Fiber optic gyro with reduced readout reflection coupling characteristics

A FOG design is disclosed that eliminates the need for spatially averaging the output of a readout optical fiber by using a short coherence length light source and decorrelating the orthogonal fiber modes in the birefringent readout optical fiber prior to them being received by the photodetector. The orientation of the optical output of the readout optical fiber with respect to the photodetector is at an angle other than normal incidence, which is designed to reduce the reflections from the photodetector back into the readout optical fiber. The coherence length of the source and the length and birefringence of the readout optical fiber are selected so that there is a complete decorrelation of the polarization states of the light as they pass through the readout optical fiber.

FIELD OF THE INVENTION 
The present invention generally relates to fiber optic gyros (FOGs). 
In recent years FOGs are achieving increased success. However, one problem 
common to many FOGs is readout errors associated with optical inteference 
at the readout photodetector. One solution to this problem has been 
spatially average the entire output of light from the optical fiber, 
thereby cancelling any optical interference effects. Such a solution is 
described in U.S. Pat. No. 5,153,676 entitled, "Apparatus And Method For 
Reducing Phase Errors in An Interferometer", issued to Ralph A. Bergh on 
Oct. 6, 1992, which patent is hereby incorporated herein in its entirety 
by this reference. 
While the Bergh approach does help reduce some phase errors due to optical 
interference at the readout photodetector, it utilizes a design that 
requires the fiber to be cleaved or polished normal to its length and the 
photodetector must be mounted with its face normal to the output of the 
fiber. Reflection occurs both at the fiber/air interface and at the 
air/photodetector interface. Because both of these surfaces are normal to 
the propagation of light, the reflected light will tend to couple back 
into the fiber. The fiber and the photodetector form a Fabry-Perot cavity 
(resonant optical cavity between two reflective surfaces) the amount of 
reflected light will vary significantly and is extremely sensitive to the 
distance between the photodetector and the fiber. These varying 
reflections can cause significant variations in the FOG output. 
Consequently, there exists a need for improvement in FOGs which reduce the 
errors associated with optical interference at the readout photodetector 
while concomitantly reducing the errors associated with reflection from 
the readout photodetector back into the optical fiber. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to reduce errors associated with 
back reflection from a readout photodetector into the optical fiber. 
It is a feature of the present invention to provide a readout photodetector 
which is oriented at a non-normal angle with respect to the light exiting 
the output fiber. 
It is an advantage of the present invention to reduce the errors associated 
with coupling reflections off the readout photodetector back into the 
optical fiber. 
It is another object of the present invention to reduce errors associated 
with optical interference at the readout photodetector. 
It is another feature of the present invention to include a short coherence 
length light source which is sufficiently short so that a decorrelation of 
polarization modes in the last leg of the optical fiber before the readout 
photodetector is sufficient to completely decorrelate the polarization 
modes in that segment. 
It is another advantage of the present invention to provide for a 
decorrelation of the polarization states in the optical fiber at the 
readout photodetector. 
The present invention provides a FOG which is designed to satisfy the 
aforementioned needs, include the above described objects, contain the 
earlier articulated features, and provide the previously stated 
advantages. The invention is carried out in a "back reflection-less" 
system in the sense that the back reflections off of the readout 
photodetector back into the optical fiber have been greatly reduced. 
Additionally, the invention is carried out in a "readout optical 
interference-less" system in the sense that the typical optical 
interference occurring at the readout photodetector is significantly 
reduced. 
Accordingly, the present invention includes a FOG having a light source 
with a short coherent length such that a decorrelation of the polarization 
states occur in the last leg of optical fiber immediately before the 
readout photodetector which is oriented at a non-normal angle with respect 
to the light exiting the output optical fiber.

DETAILED DESCRIPTION 
Now referring to the drawings, wherein like numerals refer to like text and 
matter throughout, and more particularly referring now to FIG. 1 there is 
shown a FOG readout, of the prior art, generally designated 100, having a 
photo detector 102 with a photodetector face 104 thereon. Also shown is 
optical fiber 106 which is disposed at normal incidents with respect to 
the photodetector face 104. It can be seen that some of the light emitting 
from fiber 106 would be incident upon the photodetector face 104 and then 
be reflected back into the optical fiber 106. 
Now referring to FIG. 2, there is shown a FOG readout, of the present 
invention, generally designated 200, having a readout photodetector 102 
with a photodetector face 104 thereon. Also shown is an optical fiber 106 
having a cleaved end 208 which is at a non-normal angle with respect to 
the axis of the fiber 106. The output face of the readout fiber 208 is 
cleaved or polished at an angle .phi..sub.c from normal to the length of 
the readout fiber 106. The output light exiting the fiber will be 
refracted according to Snell's Law by the angle .phi..sub.o given by: 
##EQU1## 
where n.sub.f is the optical index of the fiber, and n.sub.o is the 
optical index of the material outside of the fiber. In the preferred 
embodiment of this invention .phi..sub.c is approximately 15 degrees, the 
optical index of glass optical fibers is near 1.5, and air, vacuum, or 
inert gas with index of 1.0 surrounds the fiber. So the angle .phi..sub.o 
between the axis of the output light cone and the length of the readout 
fiber is approximately 23 degrees. At the cleave angle of 15 degrees 
reflections at the fiber air interface are not coupled back into the 
fiber. The light exiting the end of the readout fiber expands in a cone 
having an pseudo-Gaussian distribution with angle. The characteristic cone 
half angle .theta..sub.h is given by: 
##EQU2## 
where .lambda. is the wavelength of light, and D.sub.EMF is the effective 
mode field diameter of the light exiting the fiber at the cleave angle 
given by: 
EQU D.sub.EMF =D.sub.FMF .multidot.COS (.phi..sub.o) 
where D.sub.FMF is the mode field diameter of light in the fiber. At angles 
greater than .theta..sub.h there is little optical energy. To ensure that 
light reflected from the face of the photodetector is not coupled back 
into the fiber the angle .theta..sub.d between the light exiting the fiber 
and the normal to the photodetector face must be adequately greater than 
the optical output half angle .theta..sub.h. In the preferred embodiment 
of the invention a fiber with a mode field diameter of approximately 5 
microns and a source wavelength .lambda. of approximately 850 nm are used 
giving a .theta..sub.h value of about 5 degrees. The photodetector is 
mounted with its face approximately normal to the length of the readout 
fiber such that .phi..sub.d =.phi..sub.0 or 23 degrees which is much 
larger than .theta..sub.h so that no significant amount of the reflected 
light is coupled back into the readout fiber. 
The reflection coefficient from any dielectric surface such as the face of 
the photodetector is a function of both angle and the polarization state 
of the incident light. The fraction of the light energy transmitted into 
the photodetector, and therefore detectable, is given by: 
##EQU3## 
for light with its polarization axis perpendicular to the surface of the 
photodetector, known as the s wave, and by: 
##EQU4## 
for light with its polarization axis parallel to the photodetector 
surface, where: 
##EQU5## 
where n.sub.d is the optical index of the photodetector. The photodetector 
will therefore measure the energy over the cross section of the output 
cone of light asymmetrically, and will not equally sample the two output 
polarization states of the fiber. Because of this nonuniformity in 
sensitivity a photodetector angled with respect to the light exiting the 
readout fiber cannot be used to spatially average a sensors optical 
output. 
This invention utilizes a short coherence length source combined with an 
adequate length of birefringent media just prior to the photodetector to 
decorrelate the polarization modes of the output light substantially 
eliminating interference between the modes at the photodetector thus 
eliminating any need for spatial averaging and allowing the use of 
photodetector angled respect to the light exiting the fiber. 
In operation the present invention may be more fully understood in 
conjunction with the following discussion. 
If optical cross talk occurs at any point in a fiber sensor system. Light 
coupled from one optical axis of the fiber into the other will begin to 
lag or lead the original light due to the birefringence of the fiber. For 
example, if the light was originally in the slow axis, any light coupled 
into the fiber fast axis will begin to lead the original light by: 
EQU .DELTA.L=B.multidot.L 
where .DELTA.L is the difference in length traveled by the slow and the 
fast axis light, B is the fiber birefringence, and L is the length the 
light has traveled in the fiber (the optical path length is nL where n is 
the index of the fiber). The fiber birefringence is approximately related 
to the beat length of the fiber (ignoring the weak dependence of the 
birefringence on wavelength) by: 
##EQU6## 
where L.sub.B is the fiber beat length and .lambda..sub.B is the 
wavelength at which the beat length was measured. Fiber manufacturers 
often specify a fiber's beat length instead of its birefringence. 
Although the two modes are orthogonol in the fiber, once the light leaves 
the fiber the modes can locally interfere, at for instance a 
photodetector, causing variations in intensity over the surface of the 
detector. If all the light, from both polarization states, is averaged 
evenly over the cone of light emitted by the fiber these intensity 
variations will sum to zero. If however, the light is not sampled evenly, 
or if the polarization states are sampled with different efficiences, some 
potential for interference remains. This residual interference will cause 
errors in the output of the gyro. 
Interference can only occur if the portions of light traveling in the two 
fiber axes are at least partially coherent with respect to each other. Two 
samples of light emitted from a source will tend to interfere if the 
difference between the optical path lengths is less than L.sub.C0. Where 
L.sub.C0 is the free space coherence length of the source given by: 
##EQU7## 
where N is the wavelength of the source and .lambda..DELTA. is the full 
width half maximum linewidth of the source. At differential lengths 
substantially longer than the coherence length no significant interference 
will occur. In fiber of index n, the effective coherence length is 
reduced. We may write the coherence length in the fiber as: 
##EQU8## 
Where L.sub.c is the physical differential length traveled through a media 
with optical index n (not the optical path length LC0.sub.). In a fiber 
with birefringence B the differential path length between the fast and 
slow fiber birefringence axes is given by: 
EQU .DELTA.-B.multidot.L 
To ensure that the two fiber modes are not coherent with respect to one 
another we have the following requirement: 
EQU .DELTA.L&gt;L.sub.C 
For a fiber of birefringence B, the distance light must travel to 
decorrelate the two fiber modes is given by: 
##EQU9## 
If written in terms of the source parameters, the requirement becomes: 
##EQU10## 
From the above analysis we have the requirements for avoiding interference, 
between the fiber birefringence modes, at the photodetector. 
In the preferred embodiment of this invention a 840 nm wavelength 
superluminescent diode is used as a light source. Superluminescent diodes 
such as those manufactured by EG&G have typical linewidths of over 26 nm. 
A polarization maintaining fiber is used as the birefringent media just 
prior to the photodetector to decorrelate the polarization modes of the 
sensor. One polarization maintaining fiber that may be used is FS-CP-4611 
fiber manufactured by Minnesota Mining and Manufacturing Company which is 
used in the leads of their optical couplers. The FS-CP-4611 fiber has a 
typical birefringence of 2.0.times.10.sup.-4. This is lower than many 
polarization maintaining fibers but is still adequate to produce a 
reasonable requirement that the lead length L.sub.f be many times longer 
than a length of 9.3 cm when used with the above mentioned 
superluminescent diode. This requirement is easily met by a typical 
coupler lead length of 1 to 1.5 meters. 
Now referring to FIG. 3, there is shown a FOG, of the present invention, 
generally designated 300 having a light source 302 with a optical fiber 
304 extending to input/output coupler 306. Extending from coupler 306 is 
fiber 308 which extends to fiber polarizer 310 which is preferably a loop 
of birefringent single-polarization optical fiber and extends to loop 
coupler 312. Extending from loop coupler 312 is optical fiber 314 which is 
wound into a quadrupolar fiber coil 316 which is coupled to piezoelectric 
phase modulator 318 (optional) and back to loop coupler 312. Loop coupler 
312 and input/output coupler 306 are shown having low-back-reflection 
optical terminations 320 and 322 disposed respectively thereon. Extending 
from input/output coupler 306 is low-cross-talk birefringent readout 
optical fiber 324 which has a cleaved end 326 which is preferably a 15 
degree angle cleaved to fiber end. Photodetector 102 having photodetector 
face 104 is shown disposed at a non-normal angle with respect to the 
optical output of the optical output of the readout optical fiber 324. 
Reflections 328 off of the photodetector face 104 are shown exiting in a 
direction away from the optical fiber 324. 
The light source 302 is preferably a superluminescent diode such as those 
manufactured by EG&G. A typical wavelength of such source may be 840 nm 
with linewidths of over 26 nm. The birefringent fibers 304, 308, 310, 314, 
and 316 are well known in the prior art. The optional piezoelectric phase 
modulator consists of piezoceramic disc or cylinder wrapped with 
birefringent polarization-maintaining fiber. A voltage applied to this 
piezoelectric element causes it to expand or contract resulting in a 
change in the length of the wrapped fiber and an attendant change in the 
optical propagation time through the modulator. By applying a voltage 
modulation to a phase modulator located near one end of a FOG's fiber coil 
an effectively non-reciprocal optical phase modulation is applied to the 
light traversing the fiber coil producing an optical output at the readout 
photodetector sensitive to both the magnitude and direction of the FOGs 
rotation. The techniques for utilizing such a piezoelectric phase 
modulator to produce a usable modulation in the gyros optical output, and 
techniques to convert this output to a measure of the FOG's rotation rate 
are well known in the prior art. Input/output coupler 306 is preferably a 
50/50 optical coupler which is also well known in the art. Loop coupler 
312 is preferably a low-optical-cross-talk coupler in which the 
birefringence axes of the coupled fibers are aligned to give low 
polarization cross talk in the light coupled to the second coupler output. 
Readout optical fiber 324 may be a birefringent lead of the input/output 
coupler 306. One possible coupler is manufactured by Minn. Mining and 
Manufacturing Company (3M) of St. Paul, Minn. which use FS-CP-4611 fiber 
which has a typical birefringence of 2.0.times.10.sup.-4. Because the 
light in the two polarization modes of the fiber will be decorrelated 
before detection light may be coupled into either or both of the output 
fiber birefringence axes, so the birefringence axes of the input/output 
coupler need not be aligned. This reduces the manufacturing cost of this 
coupler. Decorrelation of the output polarization modes is preferably 
achieved in a coupler lead 324 of over 1 m in length. Preferably this 
coupler lead also has a soft inner layer jacket that reduces stress to the 
fiber. The lead must be packaged in such a way as to prevent external 
stress such as pinching, or sharp bending or twisting. The fiber may be 
loosely packaged to prevent stress or embedded in a soft material such as 
High Gel available from 3M for maintaining stability in vibration. When a 
fiber is packaged in this way, the coupler lead meets both requirements 
for polarization decorrelation and the low-polarization-cross-talk. To 
prevent coupling of reflective light back into the output fiber, the 
photodetector 102 must be positioned at a sufficient angle to the light 
leaving the cleaved fiber end 326 such that none of the cone of light 
reflected by the photodetector face 104 falls back onto the fiber 324. 
Now referring to FIG. 4, there is shown a second FOG embodiment of the 
invention, generally designated 400, utilizing an integrated optic chip 
(IOC) (401) such as those sold by United Technologies Photonics. The IOC 
in FIG. 4 serves the same function as the polarizer, loop coupler, and 
phase modulator shown in FIG. 3. IOCs generally have significantly wider 
optical modulation bandwidths allowing more advanced modulation schemes to 
be employed such as those that null the rotation rate induced optical 
phase shift in a closed loop manor to minimize output errors such as a 
scale factor nonlinearities. The advantages of utilizing IOCs and advanced 
optical modulation techniques in FOGs and other optical sensors are well 
known in the prior art. 
Now referring to FIG. 5, there is shown a second FOG readout, of the 
present invention, generally designated 500, having a readout 
photodetector 102 with a photodetector face 104 thereon. From the 
expression above for the photodetector transmission coefficient T.sub.p 
(.phi..sub.d) we see that if we set the angle of incidence .phi..sub.d 
equal to Brewster's angle .theta..sub.B given by: 
##EQU11## 
that T.sub.p (.theta..sub.B) will equal 1. So that if a sensor has an 
optical output which is predominately polarized, coupling to the readout 
detector is maximized by proper orientation of the output polarization 
state and by aligning the normal to the photodetector face at Brewster's 
angle, given above, to the sensor's optical output. 
In the preferred embodiment of this invention the output face of the fiber 
208 is cleaved or polished at a 15 degree angle from normal to the length 
of the fiber with such an orientation that the birefringence axis of the 
readout fiber 106 containing the predominate portion of the sensors 
optical output is aligned such that it lies in the plane of the figure. 
The photodetector is mounted at an angle .theta..sub.B of approximately 56 
degrees to the centroid beam of the output cone of light. This ensures 
both that the predominate polarization axis is aligned with the p 
reflection axis of the photodetector and that the central portion of the 
cone of light will strike the photodetector at Brewster's angle to 
maximize transmission. 
Preferably, the present invention includes: 
1. A short coherence length with linewidth .lambda. and mean wavelength 
.lambda.. 
2. A fiber optic sensor receiving light from the source and emitting some 
portion of the light as an output. 
3. A photodetector positioned to receive some of the output from the 
sensor. 
A low-optical-cross-talk, birefringent media, with sufficient length to 
decorrelate the two polarization modes emitted by the sensor, interposed 
between the sensor output and the photodetector. A media having optical 
index n and birefringence B must be of a length L.sub.f such that: 
##EQU12## 
Throughout the above discussion the invention has been referred to as a 
fiber optic gyro or FOG for clarity and to focus the discussions. It 
should be obvious that the above method for simultaneously reducing 
readout backreflections and spatial interference at the output may be 
applied to any optical interferometric sensor such as hydrophones, 
magnetic field sensors, or position sensors. 
It is thought that the FOG, of the present invention, and many of its 
attendant advantages will be understood from the foregoing description and 
it will be apparent that various changes may be made in the form, the 
construction and arrangement of the parts thereof without departing from 
the spirit and scope of the invention or sacrificing all of their material 
advantages. The form herein being described is merely a preferred or 
exemplary embodiment thereof.