the optical fiber in which the sensing loop is formed having ends that are coupled to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
a 3 x 3 optical coupler that includes first, second and third optical waveguides formed in a substrate and arranged to have couping ratios such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of temperature changes in the 3x3 optical coupler;
an optical signal source arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and the optical fiber in which the sensing loop is formed having ends that are coupled to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
2. A fiber optic rotation sensor for sensing rotation of a sensing loop of optical fiber about a sensing axis perpendicular to the plane of the sensing loop, comprising:
a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides arranged to have couping ratios such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of temperature changes inthe 3x3 optical coupler;
an optical signal source arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and the optical fiber in which the sensing loop is formed having ends that are coupled to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop, the first, second and third optical waveguides being formed such that the optical splittingratios are 0.4108:0.1783:0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterpropagating waves is 0.4108A2and the optical intensity output by the first optical waveguide is 0.1783A2.
a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides arranged to have couping ratios such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of temperature changes inthe 3x3 optical coupler;
an optical signal source arranged to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and the optical fiber in which the sensing loop is formed having ends that are coupled to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop, the first, second and third optical waveguides being formed such that the optical splittingratios are 0.4108:0.1783:0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterpropagating waves is 0.4108A2and the optical intensity output by the first optical waveguide is 0.1783A2.
3. A method for measuring rotations with a fiber optic rotation sensor that senses rotation of a sensing loop of optical fiber about a sensing axis perpendicular to the plane of the sensing loop, comprising the steps of:
forming a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides;
arranging the first, second and third optical waveguides to have an interaction length in which light couples between the first, second and third optical waveguides;
forming the first, second and third optical waveguides such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of thermally-induced changes in the interaction length;
arranging an optical signal source to provide an input optical signal to the first optical waveguide such that the 3x3 optical coupler couples portions of the input optical signal from the first optical waveguide into the second and third optical waveguides; and coupling the ends of the fiber in which the optical fiber sensing loop is formed to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
forming a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides;
arranging the first, second and third optical waveguides to have an interaction length in which light couples between the first, second and third optical waveguides;
forming the first, second and third optical waveguides such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of thermally-induced changes in the interaction length;
arranging an optical signal source to provide an input optical signal to the first optical waveguide such that the 3x3 optical coupler couples portions of the input optical signal from the first optical waveguide into the second and third optical waveguides; and coupling the ends of the fiber in which the optical fiber sensing loop is formed to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop.
4. A method for measuring rotations with a fiber optic rotation sensor that senses rotation of a sensing loop of optical fiber about a sensing axis perpendicular to the plane of the sensing loop, comprising the steps of:
forming a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides;
arranging the first, second and third optical waveguides to have an interaction length in which light couples between the first, second and third optical waveguides;
forming the first, second and third optical waveguides such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of thermally-induced changes in the interaction length;
arranging an optical signal source to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and coupling the ends of the fiber in which the optical fiber sensing loop is formed to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop; andforming the first, second and third optical waveguides such that the optical splitting ratios are 0.4108:0.1783:0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterpropagating waves is 0.4108A2 and the optical intensity output by the first optical waveguide is 0.1783A2.
forming a 3x3 optical coupler formed in a substrate and that includes first, second and third optical waveguides;
arranging the first, second and third optical waveguides to have an interaction length in which light couples between the first, second and third optical waveguides;
forming the first, second and third optical waveguides such that the fractions of light coupled from any one of the first, second and third optical waveguides to the other two optical waveguides are constant, independent of thermally-induced changes in the interaction length;
arranging an optical signal source to provide an input optical signal to the first optical waveguide such that portions of the input optical signal are coupled from the first optical waveguide into the second and third optical waveguides; and coupling the ends of the fiber in which the optical fiber sensing loop is formed to the second and third optical waveguides to receive optical signals that form counterpropagating optical waves in the sensing loop and to combine the counterpropagating optical waves after they have traversed the sensing loop; andforming the first, second and third optical waveguides such that the optical splitting ratios are 0.4108:0.1783:0.4108, so that when light intensity A2 is input to the first optical waveguide, the optical intensity output by each of the second and third optical waveguides to the optical fiber to form the counterpropagating waves is 0.4108A2 and the optical intensity output by the first optical waveguide is 0.1783A2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA002211992A CA2211992A1 (en) | 1995-12-08 | 1995-12-08 | Optimum coupler configuration for fiber optic rate gyroscope using 3x3 coupler |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA002211992A CA2211992A1 (en) | 1995-12-08 | 1995-12-08 | Optimum coupler configuration for fiber optic rate gyroscope using 3x3 coupler |
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| Publication Number | Publication Date |
|---|---|
| CA2211992A1 true CA2211992A1 (en) | 1997-06-19 |
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| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA002211992A Abandoned CA2211992A1 (en) | 1995-12-08 | 1995-12-08 | Optimum coupler configuration for fiber optic rate gyroscope using 3x3 coupler |
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| CA (1) | CA2211992A1 (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116007605A (en) * | 2023-03-30 | 2023-04-25 | 中国船舶集团有限公司第七〇七研究所 | Interference type integrated optical gyroscope and optical fiber coupling method thereof |
-
1995
- 1995-12-08 CA CA002211992A patent/CA2211992A1/en not_active Abandoned
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116007605A (en) * | 2023-03-30 | 2023-04-25 | 中国船舶集团有限公司第七〇七研究所 | Interference type integrated optical gyroscope and optical fiber coupling method thereof |
| CN116007605B (en) * | 2023-03-30 | 2023-06-02 | 中国船舶集团有限公司第七〇七研究所 | Interference type integrated optical gyroscope and optical fiber coupling method thereof |
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