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Claims  |
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We claim:
1. A fiber optic rotation sensor, comprising:
a loop comprised of birefringent optical fiber having two orthogonal
polarization modes;
a coupler for coupling light to said loop;
a light source for producing said light, said light propagating in said two
orthogonal polarization modes;
means disposed between said light source and said coupler for equalizing
the intensity of the light in said modes such that said light is divided
substantially equally between said two orthogonal polarization modes;
means disposed between said light source and said equalizing means for
reducing correlation of the phase between light in said one mode and light
in the other mode prior to reaching said equalizing means, said reducing
means comprising a birefringence modulator and a portion of birefringent
optical fiber having a length greater than the coherence length of the
optical fiber;
a polarizer, disposed between said equalizing means and said coupler, to
receive said light which is divided between said modes;
said coupler receiving the light passing through said polarizer and
splitting the light to provide a pair of waves which counterpropagate
about said loop, said coupler recombining said waves to form an output
signal and coupling said output signal for propagation to said polarizer;
and
detection means for detecting said output signal after passing through said
polarizer.
2. The sensor as defined in claim 1, further including a line portion of
said optical fiber between said light source and said coupler, wherein
said equalizing means, said means for reducing correlation, and said
polarizer are optically interconnected by said line portion.
3. The sensor as defined in claim 1, further including a second means
disposed between said polarizer and said coupler for reducing correlation
for light propagating between said polarizer and said coupler.
4. The sensor as defined in claim 1, wherein said detection means includes
a photodetector and a second coupler disposed between said polarizer and
said light source for coupling said output signal to said photodetector.
5. The sensor as defined in claim 1, wherein said polarizer comprises a
fiber optic polarizer.
6. The sensor as defined in claim 1, wherein said equalizing means
comprises a splice in a length of optical fiber between said light source
and said polarizer, the axes of birefringence of said fiber on one side of
the splice being oriented at an angle of 45.degree. with respect to the
axes of birefringence of said fiber on the other side of said splice.
7. The sensor as defined in claim 1, wherein said light source is a broad
band light source.
8. The sensor as defined in claim 7, wherein said light source is a super
luminescent diode.
9. A fiber optic rotation sensor, comprising:
a loop comprised of birefringent optical fiber having two orthogonal
polarization modes;
a coupler for coupling light to said loop;
a light source for producing said light, said light propagating in said two
orthogonal polarization modes;
means disposed between said light source and said coupler for equalizing
the intensity of the light in said modes such that said light is divided
substantially equally between said two orthogonal polarization modes;
means disposed between said light source and said equalizing means for
reducing correlation of the phase between light in said one mode and light
in the other mode prior to reaching said equalizing means;
polarizing means, disposed between said equalizing means and said coupler,
to receive said light which is divided between said modes;
second means, disposed between said polarizer and said coupler for reducing
correlation of light propagating between said polarizer and said coupler,
said second means comprising a birefringence modulator that induces a
periodic time varying birefringence in said optical fiber, said time
varying birefringence causing a phase error in said output that has an
average magnitude substantially equal to zero over the period of said time
varying birefringence.
said coupler receiving the light passing through said polarizing means and
splitting the light to provide a pair of waves which counterpropagate
about said loop, said coupler recombining said waves to form an output
signal and coupling said output signal for propagation to said polarizing
means; and
detection means for detecting said output signal after passing through said
polarizing means.
10. In an optical fiber rotation sensor, a method for reducing phase errors
caused by environmentally-induced birefringence in said optical fiber,
comprising the steps of:
introducing light into an input portion of an optical fiber having first
and second polarization modes for the propagation of said light;
causing light in said first polarization mode to become uncorrelated with
light in said second polarization modes by (i) passing the light through a
segment of birefringent optical fiber having a length greater than the
coherence length of the optical fiber and (ii) inducing a periodic time
varying birefringence in the birefringent optical fiber so that the phase
of light in the first polarization mode is periodically varied with
respect to the phase of light in second polarization mode to provide
uncorrelated light;
dividing the light in each of said polarization modes into equal portions
so that any light originally in said first polarization mode is divided
equally between said two polarization modes and so that any light
originally in said second polarization mode is also divided equally
between said two polarization modes to provide light of equalized
intensity;
passing the uncorrelated light of equalized intensity in each of said
polarization modes through a polarizing means such that substantially all
of the light in said first polarization mode is transmitted by said
polarizing means and substantially all of the light in said second
polarization mode is blocked by said polarizing means;
dividing the light transmitted by said polarizing means into two
substantially equal portions and propagating one of said portions in a
clockwise direction around an optical sensing loop while propagating the
other of said portions in a counterclockwise direction around said optical
sensing loop, wherein a portion of the light in said first polarization
mode is coupled to said second polarization mode and a portion of the
light in said second polarization mode is coupled to said first
polarization mode;
combining said clockwise propagating light portion with said
counterclockwise propagating light portion to provide an optical output
signal;
passing said optical output signal through said polarizing means so that
said polarizing means transmits substantially all of the light in said
first polarization mode and blocks substantially all of the light in said
second polarization mode; and
detecting said optical output signal after passing through said polarizing
means to provide a rotation output signal responsive to the angular
rotation of said optical sensing loop.
11. The method of claim 10, wherein said step of inducing a periodic
time-varying birefringence in the birefringent optical fiber comprises the
step of periodically squeezing the optical fiber along one of its axes of
birefringence.
12. The method of claim 10, wherein said step of dividing the light in each
of said polarization modes into equal portions comprises the steps of:
propagating the light along a first set of axes of birefringence in a first
portion of an optical fiber; and
optically coupling said light propagating along said first set of axes of
birefringence to a second set of axes of birefringence in a second portion
of an optical fiber, said second set of axes oriented at an angle of
45.degree. with respect to said first set of axes.
13. A fiber optic interferometer, comprising:
a source of light;
a loop of optical fiber;
a coupler which couples light to said loop so as to provide a pair of
counterpropagating light waves in said loop, said coupler combining said
counterpropagating waves to form an optical output signal;
a polarization preserving, birefringent fiber for guiding light propagating
between said source and said coupler;
a polarizer positioned between said light source and said coupler, said
polarizer being aligned with an axis of birefringence of said birefringent
fiber so as to block light propagating in one polarization mode of said
fiber while passing light in the other polarization mode of said fiber;
a detector for detecting said optical output signal; and
an intensity equalizer positioned to receive light from said source prior
to reaching said polarizer, said intensity equalizer substantially
equalizing the optical intensity of light incident thereon for each of
said polarization modes.
14. A fiber optic interferometer as defined in claim 13, additionally
comprising a birefringence modulator between said light source and said
intensity equalizer for modulating the birefringence of said waveguide in
accordance with a time varying signal.
15. A fiber optic interferometer as defined by claim 13, wherein said
modulator modulates in accordance with a triangular waveform and wherein
the modulation amplitude is substantially equal to an integer number of
2.pi. radians.
16. A fiber optic interferometer as defined by claim 13, wherein said loop
of optical fiber is comprised of birefringent optical fiber.
17. A fiber optic interferometer, as defined by claim 13, wherein said
intensity equalizer comprises a pair of optical fiber segments having axes
of birefringence oriented at 45.degree. relative to each other.
18. An interferometer, comprising:
a sensing loop;
a source of light;
a first coupler for coupling light to and from said loop;
a detector;
a second coupler for coupling light output from said loop to said detector;
a polarizer between said first and second couplers;
an intensity equalizer between said polarizer and said light source; and
an optical path comprised of birefringent optical fiber for guiding light
propagating from said source to said first coupler, said fiber having an
axis of birefringence aligned with an axis of polarization of said
polarizer.
19. An interferometer, as defined by claim 18, wherein said intensity
equalizer comprises a pair of optical fiber segments having axes of
birefringence oriented at 45.degree. to each other.
20. An interferometer, as defined by claim 18, wherein said loop is
comprised of optical fiber.
21. An interferometer, as defined by claim 24, wherein said optical fiber
is birefringent.
22. An interferometer, as defined by claim 18, additionally comprising a
birefringence modulator for modulating birefringence of said optical
fiber.
23. An interferometer, as defined by claim 18, wherein said intensity
equalizer is disposed between said polarizer and said second coupler.
24. An interferometer comprising:
a light source;
a sensing loop;
a polarizer between said light source and said loop; and
an optical path comprising a birefringent medium having two polarization
modes and two axes of birefringence, said optical path extending from said
source to said loop, and propagating light therein, said polarizer being
aligned with one of said axes of birefringence so as to block light
propagating in one of said polarization modes, while passing light in the
other of said two polarization modes, said light having substantially
equal intensities in said two polarization modes upon reaching said
polarizer, such that said polarizer transmits only a portion of said light
to said loop.
25. An interferometer, as defined by claim 24, wherein said light source
emits polarized light having a polarization, said polarization aligned
with one of said axes of birefringence so as to introduce light into
substantially only said one polarization mode, said axes of birefringence
being perturbed at a location between said light source and said
polarizer, so as to provide light of substantially equal intensities in
said polarization modes.
26. An interferometer, as defined by claim 24, wherein said birefringent
medium comprises first and second optical fiber segments having axes of
birefringence at 45.degree. relative to each other.
27. An interferometer, as defined by claim 24, further comprising a
birefringence modulator for modulating said birefringence.
28. An interferometer, as defined by claim 27, wherein said birefringence
modulator is disposed between said light source and said polarizer. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
The present invention relates to rotation sensors for use in, e.g.,
gyroscopes, and particularly to fiber optic rotation sensors.
Fiber optic rotation sensors typically comprise a loop of single-mode
optical fiber to which a pair of light waves are coupled for propagation
in opposite directions around a loop. If the loop is rotated, the
counter-propagating waves will undergo a phase shift, due to the
well-known Sagnac effect, yielding a phase difference between the waves
after traverse of the loop. By detecting this phase difference, a direct
indication of the rotation rate of the loop may be obtained.
If the optical path lengths about the loop for the counter-propagating
waves are equal when the loop is at rest, the interferometer is said to be
"reciprocal". In practice, however, fiber interferometer loops are
ordinarily not reciprocal, due to the fact that present, commercially
available optical fibers are not optically perfect, but are birefringent
(i.e., doubly refractive), resulting in two orthogonal polarization modes,
each of which propagates light at a different velocity. One of the
polarization modes, therefore, provides a "fast channel", while the other
provides a "slow channel." In addition, the fiber birefringence is
sensitive to environmental factors, such as temperature, pressure,
magnetic fields, etc., so that, at any given point along the fiber, the
birefringence can vary over time in an unpredictable manner. Birefringence
affects the counter-propagating waves in a complex way, however, the
effect may be viewed as causing a portion of the waves to be coupled from
one of the polarization modes to the other, i.e., from the "fast channel"
to the "slow channel" or vice versa. The result of such coupling between
modes is that each of the counter-propagating waves may travel different
optical paths around the loop, and thus, require different time periods to
traverse the fiber loop, so that there is a phase difference between the
waves when the loop is at rest, thereby making the interferometer
nonreciprocal.
The foregoing may be more fully understood through a rather simplistic,
extreme example in which it is assumed that there is birefringence-induced
coupling only at one point in the fiber loop, and that this point is
located near one end of the loop. It is also assumed that such
birefringence-induced coupling is sufficient to cause light energy to be
entirely coupled from one polarization mode to the other, and that there
is no coupling between modes anywhere else in the fiber loop. If the
counter-propagating waves are introduced into the loop in the fast
channel, one of the waves will immediately be coupled to the slow channel
while the other wave will traverse most of the loop before being coupled
to the slow channel. Thus, one of the waves will traverse most of the loop
in the fast channel, while the other will traverse most of the loop in the
slow channel, yielding a phase difference between the waves when the loop
is at rest. If this birefringence-induced phase difference were constant,
there would, of course, be no problem, since the rotational induced Sagnac
phase difference could be measured as a deviation from this constant
birefringence-induced phase difference. Unfortunately, however, such
birefringence-induced phase differences vary with time, in an
unpredictable manner, and thus, these birefringence-induced phase
differences are indistinguishable from rotationally-induced, Sagnac phase
differences. Thus, time varying changes in birefringence are a major
source of error in fiber optic rotation sensors.
The prior art has addressed the problem of nonreciprocal,
birefringence-induced phase differences in a variety of ways. In one
approach, described by R. A. Bergh, et al. in "All-single mode fiber-optic
gyroscope with a long-term stability," OPTICS LETTERS, Volume 6, No. 10,
October 1981, pp. 502-504, a fiber optical polarizer is utilized to block
light in one of the two orthogonal polarization modes while passing light
in the other. This ensures that only a single optical path is utilized,
thereby providing reciprocity. This approach is also described in U.S.
Pat. No. 4,410,275. Another approach involves utilizing unpolarized light,
which has been found to result in cancellation of birefringence-induced
phase differences upon combining the counter-propagating waves after
traverse of the loop. The degree of cancellation is proportional to the
degree to which the light waves are unpolarized. This approach is
described in detail in U.S. Pat. No 4,529,312.
It is also known in the art to utilize polarization-conserving fibers to
reduce coupling between the modes. Polarization-conserving fibers are
essentially high birefringence fibers, in which the fiber is mechanically
stressed during manufacture to increase the difference in the refractive
indices of the two polarization modes. This reduces coupling between the
modes, since the high birefringence tends to preserve the polarization of
the light waves. In effect, changes in birefringence due to environmental
factors are overwhelmed by the birefringence created during manufacture of
the fiber.
SUMMARY OF THE INVENTION
The present invention comprises a fiber optic Sagnac interferometer
employing birefringent fiber. Such birefringent fiber reduces the average
optical power transferred from one polarization mode to the other to about
one percent or less over 1 km of fiber. As an approximation, the maximum
phase error due to coupling between modes is equal to the fraction of
power transferred between the modes. Thus, for a 1 km fiber loop having a
power transfer rate of 1% per km, the maximum phase error would be 0.01 or
10.sup.-2 radians.
The birefringent optical fiber is formed into a loop by using a directional
coupler to close the loop. A light source, which is preferably a broadband
light source, such as a superluminescent diode, produces light having a
short coherence length. The light source and the fiber are arranged such
that the light is introduced into the fiber and propagates in the fiber in
two orthogonal polarization modes. An equalizing means is positioned
between the light source and the loop-closing coupler, for equalizing the
intensity of the light in the two orthogonal polarization modes such that
the light is divided substantially equally between the two orthogonal
polarization modes. An uncorrelating means is disposed between the light
source and the equalizing means to reduce the correlation of the phase
between the light in the one mode and the light in the other mode prior to
reaching the equalizing means. A polarizing means is disposed between the
equalizing means and the coupler to receive the light which is divided
between the two modes. Preferably, the polarizing means is a fiber optic
polarizer that is formed on the optical fiber. For example, the polarizer
can be constructed in accordance with U.S. Pat. No. 4,386,822. The
polarizing means blocks light in one of the polarization modes while
passing light in the other of the polarization modes. Thus, substantially
all of the light is in one of the two polarization modes upon reaching the
coupler. The coupler splits the light after passing through the polarizing
means to provide a pair of waves which counterpropagate about the loop
portion of the fiber. The coupler recombines the waves after
counterpropagating to form an output signal that is propagated to the
polarizing means. A detection means is included for detecting the output
signal after passing through the polarizing means. Preferably, the
detection means includes a photodetector and a second coupler, disposed
between the polarizer and the light source for coupling the output signal
from the polarizer to the photodetector.
The optical path between the light source and the coupler closing the loop
is preferably a line portion of the same optical fiber that forms the
loop.
In preferred embodiments of the present invention, a second means is
disposed between the polarizer and the coupler for reducing the
correlation between the polarization modes of the light propagating
between the polarizer and the coupler.
In preferred embodiments of the present invention, the equalizing means is
a splice in a length of optical fiber between the light source and the
polarizer. Two ends of the optical fiber are juxtaposed at the splice. The
end of the optical fiber on one side of the splice has its axes of
birefringence oriented at an angle of 45.degree. with respect to the axes
of birefringence of the end of the fiber on the other side of the splice.
The means for reducing correlation of the phase between the light in one
mode and the light in the other mode advantageously includes a
birefringence modulator. The birefringence modulator in preferred
embodiments is constructed by placing a length of optical fiber between
two slabs of rigid material, such as quartz, with the fast axis of
polarization oriented perpendicular to the two slabs. A piezoelectric
transducer is positioned on one of the slabs, and the sandwich of
materials thus formed is clamped together. The piezoelectric transducer is
driven by a deterministic signal, such as a triangular waveform, to
periodically stress the optical fiber along its fast axis of
birefringence. The periodic stress causes a time-varying birefringence in
the optical fiber. The phase error induced by birefringence is thus caused
to vary over a range such that the average phase error caused by
birefringence and detected by the detection means is substantially equal
to zero, thus substantially reducing environmentally caused phase error.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic drawing of an exemplary rotation sensor, showing a
single, continuous strand of optical fiber, to which light from a light
source is coupled, and showing the sensing loop, formed from such single,
continuous strand; in addition, FIG. 1 shows a detection system for
detecting the phase difference between waves counterpropagating through
the fiber loop.
FIG. 2 is a schematic drawing illustrating a conceptual model of the fiber
loop of FIG. 1, showing, for an exemplary pair of polarization modes, the
electric field components of the counterpropagating waves as they traverse
the fiber loop.
FIG. 3 is a schematic drawing of the conceptual model of FIG. 2, showing
the electric field components of the counterpropagating waves after they
have traversed the fiber loop.
FIG. 4 is a vector diagram of the optical output signal, showing a vector
directed along the real axis, which represents the vector sum of the "dc"
terms resulting from the electric field components shown in FIG. 3, and
another vector, rotating in the manner of a phasor, which represents the
vector sum of the interference terms resulting from the electric field
components shown in FIG. 3, and further illustrating the response of the
vector representing the interference terms to (1) the rotationally-induced
Sagnac phase difference, and (2) phase errors caused by non-rotationally
induced phase differences.
FIG. 5 is a graph, corresponding to the vector diagram of FIG. 4, of the
optical intensity, as measured by the detector, versus the Sagnac phase
difference, illustrating the effect of non-rotationally induced phase
errors.
FIG. 6 is a schematic drawing of an embodiment of the rotation sensor of
the present invention showing a birefringence modulator disposed between
the first and second directional couplers.
FIG. 7 is a partial perspective view of the birefringence modulator of the
present invention, showing the optical fiber sandwiched between the two
quartz slabs and driven by a piezoelectric transducer, and also including
a schematic representation of a signal source for driving the
piezoelectric transducer.
FIG. 8 is a cross sectional view of the birefringence modulator taken along
the lines 8--8 in FIG. 7.
FIG. 9 is a graphical representation of the relationship between a
temperature function on the horizontal axis and an angular offset error
caused by birefringence on the vertical scale.
FIG. 10 is a graphical representation of the piezoelectric driving signal
as a function of time.
FIG. 11 is a graphical representation of the variation in angular offset
error caused by the birefringence modulator as a function of time.
FIG. 12 is a graphical representation of the relationship between the
angular offset error caused by the combined effect of the temperature and
the birefringence modulator, showing the averaging of the angular offset
error to zero.
FIG. 13 is a graphical representation of the relationship between the
angular offset error caused by the combined effect of the temperature and
the birefringence modulator as in FIG. 12, but for a different magnitude
of the temperature function, again showing the averaging of the angular
offset error to zero.
FIG. 14 is a graphical representation of the amplitude type error as a
function of the birefringence modulation showing that the amplitude type
error reduces to zero when the amplitude of the birefringence modulation
is a multiple of 2.pi..
FIG. 15 is a vector diagram of the interference terms resulting from Group
III electric field components;
FIG. 16 is a vector diagram showing a resultant vector which represents the
vector sum of the two vectors of FIG. 15, and illustrating the phase error
associated with such a resultant vector sum.
FIG. 17 is a vector diagram showing the vectors of FIG. 15 equalized in
magnitude.
FIG. 18 is a vector diagram of a resultant vector, which represents the
vector sum of the vectors of FIG. 17, illustrating that phase errors may
be eliminated by equalizing the magnitudes of the vectors.
FIG. 19 is a graph of the optical intensity, as measured by a detector,
versus the Sagnac phase difference, illustrating the effect of changes in
the magnitude of the interference factor of FIG. 4, assuming a phase error
of zero.
FIG. 20 is a schematic drawing of an embodiment of the rotation sensor of
the present invention showing a means for uncorrelating the light in the
two polarization modes of the fiber, a 45.degree. splice, and a polarizer
disposed between the first and second directional coupler.
FIGS. 21A-21E graphically illustrate the effect of the uncorrelating means,
the 45.degree. splice, and the polarizer on the intensity type phase
errors when substantially all of the light is incident to the 45.degree.
splice in one polarization mode.
FIGS. 22A-22I graphically illustrate the effect of the uncorrelating means,
the 45.degree. splice, and the polarizer when the light incident to the
45.degree. splice comprises uncorrelated light in both of the polarization
modes.
FIG. 23 is a schematic drawing of the preferred embodiment of the present
invention that includes the birefringence modulator of FIGS. 6-8 in
combination with the uncorrelating means, the 45.degree. splice and the
polarizer of FIG. 20.
FIG. 24 is an alternative embodiment of the present invention showing a
birefringence modulator, asymmetrically located in the loop portion of the
sensor, to reduce intensity type phase errors in the senor.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
FIG. 1 illustrates an exemplary rotation sensor comprising a light source
10 for introducing a cw light wave into a single, continuous length or
strand of single mode optical fiber 11. As used herein, "single mode
fiber" means that the fiber supports only one fundamental mode for the
particular source light used, as opposed to multimode fiber which supports
more than one spatial mode. However, it will be recognized that a single
mode fiber includes two orthogonal polarization modes, each of which
propagates light at a different velocity.
The fiber 11 passes through ports, labeled A and C, of a first directional
coupler 12, through an intermediate portion 13 of fiber, and then through
ports, labeled A and C of a second directional coupler 14. Thus, the fiber
11 extends from the light source 10 to port A of the coupler 12 and
extends from port C of the coupler 12 via the intermediate portion 13 to
port A of the coupler 14. The portion of the fiber 11 extending from port
C of the coupler 14 is wound into a loop 16. By way of specific example,
the loop 16 may comprise about 1400 turns, each bounding an area of about
150 sq. cm for a total loop length of 600 meters. The end of the fiber 11,
from the loop 16, is passed through ports, labeled D and B, of the coupler
14, with port D adjacent to the loop 16. A small portion 17 of the fiber
11 extends from port B of the coupler 14 and terminates nonreflectively,
without connection.
A second length of fiber 19 is passed through the ports labeled D and B of
the coupler 12. The portion of the fiber 19 projecting from port D
terminates nonreflectively, without connection. However, the portion of
the fiber 19 projecting from port B of the coupler 12 is optically coupled
to a photodetector 20, which produces an output signal proportional to the
intensity of the light impressed thereon.
The directional couplers 12 and 14 are advantageously constructed in
accordance with U.S. Pat. No. 4,536,058, and U.S. Pat. No. 4,493,528, both
of which are incorporated herein .by reference. Preferably, the couplers
12 and 14 are constructed such that light incident to a coupler at one
port, e.g., the port A, is coupled in equal amounts to each of the
opposite ports, e.g., the ports C and D.
The rotation sensor of FIG. 1 also includes detection electronics 22,
comprising a lock-in amplifier 24, a signal generator 26, and a phase
modulator 28. By way of specific example, the phase modulator 28 may
comprise a PZT cylinder, having a diameter of e.g. about 1 to 2 inches,
about which a portion of the fiber loop 16 is wrapped, e.g., 4 to 10
times. The fiber is bonded to the PZT cylinder 28 by a suitable adhesive,
so that the fiber 11 will be stretched upon radial expansion of the
cylinder 28. In this regard, the phase modulator 28 is driven by an AC
modulating signal, having a frequency in the range of, e.g., 10-1000 kHz,
which is provided on a line 30 from the signal generator 26. For proper
operation of the detection electronics 22, it is important that the phase
modulator 28 be located on one side of the loop 16, e.g., adjacent to the
port D of the coupler 14, rather than at the center of the sensing loop
16.
The AC modulation signal from the generator 26 is also supplied on a line
32 to the lock-in amplifier 24. A line 34 connects the lock-in amplifier
24 to receive the detector 20 output signal. The amplifier 24 utilizes the
modulation signal from the generator 26 as a reference for enabling the
amplifier 24 to synchronously detect the detector output signal at the
modulation frequency. Thus, the amplifier 24 effectively provides a band
pass filter at the fundamental frequency (i.e., the frequency of
modulation) of the phase modulator 28, blocking all other harmonics of
this frequency. It will be understood by those skilled in the art that the
magnitude of this harmonic component of the detector output signal is
proportional, through an operating range, to the rotation rate of the loop
16. The amplifier 24 outputs a signal which is proportional to this first
harmonic component, and thus, provides a direct indication of the rotation
rate.
Additional details of the detection electronics 22 are described in U.S.
Pat. No. 4,410,275, incorporated herein by reference. This detection
system is also described by R.A. Bergh, et al., in "All-single-mode
fiber-optic gyroscope with a long-term stability," OPTICS LETTERS, Vol. 6,
No. 10, October 1981, pp. 502-504, also incorporated herein by reference.
In the rotation sensor shown in FIG. 1, the fiber 11 comprises a highly
birefringent single mode fiber, e.g., of the type described in the
article, by R.D. Birch, et al., in "FABRICATION OF
POLARISATION-MAINTAINING FIBRES USING GAS-PHASE ETCHING," Electronics
Letters, Vol. 18, No. 24, Nov. 25, 1982, pp. 1036-1038.
The light source 10 should provide light which has a short coherence
length. A preferred light source for use as the source 10 is a
superradiance diode, e.g., of the type described in the article by C.S.
Wang, et al., in "High-power low-divergence superradiance diode," Applied
Physics Letters, Vol. 41, No. 7, Oct. 1, 1982, pp. 587-589. This type of
diode is also commonly called a superluminescent diode (SLD).
The photodetector 20 is a standard pin or avalanche-type photodiode, which
has a sufficiently large surface area to intercept substantially all of
the light exiting the fiber 19, when positioned normal to the fiber axis.
The diameter of the photodetector 20 is typically in the range of about 1
millimeter, the exact size depending upon the diameter of the fiber 19,
the numerical aperture of the fiber 19 (which defines the divergence of
the light as it exits the fiber 19) and the distance between the end of
the fiber 19 and the photodetector 20.
In operation, a light wave W.sub.i is input from the light source 10 for
propagation through the fiber 11. As the wave W.sub.i passes through the
coupler 12, a portion of the light (e.g. 50%) is lost through port D. The
remaining light propagates from port C of the coupler 12 via the
intermediate fiber portion 13 to the coupler 14, where the light is split
evenly into two waves W.sub.1, W.sub.2, which propagate in opposite
directions about the loop 16. After traverse of the loop 16, the waves
W.sub.1, W.sub.2 are recombined by the coupler 14 to form an optical
output signal W.sub.0. A portion of the recombined wave W.sub.0 may be
lost through the port B of the coupler 14, while the remaining portion
travels from port A of the coupler 14 via the intermediate fiber portion
13 to port C of the coupler 12, where it is again split, with a portion
thereof (e.g., 50%) transferred to the fiber 19. Upon exiting the end of
the fiber 19, the wave W.sub.0 is impressed upon the photodetector 20,
which outputs an electrical signal that is proportional to the optical
intensity of the wave W.sub.0.
The intensity of this optical output signal will vary in proportion to the
type (i.e., constructive or destructive) and amount of interference
between the waves W.sub.1, W.sub.2, and thus, will be a function of the
phase difference between the waves W.sub.1, W.sub.2. Assuming, for the
moment, that the fiber 11 is "ideal") (i.e., that the fiber has no
birefringence, or that the birefringence does not change with time),
measurement of the optical output signal intensity will provide an
accurate indication of the rotationally induced Sagnac phase difference,
and thus, the rotation rate of the fiber loop 16.
Discussion of Phase Errors in the Rotation Sensor
As indicated above, present state-of-the-art, fibers are far from "ideal",
in that 1) they are birefringent, and 2) the birefringence is
environmentally sensitive and tends to vary in accordance with fiber
temperature, pressure, or the like, thus, yielding nonrotationally induced
phase differences (i.e., phase errors), which are indistinguishable from
the rotationally induced Sagnac phase difference.
These phase errors may be more fully understood through reference to FIG.
2, which depicts a conceptual model of the two orthogonal polarization
modes of a single mode fiber. Each polarization mode has a propagation
velocity different from that of the other polarization mode. Further, it
is assumed that there is coupling of light energy between modes, which may
be caused e.g. by variations or perturbations in the principal axes of
birefringence of the fiber. Such coupling of energy will be referred to
herein as "cross coupling."
The conceptual fiber model of FIG. 2 will be utilized to represent the
sensing loop 16 (FIG. 1). The counterpropagating waves W.sub.1, W.sub.2,
are schematically represented as being coupled, by the coupler 14, to the
loop 16, by the dashed arrows. The two polarization modes of the single
mode optical fiber are schematically represented in FIG. 2 by a first
line, connecting a pair of terminals C' and D', and a second line,
parallel to the first line, connecting a second pair of terminals C" and
D". The terminals C' and C" on the left side of FIG. 2 correspond to the
port C of the coupler 14, while the terminals D' and D" on the right side
of FIG. 2 correspond to the port D of the coupler 14. The above mentioned
first and second lines connecting the terminals will be used to represent
arbitrary modes i and j, respectively, of the fiber loop 16.
Cross coupling between the modes i and j is represented by a pair of lines,
labeled "Branch 1" and "Branch 2", respectively. Branch 1 represents cross
coupling between the terminals C" and D' while branch 2 represents cross
coupling between terminals C' and D". The intersection of branch 1 with
branch 2, designated by the reference numeral 50, will be referred to as
the "coupling center". It will be understood that no coupling exists
between the two branches 1 and 2. The coupling center 50 is shown as being
offset from the center of the fiber loop 16 to illustrate that the
coupling between the polarization modes is not uniform along its length.
Therefore, cross coupled light will travel a longer path in one of the
modes than the other, yielding a nonrotationally induced phase difference
therebetween. Moreover, it will be understood that, in reality, the fiber
birefringence, being environmentally sensitive, varies with time, thus
making the optical paths travelled by the cross-coupled light also time
varying.
As shown in FIG. 2, the wave of W.sub.1 is coupled to the fiber loop 16 so
that the modes i and j are launched with electric field amplitudes
E.sub.i.sup.+ and E.sub.j.sup.+, respectively. Similarly, the wave
W.sub.2 is coupled to launch each of the modes i and j with electric field
amplitudes E.sub.i.sup.- and E.sub.j.sup.-, respectively. The plus (+)
and minus (-) superscripts designate the direction of propagation, the
clockwise direction about the loop 16 being designated by the plus (+)
sign, and the counterclockwise direction around the loop 16 being
designated by the minus (-) sign.
As light in each of the modes i and j traverses the fiber loop 16, energy
is coupled between the modes, so that each electric field is divided into
two components, namely, a "straight through" component, designated by the
subscript "s", and a "cross coupled" component, designated by the
subscript "c". Thus, E.sub.i.sup.+ is divided into a straight through
component E.sub.is.sup.+ remains in mode i during traverse of the loop
16, and a cross coupled component E.sub.jc.sup.+, which is cross coupled
to mode j during traverse of the loop 16. Similarly, E.sub.i.sup.- is
divided into components E.sub.is.sup.- and E.sub.jc.sup.- ; E.sub.j.sup.+
is divided into components E.sub.ic.sup.+ and E.sub.js.sup.+ ;
E.sub.j.sup.- is divided into components E.sub.js.sup.- and
E.sub.ic.sup.-.
After the light waves have traversed the fiber loop 16, the light at
terminal C' will comprise components E.sub.is.sup.- and E.sub.ic.sup.- ;
the light at terminal C" will comprise component E.sub.js.sup.- and
E.sub.jc.sup.- ; the light at terminal D' will comprise components
E.sub.is.sup.+ and E.sub.ic.sup.+ ; and the light at terminal D" will
comprise components E.sub.js.sup.+ and E.sub.jc.sup.+, as shown in FIG.
3. These 8 electric field components are combined by the coupler 14 to
form the optical output signal W.sub.0. It will be recognized by those
skilled in the art that, in general, superposition of any two electric
field components, e.g., E.sub.is.sup.+ and E.sub.ic.sup.+, will yield a
resultant intensity (I), as measured by the detector 20, which may be
defined as follows:
I=.vertline.E.sub.is.sup.+ .vertline..sup.2 +.vertline.E.sub.ic.sup.+
.vertline..sup.2 +2.vertline.E.sub.is.sup.+ .vertline. .vertline.E.sub.ic
.vertline. cos.phi. (1)
where, in this particular example, .phi. is the phase difference between
field components E.sub.is.sup.+ and E.sub.ic.sup.+.
The first two terms of equation (1), namely .vertline.E.sub.is.sup.+
.vertline..sup.2 and .vertline.E.sub.ic.sup.+ .vertline..sup.2 are
steady-state or "d.c." terms, while the last term is an "interference"
term having a magnitude depending upon the phase difference .phi. between
the fields E.sub.is.sup.+ and E.sub.ic.sup.+.
In general, all 8 of the above fields E.sub.is.sup.-, E.sub.ic.sup.-,
E.sub.js.sup.-, E.sub.jc.sup.-, E.sub.is.sup.+, E.sub.ic.sup.+,
E.sub.js.sup.+ and E.sub.jc.sup.+, will interfere with each other to
provide an optical intensity at the detector 20 (FIG. 1) comprised of 8
"dc" terms, which are not phase-dependent, and 28 "interference" terms
which are phase-dependent. The number of combinations of phase-dependent
terms is actually n(n-1) or 56 phase-dependent terms. However, one-half of
these terms are simply the re-ordered forms of the other half, yielding 28
non-redundant terms.
The 8 dc terms are shown in FIG. 4 as a single vector sum, labeled
I.sub.dc, while the 28 interference terms are shown in FIG. 4 as a single
vector, labeled I.sub.i. These vectors I.sub.dc and I.sub.i are plotted in
a complex plane. Upon rotation of the fiber loop 16 (FIG. 1) the
phase-dependent vector I.sub.i rotates, in the manner of a phasor, through
an angle equal to the rotationally reduced phase difference .phi.s due to
the Sagnac effect. The projection of the interference vector I.sub.i upon
the real axis, when added to the vector I.sub.dc, yields the total optical
intensity I.sub.DET of the optical output signal W.sub.0, as measured by
the detector 20 (FIG. 1). In FIG. 5, this optical intensity I.sub.DET is
plotted as function of the Sagnac phase difference .phi.s, as illustrated
by the curve 52.
As indicated above in reference to FIG. 2, cross coupling between the modes
i and j can cause the fiber loop 16 to be nonreciprocal, resulting in a
nonrotationally induced phase difference between the above described
electric field components, and yielding an accumulated phase error
.phi..sub.e, which is indistinguishable from the rotationally induced
Sagnac phase difference .phi..sub.s. The phase error .phi..sub.e causes
the phasor I.sub.i to be rotated, e.g., from the position shown in solid
lines to the position shown in dotted lines in FIG. 4. This results in the
curve 52 of FIG. 5 being translated by an amount .phi..sub.e, e.g., from
the position shown in solid lines to the position shown in dotted lines in
FIG. 5.
Elimination or reduction of the accumulated phase error .phi..sub.e
requires an analysis of the 28 interference terms resulting from
superposition of the 8 electric field components discussed in reference to
FIG. 2. At the outset, it will be recognized that interference between
electric field components E.sub.is.sup.+ with E.sub.is.sup.-, and
E.sub.js.sup.+ with E.sub.js.sup.-, result in no phase error
contribution, since the light represented by these components is not cross
coupled, and traverses the loop in a single one of the modes. However, the
remaining 26 interference terms can contribute to the accumulated phase
error .phi..sub.e. These 26 interference terms correspond to 26 pairs of
electric field components which may be classified with 3 groups, namely,
Group I, Group II, and Group III, as follows:
Although o | | |
