Note: Descriptions are shown in the official language in which they were submitted.
CA 02211992 1997-07-31
WO 97/Z1981 PCT/US95/16178
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
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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.
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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-
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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
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WO 97/21981 PCT/US95/16178
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)
CA 02211992 1997-07-31
WO 97/21981 PCT/US95/16178
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)
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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
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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)
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WO 97/21981 PCT/US95/16178
-10-
~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:
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WO 97/21981 PCT/US95/16178
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)
CA 02211992 1997-07-31
WO 97121981 PCT/US95/16178
-12-
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.
