Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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GATED FIBER OPTIC ROTATION SENSOR
WITH LINEARIZ ED SCALE FACTOR
~ack~round of the Invention
The present invention relates to rotation sensors,
such as gyroscopes, and particularly to a fiber optic
rotation sensor which has an extended dynamic range.
Fiber optic rotation sensors typically comprise a loop
of fiber optic material to which light waves are coupled
for propagation around the loop in opposite directions.
Rotation of the loop creates a relative phase difference
between counter-propagating waves, in accordance with the
well known "Sagnac effect", with the amount of phase
difference corresponding to the velocity of rotation The
counter-propagating waves, when recombined, interfere
constructively or destructively to produce an optical
output signal which varies in intensity in accordance with
the rotation rate of the loop. Rotation sensing is
commonly accomplished by detection of this optical output
signal.
Various techniques have been devised to increase the
sensitivity of fiber optic rotation sensors to small
rotation velocities. However, most of these techniques
have not been useable for detecting very large rotation
velocities because the output functions tend to repeat
themselves at various velocities of rotation. As a
result, the output signal cannot be utilized to determine
which of those possible rotation velocities having the
same output signal waveform is responsible for the
particular output signal waveform observed.
Thus, it would be a great improvement in the art to
provide a phase modulation technique wherein rotation
could be accurately and reliably sensed over a very broad
range of rotation velocities. Such a technique, and means
for its accomplishment are described herein.
Brief Summary of the Invention
The present invention comprises a rotation sensor and
method of its operation for accurately and reliably
sensing a broad range of rotational velocities. The
rotation sensor comprises all fiber optic components, such
as a fiber optic directional coupler which (a) splits the
light from the source into two waves that propagate around
the sensing loop in opposite directions, and (b) combines
the counter-propagating waves to provide an optical output
signal. Proper polarization of the applied light, the
counter-propagating waves, and the optical output signal
is established, controlled, and maintained by a fiber
optic polarizer and fiber optic polarization
controllers. A second fiber optic coupler is provided to
couple the optical output signal from the continuous
strand to a photodetector which outputs an electrical
signal that is proportional to the intensity of the
optical signal.
Improved operating stability and sensitivity of the
rotation sensor is achieved by phase modulating the
counter-propagating waves at a first frequency (the bias
phase modulation frequency) using a first phase modulator,
thereby biasing the phase of the optical output signal. A
phase sensitive detection system is utilized to mçasure
the first harmonic component of the optical output signal
intensity. In the detection system disclosed, the
amplitude of this first harmonic component is proportional
to the rotation rate of the loop.
A second phase modulation signal is provided at an
arbitrary frequency which is much lower than that of the
bias frequency. It is preferable that the second phase
modulation frequency not be harmonically related to the
first phase modulation frequency. This second phase
modulation signal may be imposed on the system through the
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first phase modulator or, alternatively, a second phase
modulator may be utilized. The optical output signal is
gated in synchronism with the second phase modulation
frequency, such that the output signal represents the
phase difference modulation produced, for example, during
the positive half cycle of the second phase modulation,
while presenting a value of zero during the negative half
cycle of the second phase modulation. By adjusting the
amplitude of the second modulation signal, the influence
of the Sagnac phase shift can be effectively cancelled so
that the time average value of the optical output signal
during the positive half cycle of the second modulation is
zero. Thus, it is seen that the amplitude of the second
modulation signal is utilized as the means for cancelling
the Sagnac phase shift, and thus this magnitude is
representative of the amount of Sagnac phase shift which
is present in the system. -
In order to adjust the magnitude of the second phase
modulation signal, the first phase modulation frequency
component in the gated portion of the output signal is
used to generate a feedback error signal which is fed back
to control the amplitude of the second phase modulation
driving signal.
A feedback error correction modulator controls the
amplitude of the second modulation driving signal in
accordance with the feedback error signal, which
corresponds to the amplitude of the optical output signal
which is caused by the Sagnac phase shift.
Stored in a memory is rotation rate data related by a
transfer function to the amplitude of the second phase
modulation that cancels the first phase modulation
frequency component in the optical output signal caused by
rotation. The "cancellation" amplitude of the lower
frequency signal that is sufficient to cancel or limit the
first phase modulation frequency component caused by the
Sagnac effect is then converted to the rotation rate by
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accessing the memory using the amplitude of the
cancellation signal as the address. The rotation rate
data so accessed can then be used directly or converted
into a signal which can be interpreted to derive the
Sagnac phase shift or the velocity of rotation.
It has been found that amplitude modulation in odd
harmonics of the optical output signal, caused by the
phase modulator (either directly or indirectly, through
polarization modulation), may be eliminated by operating
the phase modulator at a specific frequency. Since the
detection system utilized detects only an odd harmonic
(e.g., the first harmonic), the effects of phase modulator
induced amplitude modulation may be eliminated by
operating at such frequency. This eliminates a
significant source of error in rotation sensing, and
thereby increases the accuracy of the rotation sensor.
In another preferred embodiment of the invention, a
modification of phase modulation waveforms provides a
phase difference modulation whose amplitude has the same
wavelength dependence to the applied driving signal as the
Sagnac phase shift has to the rotation rate. Thus, a
substantially linear scale factor is created. With a
linearized scale factor, the amplitude of the phase
difference modulation at the second frequency is
proportional to the Sagnac phase shift in the counter-
propagating light waves in the rotation sensor loop. In
this embodiment, the phase difference modulation comprises
a substantially constant, DC value which can be adjusted
to cancel the DC phase difference modulation of the
counter-propagating light waves (the Sagnac phase shift)
with a simplified, linear function.
One means for creating a substantially linear scale
factor is through use of a phase ramp which is applied to
the counter-propagating waves by means of a modulator
located at an asymmetric location in the sensing loop of
the gyroscope. Application of the phase ramp produces a
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DC differential phase shift between counter-propagating
waves. However, commonly used fiber optic phase
modulators cannot provide a phase ramp. Thus, the phase
ramp is simulated through use of periodically repeating
waveforms having a ramp portion.
One such waveform is a saw-tooth wave, which may
be simulated by combining the phase modulation at one
frequency with that modulation at its second harmonic
frequency-, and adjusting the phase and amplitude
relationships to approximately simulate the saw-tooth
modulation waveform. Because of the resetting process
at the peak of each sawtooth modulation waveform, and
because of the reciprocity of the two optical paths of
the counter-propagating waves, the phase difference
cannot be constant in time. This problem is overcome
by substituting the saw-tooth waveform for the second
modulation signal of the embodiment first described
above. With that substitution, the optical output
signal is gated on during the period of time when the
ramp portion of the saw-tooth wave is present, and the
output signal is gated off at all other times. Thus,
by adjusting the amplitude or frequency of the second
modulation in the manner described above, the DC Sagnac
phase shift can be nulled out by the DC phase difference
modulation produced by the phase ramp when the output
signal is gated on, and the zero Sagnac phase shift is
also simulated during the period when the output signal is gated off.
Gating of the output signal may take place at the
light source or at or after the detector. The slope of
the phase ramp which determines the diffexential phase
shift is controlled by adjusting the modulation amplitude
of the saw-tooth wave modulation signal. This is
accomplished by use of the error feedback signal, and
the error correction modulator, as was described above.
f
Of course, a triangle waveform phase modulation is yet
another type of waveform which may be utilized in the same
manner as the saw-tooth wave modulation. Such a triangle
waveform may be created through combination of the
modulation frequency and the third harmonic of that
modulation frequency.
Brief Description of the Drawings
These and other advantages of the present invention
are best understood with reference to the drawings in
which:
FIGURE l.is a schematic drawing of a basic rotation
sensor, showing the fiber optic components positioned
along a continuous, uninterrupted strand of fiber optic
material, and further showing the signal generator,
photodetector, lock-in amplifier, and display associated
with the detection system;
FIGURE 2 is a sectional view of one embodiment of a
fiber optic directional coupler for use in the rotation
sensor of Figure l;
FIGURE 3 is a sectional view of one embodiment of a
fiber optic polarizer for use in the rotation sensor of
Figure l;
FIGURE 4 is a perspective view of one embodiment of a
fiber optic polarization controller for use in the
rotation sensor of Figure l;
FIGURE S is a schematic diagram of the rotation sénsor
of Figure l with the polarizer, polarization controllers,
and phase modulator removed therefrom;
FIGURE 6 is a graph of the intensity of the optical
output signal, as measured by the photodetector, as a
function of the rotationally induced Sagnac phase
difference, illustrating the effects of...birefringence
induced phase differences and birefringence induced
amplitude fluctuations;
FIGURE 7 is a graph of phase difference as a function
of time showing the phase modulation of each of the
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counter-propagating waves and the phase difference between
the counter-propagating waves;
FIGURE 8 is a schematic drawing illustrating the
effect of the phase modulation upon the intensity of the
optical output signal, as measured by the detector, when
the loop is at rest;
FIGURE 9 is a schematic drawing showing the effect of
the phase modulation upon the intensity of the optical
output signal as measured by the detector when the loop is
rotating;
FIGURE lO is a graph of the amplifier output signal as
a function of the rotationally induced Sagnac phase
difference, illustrating an operating range for the
rotation sensor of Figure l;
FIGURE ll is a diagram of one preferred embodiment of
a gated closed loop rotation sensor with extended dynamic
range;
FIGURE 12 is a diagram of the overall phase shift
resulting from the bias phase modulation and the lower
frequency phase modulation in conjunction with a constant
bias resulting from the Sagnac effect;
FIGURE 13 is a diagram of the overall phase shift for
lower frequency phase modulation in conjunction with a
constant bias resulting from the Sagnac effect, and the
optimal output signal which results from gating.
FIGURE 14 is a graph of the scale -factor of the
rotation sensor illustrated in Figure ll;
FIGURE 15 is a circuit diagram for an error correction
modulator;
3~ FIGURE 16 is a diagram of the response of the
modulator of Figure 15 to a sample error signal;
FIGURE l7 is a diagram of a preferred error correction
modulator;
FIGURE 18 is a schematic diagram of the overall sensor
using the error correction modulator of Figure l7;
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FIGURE 19 is a diagram of another error correction
modulator which could be used in the embodiment of
Figure 11;
FIGURE 20 is a diagram of the preferred embodiment of
an output circuit for the rotation sensor for converting
the amplitude of the lower frequency driving signal to the
rotation rate;
FIGURE 21 is a diagram of an output display circuit
which could be used in linear regions of the scale factor;
FIGURE 22 is a diagram of another output display
circuit which could be used in linear regions of the scale
factor; and
FIGURE 23 is a graph illustrating the relative phase
difference between the interfering waves which are
modulated by a ramp waveform;
FIGURE 24 is a diagram illustrating the relative phase
between the interfering waves which are modulated by a
saw-tooth waveform, and the phase difference between those
interfering waves;
FIGURE 25 is a graphical illustration of one method of
forming a saw-tooth wave and further illustrating the
relative phase between the interfering waves which are
modulated by the saw-tooth waveform, as well as
illustrating the phase difference between those
interfering waves;
FIGURE 26 is a diagram of the overall phase.shift
resulting from the bias phase modulation and the lower
frequency saw-tooth waveform phase modulation in
conjunction with a constant bias resulting from the Sagnac
effect, and the output signal which results from gating;
FIGURE 27 is a diagram of one preferred embodiment of
a gated, closed loop rotation sensor having extended
dynamic range and a substantially linearized scale factor;
FIGURE 28 is a graph of the scale factor of the sensor
illustrated in Figure 27; and
FIGURE 29 is a diagram of another preferred embodiment
of a gated, closed loop rotation sensor having extended
dynamic range and a substantially linear transfer
function.
Detailed Description of the Preferred Embodiment
Before proceeding with a discussion of the preferred
embodiment of the invention, a discussion of the basic
rotation sensor used in the invention is necessary for a
fuller understanding of the improvement. Figure 1 shows a
rotation sensor having a basic structure which is of the
type used in the present invention. It includes a light
source 10 for introducing light into a continuous length
or strand of optical fiber 12, a portion of which is wound
into a sensing loop 14. As used herein, the reference
numeral 12 designates generally the entire continuous
strand of optical fiber, while the numeral 12 with letter
suffixes (A, B, C, etc.) designates portions of the
optical fiber 12.
In the embodiment shown, the light source 10 comprises
a galium arsenide (GaAs) laser which produces light having
a wave length on the order of 0.82 microns. By way of
specific example, the light source 10 may comprise a model
GO-DIP laser diode, commercially available from General
Optronics Corp., 3005 Hadley Road, South Plainfield, New
Jersey. The fiber optic strands such as the strand 12 are
preferably single mode fibers having, for examplé, an
outer diameter of 80 microns and a core diameter of 4
microns. The loop 14 comprises a plurality of turns of
the fiber 12 wrapped about a spool or other suitable
support (not shown). By way of specific example, the loop
14 may have approximately 1000 turns of fiber wound on a
form having a diameter of 14 centimeters.
Preferably, the loop 14 is wound symmetrically,
starting from the center, so that symmetrical points in
the loop 14 are in proximity. It is believed that this
reduces the environmental sensitivity of the rotation
--10--
sensor, since such symmetry causes time varying
temperature and pressure gradients to have a similar
effect on both of the counter-propagating waves.
- Light from the source 10 is optically coupled to one
end of the fiber 12 by butting the fiber 12 against the
light source 10. Various components for guiding and
processing the light are positioned or formed at various
locations along the continuous strand 12. For the purpose
of describing the relative locations of these components,
the continuous fiber 12 will be described as being divided
into seven portions, labeled 12A through 12G,
respectively, with the portion 12A through 12E being on
the side of the loop 14 that is coupled to the source 10,
and the portions 12F and 12G being on the opposite side of
the loop 14.
Adjacent to the light source 10, between the fiber
portions 12A and 12B, is a polarization controller 24. A
type of polarization controller suitable for use as the
controller 24 is described in detail in U.S. Patent No.
4,389,090 issued June 21, 1983 entitled "Fiber-Optic
Polarization Controller", assigned to the assignee of
the present invention. A brief description of the
polarization controllers 24 will be provided subsequently.
However, it should be presently understood that this
controller 24 permits adjustment of both the state and
direction of polarization of the applied light.
The fiber 12 then passes through ports labeled A and B
of a directional coupler 26, located between the fiber
portions 12B and 12C. The coupler 26 couples optical
power to a second strand of optical fiber which passes
through the ports labeled C and D of the coupler 26, the
port C being on the same side of the coupler as the port
A, and the port D being on the same side of the coupler as
the port B. The end of the fiber 28 extending from the
port D terminates non-reflectively at the point labeled
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"NC" (for snot connected") while the end of the fiber 29
extending from the port C is optically coupled to a
photodetector 30. By way of specific example, the
photodetector 30 may comprise a standard, reverse biased,
silicon, PIN-type, photo diode. The coupler 26 is
described in detail in U.S. Patent No. 4,536,058
issued August 20, 1985 entitled "Fiber-Optic Directional
Coupler" and in U.S. Patent No. 4,493,528 issued
January 15, 1985 entitled "Fiber-Optic Directional
Coupler" both of said patent applications being
assigned to the assignee of the present invention.
The fiber portion 12C extending from port B of the
coupler 26 passes through a polarizer 32, located between
the fiber portions 12C and 12D. A monomode optical fiber
has two polarization modes of travel for any light wave.
Ihe polarizer 32 permits passage of light in one of the
polarization modes of the fiber 12, while preventing
passage of light in the other polarization mode.
Preferably, the polarization controller 24 mentioned above
is used to adjust the polarization of the applied light so
that such polarization is substantially the same as the
polarization mode passed by the polarizer 32. This
reduces the loss of optical power as the applied iight
propagates through the polarizer. A preferred type of
polarizer for use in the present invention is described in
detail in U.SO Patent No. 4,386,822 issued June 7, 1983
entitled "Polarizer and Method" assigned to the assignee
of the present invention.
After passing through the polarizer 32, the fiber 12
passes through ports labeled R and B of a directional
coupler 34, located between the fiber portions 12D and
12E. This coupler 34 is preferably of the same type as
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-12-
described above in reference to the coupler 26. The fiber
12 is then wound into the loop 14, with a polarization
controller 36 located between the loop 14 and fiber
portion 12~. This polarization controller 36 may be of
the type discussed in reference to the controller 24, and
is utilized to adjust the polariæation of the light waves
counter-propagating through the loop 14 so that the
optical output signal, formed by interference of these
counter-propagating waves, has a polarization which will
be efficiently passed by the polarizer 32 with minimal
optical power loss. Thus, by utilizing both the
polarization controllers 24 and 36, the polarization of
the light propagating through the fiber 12 may be adjusted
for maximum optical power output.
A phase modulator 38 driven by an AC signal generator
40 is mounted in the fiber segment 12F between the loop I4
and the second directional coupler 34. This modulator 38
comprises a PZT cylinder, around which the fiber 12 is
wrapped. The fiber 12 is bonded to the cylinder so that
when it expands radially in response to the modulating
signal from the generator 40, it stretches the fiber l2.
An alternative type of modulator (not shown), suitable
for use with the present invention, comprises a PZT
cylinder which longitudinally stretches four segments of
the fiber 12 bonded to short lengths of capillary tubing
at the ends of the cylinder. Those skilled in the art
will recognize that this alternative type of modulator may
impart a lesser degree of polarization modulation to the
propagating optical signal than the modulator 38; however,
it will be seen subsequently that the modulator 38 may be
operated at a frequency which eliminates the undesirable
effects of polarization modulation. Thus, either type of
modulator is suitable for use in the present invention.
The fiber 12 then passes through ports labeled C and D
of the coupler 34, with the fiber portion 12F extending
from the port D and the fiber portion 12G extending from
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the port C. Fiber portion 12G terminates non-reflectively
at a point labeled "NC" (for "not connected").
The output signal from the AC generator 40 is supplied
on a line 44 to a lock-in amplifier 46 as a reference
signal, which lock-in amplifier 46 also is connected to
receive the output of the photodetector 30 by a line 48.
This signal on the line 44 to the amplifier 46 provides a
reference signal for enabling the amplifier 46 to
synchronously detect the detector output signal at the
modulation frequency, i.e., the first harmonic component
of the optical output signal, of the modulator 38 while
blocking all other harmonics of this frequency.
Lock-in amplifiers are well known in the art and are
commercially available
It will be seen below that the magnitude of the first
harmonic component of the detector output signal is
proportional through a certain limited operating range to
the rotation rate of the loop 14. The amplifier 46
outputs a signal which is proportional to this first
harmonic component, and thus provides a direct indication
of the rotation rate, which may be visually displayed on a
display panel 47. However, the scheme of detection shown
in Figure l can only be used for relatively small rotation
rates as will be seen in connection with the discussion of
Figure 9.
The Couplers 26 and 34
A preferred fiber optic directional coupler for use as
the couplers 26 and 34 in the rotation sensor or gyroscope
of the present invention is illustrated in Figure 2. The
coupler comprises two optical fiber strands labeled 50A,
50B in Figure 2, of a single mode fiber optic material
having a portion of the cladding removed from one side
thereof. The two strands 50A and 50B are mounted in
respective arcuate slots 52A and 52B, formed in respective
blocks 53A and 53B. The strands 50A and 50B are
positioned with the portions of the strands where the
~23~2
-14-
cladding has been removed in close spaced relationship, to
form a region of interaction ~4 in which the light is
transferred between the core portions of the strands. The
amount of material removed is such that the core portion
of each strand 50A and 50B is within the evanescent field
of the other. The center-to-center spacing between the
strands at the center of the coupler is typically less
than about 2-3 core diameters.
It is important to note that the light transferred
between the strands at the region of interaction 54 is
directional. That is, substantially all of the light
applied to input port A is delivered to the output ports B
and D, without contra-directional coupling to port C.
Likewise, substantially all of the light applied to input
port C is delivered to the output ports B and D. Further,
this directivity is symmetrical. Thus, light supplied to
either input port B or input port D is delivered to the
output ports A and C. Moreover, the coupler is
essentially non-discriminatory with respect to
polarizations, and thus preserves the polarization of the
coupled light. Thus, for example, if a light beam having
a vertical polarization is input to port A the light
coupled from port A to port D, as well as the light
passing straight through from port A to port B, will
remain vertically polarized.
From the foregoing, it can be seen that the coupler
may function as a beam-splitter to divide the applied
light into two counter-propagating waves Wl, W2 (Figure
1). Further, the coupler may additionally function to
recombine the counter-propagating waves after they have
traversed the loop 14 (Figure 1).
In the embodiment shown, each of the couplers 26, 34
has a coupling efficiency of fifty percent, as this choice
of coupling efficiency provides maximum optical power at
the photodetector 30 (Figure 1). As used herein, the term
"coupling efficiency" is defined as the power ratio of the
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coupled power to the total output power, expressed as a
percent. For example, referring to Figure 2, if light is
applied to port A, the coupling efficiency would be equal
to the ratio of the power at port D to the sum of the
power output at ports B and D. Further, a coupling
efficiency of 50% for the coupler 34 insures that the
counter-propagating waves Wl, W2 are equal magnitude.
The Polarizer 32
A preferred polarizer for use in the rotation sensor
of Figure 1 is illustrated in Figure 3. This polarizer
includes a birefringent crystal 60, positioned within the
evanescent field of light transmitted by the fiber 12.
The fiber 12 is mounted in a slot 62 which opens to the
upper face 63 of a generally rectangular quartz block
64. The slot 62 has an arcuately curved bottom wall, and
the fiber is mounted in the slot 62 so that it follows the
contour of this bottom wall. The upper surface 63 of the
block 64 is lapped to remove a portion of the cladding
from the fiber 12 in a region 67. The crystal 60 is
mounted on the block 64, with the lower surface 68 of the
crystal facing the upper surface 63 of the block 64, to
position the crystal 60 within the evanescent field of the
fiber 12.
The relative indices of refraction of the fiber 12 and
the birefringent material 60 are selected.so that the.-wave
velocity of the desired polarization mode is greater in
the birefringent crystal 6d than in the fiber 12, while
the wave velocity of an undesired polarization mode is
greater in the fiber 12 than in the birefringent crystal
60. The light of the desired polarization mode remains
guided by the core portion of the fiber 12, whereas light
of the undesired polarization mode is coupled from the
fiber 12 to the birefringent crystal 60. Thus, the
polarizer 32 permits passage of light in one polarization
mode, while preventing passage of light in the other
polarization mode. As previously indicated, the
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polarization controllers 24, 36 (Figure 1) Jay be utilized
to adjust the polarizations of the applied light and
optical output signal, respectively, so that optical power
loss through the polarizer is minimized.
The Polarization Controllers 24, 36
One type of polarization controller suitable for use
in the rotation sensor of Figure 1 is illustrated in
figure 4. The controller includes a base 70 on which a
plurality of upright blocks 72A through 72D are mounted.
Between adjacent ones of the blocks 72, spools 74A through
74C are tangentially mounted on shafts 76A through 76C,
respectively. The shafts 76 are axially aligned with each
other, and are rotatably mounted between the blocks 72.
The spools 74 are generally cylindrical and are positioned
tangentially to the shafts 76.
The strand 12 extends through axial bores in the
shafts 76 and is wrapped about each of the spools 74 to
form three coils 78A through 78C. The radii of the coil
78 are such that the fiber 12 is stressed to form a
birefringent medium in each of the coils 78. The three
coils 78A through 78C may be rotated independently of each
other about the axis of the shafts 74A through 74C
respectively to adjust the birefringence of the fiber 12
and, thus, to control the polarization of the light
passing through the fiber 12.
The diameter and number of turns in the coils i8 are
such that the outer coils 78A and C provide a spatial
delay of one-quarter wave length, while the-central coil
78D provides a spatial delay of one-half wave length. The
quarter wave length coils 78A and C control the elipticity
of the polarization, and the half wave length coil 78
controls the direction of polarization. This provides a
full range of adjustment of the polarization of the light
propagating through the fiber 12.
It will be understood, however, that the polarization
controller may be modified to provide only the two quarter
wave coils 78A and C, since the direction ox polarization
(otherwise provided by the central coil 78B) may be
controlled indirectly through proper adjustment of the
elipticity of polariæation by means of the two quarter
wave coils 78A and C. Accordingly, the polarization
controllers 24 and 36 are shown in Figure 1 as including
only the two quarter wave coils 78A and C. Since this
configuration reduces the overall size of the controllers
24-36, it may be advantageous for certain applications of
the present invention involving space limitations.
Thus, the polarization controllers 24 and 36 provide
means for establishing, maintaining and controlling the
polariæation of both the applied light and the counter-
propagating waves.
Operation Without Phase Modulation
Or Polarization Control
In order to fully understand the function and
importance of the polarizer 32 (Figure 1) and phase
modulator 38, the operation of the rotation sensor will
first be described as if these components had been removed
from the system. Accordingly Figure 5 shows the rotation
sensor of Figure 1 in schematic block diagram form, with
the modulator 38, polarizer 32, and associated components
removed therefrom.
Light is coupled from the laser source 10 to the fiber
12 for propagation therein. The light enters port A of
the coupler 26, where a portion of the light is lost
through port D. The remaining portion of the light
propagates from port B to port A of the coupler 34, where
it is split into two counter-propagating waves Wl, W2 of
equal amplitude. The wave Wl propagates from the port B
in a clockwise direction about the loop 14, while the wave
W2 propagates from port D in a counter-clockwise direction
around the loop 14.
After the waves Wl, W2 have traversed the loop 14,
they are recombined by the coupler 34 to form an optical
~3~%52
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output signal, which propagates from port A of the coupler
34 to port B of the coupler 26. A portion of the optical
output signal is coupled from port B to port C of the
coupler 26 for propagation along the fiber 29 to the
photodetector 30. This photodetector 30 outputs an
electrical signal which is proportional to the intensity
of the light impressed thereon by the optical output
signal.
The intensity of the optical output signal will vary
in accordance with the amount and type, i.e., constructive
or destructive, of interference between the waves Wl, W2
when they are recombined or interfered at the coupler
34. Ignoring, for the moment, the effects of fiber
birefringence, the waves Wl, W2 travel the same optical
path around the loop 14. Thus, assuming the loop 14 is at
rest, when the waves Wl, W2 are recombined at the coupler
34, they will interfere constructively, with no phase
difference therebetween, and the intensity of the optical
output signal will be at a maximum. However, when the
loop 14 is rotated, the counter-propagating waves Wl,-W2,
will be shifted in phase in accordance with the Sagnac
effect, so that when they are superposed at the coupler
34, they destructively interfere to reduce the intensity
of the optical output signal. Such Sagnac phase
difference between the waves Wl, W2, caused by rotation of
the loop 14, is defined by the following relationship:
OR a Q (1)
where:
A is the area bounded by the loop 14 of optical
fiber;
N is the number of turns of the optical fiber
about the area A;
~3~2~
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Q is the angular velocity of the loop about an
axis which is perpendicular to the plane of the loop;
and
and c are the free space values of the wave
` 5 length and velocity, respectively, of the light
applied to the loop.
The intensity of the optical output signal (IT is a
function of the Sagnac phase difference (OR) between the
waves Wl, W2, and is defined by the following equation:
IT = Il + I2 2 cos(Q~R) (2)
where Il and I2 are the individual intensities of the
waves Wl, W2, respectively.
From equations (l) and (2) it may be seen that the
intensity of optical output signal is a function of the
rotation rate (Q). Thus, an indication of such rotation
rate may be obtained by measuring the intensity of the
optical output signal, utilizing the detector 30.
Figure 6 shows a curve 80, which illustrates this
relationship between the intensity of the optical output
signal (IT) and the Sagnac phase difference (OR) between
the counter-propagating waves Wl, W2. The curve 80 has
the shape of a cosine curve, and the intensity of the
optical output signal is at a maximum when the Sagnac
phase difference is zero. where the phase difference
between the counter-propagating waves Wl, W2 is caused
entirely by rotation of the loop 14, the curve 80 will
vary symmetrically about the vertical axis. However, as
discussed in U.S. Patent No. 4,529,312 issued July 16,
1985 entitled "Fiber-Optic Rotation Sensor Utilizing
Unpolarized Light", with polarized light an additional,
non-reciprocal, phase difference between the counter-
propagating waxes Wl, W2 may be caused by the residual
birefringence of the optical fiber 12.
2~
-20-
This additional non-reciprocal phase
difference will not occur if completely unpolarized light
- is used.
Birefringence induced phase differences occur because
light traveling in each of the two polarization modes of
the single mode fiber 12 travels at a different
velocity. Birefringence will cause coupling of part of
the light traveling in one polarization mode into the
other mode. This creates a non-rotationally induced phase
difference between the waves Wl, W2, which causes the
waves Wl, W2 to interfere in a manner that distorts or
shifts the curve 80 of Figure 6. Such a shift is
illustrated by the curve 82, shown in phantom lines in
Figure 6.
Such birefringence induced, non-reciprocal phase
difference is indistinguishable from a rotationally
induced Sagnac phase difference, and is dependent on
environmental factors which vary fiber birefringence, such
as temperature and pressure. Thus, fiber b;refringence-is
the cause of a major source of error in fiber optic
rotation sensors.
O eration With the Polarizer 32
P
The problem of non-reciprocal operation due to fiber
birefringence is solved in the rotation sensor of the
present invention by means of the polarizer 32 (Figure 1)
which, as discussed above, permits utilization of only a
single polarization mode. When the polarizer 32 is
introduced into the system at the point designated by the
reference numeral 84 in Figure 5, light passing through
the polarizer 32 propagates into the loop 14 in one
selected polarization mode. Further, when the counter-
propagating waves are recombined to form the optical
output signal, any light that is not of the same
polarization as the light applied to the loop is prevented
from reaching the photodetector 30, since the optical
~3~
output signal passes through the polarizer 32. Thus, the
optical output signal, as it travels from port A of
coupler 34 to port B of coupler 26, will have precisely
the same polarization as the light applied to the loop.
Therefore, by passing the input light and optical
output signal through the same polarizer 32, only a single
optical path is utilized, thereby eliminating the problem
of birefringence induced phase difference caused by the
different velocities of propagation in the two possible
0 polarization modes. That is, by filtering out all light
which is transferred from the selected mode to the
unselected mode by the birefringence in the fiber, it is
possible to eliminate all light waves in the unselected
mode which might gain or lose phase relative to the
selected mode because of the different velocity of
propagation. Further, it should be noted that the
polarization controllers 24, 36 (Figure l) may be used to
adjust the polarization of the applied light, and optical
output signal, respectively, to reduce optical power loss
at the polarizer 32, and thus, maximize the signai
intensity at the detector 30.
Operation With the Phase Modulator 38
Referring again to Figure 6, it will be seen that,
because the curve 80 is a cosine function, the intensity
of the optical output signal is nonlinear for small Sagnac
phase differences (OR) between the waves Wl, W2.
Further, the optical output signal intensity is relatively
insensitive to changes in phase difference, for small
values of OR Such nonlinearity and insensitivity makes
it difficult to transform.the optical intensity (IT)
measured by detector 30 into a signal indicative of the
rate of rotation of the loop 14 (via equation 1).
Further, although birefringence induced phase
differences between the waves Wl, W2 are eliminated, as
discussed above by use of the polarizer 32, nevertheless
cross coupling between polarization modes caused by fiber
~3~2~%
-22-
birefringence occurs. This cross coupling reduces the
optical intensity of the optical output signal since the
cross coupled light is prevented from reaching the
photodetector 30 on the polarizer 32. Thus, changes in
fiber bireringence cause the amplitude of the curve 80 of
Figure 6 to vary, for example, as illustrated by the curve
84. It will be understood that curves 80, 82, 84 of
Figure 6 are not drawn to scale.
The foregoing problems are solved by means of a
synchronous detection system utilizing the phase modulator
38, signal generator 40 and lock-in amplifier 46 shown in
Figure 1.
Referring to Figure 7, the phase modulator 38
modulates the phase of each of the propagating waves Wl,
W2 at the frequency of the signal generator 40. However,
as may be seen from Figure 1, the phase modulator 38 is
located at one end of the loop 14. Thus, the modulation
of the wave Wl is not necessarily in phase with the
modulation of the wave W2. Indeed, it is preferable for
proper operation of this synchronous detection system thaw
the modulation of the waves Wl, W2 be 180 out of phase.
Referring to Figure 7, it is preferable that the
modulation of the wave Wl, represented by the sinusoidal
curve 90, be 180 out of phase with the modulation of the
wave W2, represented by the curve 92. Use of a modulation
frequency which provides such 180 phase difference
between the modulation of the wave Wl relative to that of
W2 is particularly advantageous in that it eliminates
modulator induced amplitude modulation in the optical
output signal measured by the detector 30. This
modulation frequency (fm) may be calculated using the
following equation:
fm ~~ (3)
so
-23-
where:
L is the differential fiber length between the
coupler 34 and the modulator 38 for the counter-
propagating waves Wl, W2, i.e., the distance, measured
along the fiber, between the modulator 38 and a
symmetrical point on the other side of the loop 14;
neq is the equivalent refractive index for the
single mode fiber 12; and
c is the free space velocity of the light applied
to the loop 14.
At this modulation frequency (fm) which is called the
"proper" frequency, the phase difference l between
the counter-propagating waves Wl, W2, stemming from phase
modulation of these waves in accordance with the curves 90
and 92, is illustrated by the sinusoidal curve 94 in
Figure 7. The curve 94 is obtained by subtracting the
curve 92 from the curve 90 to obtain the phase difference.
between W1 and W2. This modulation of the phase
difference between the waves Wl, W2 will also modulate the
intensity (IT) of the optical output signal in accordance
with the curve 80 of Figure 6 just as a Sagnac phase shift
would, since such phase modulation l is
indistinguishable from rotationally induced Sagnac phase
differences OR .
The foregoing may be understood more fully through
reference to Figures 8 and 9 which graphically illustrate
the effect of (a) the phase modulation l defined by
the curve 94 of Figure 7, and (b) the .Sagnac phase
difference ~R~ upon the intensity (IT) of the optical
output signal. Before proceeding with a discussion of
Figures 8 and 9, it should first be understood that the
intensity (IT) of the modulated optical output signal is a
function of the total phase difference between the waves
Wl, W2. Such total phase difference is comprised of both
the rotationally induced Sagnac phase difference OR and
the time varying modulation induced phase difference l
~3~
-24-
The total phase difference Q~ between the waves Wl, W2
may be expressed as follows:
OR l ( )
Accordingly, since the effects of the modulation induced
phase difference as well as the rotationally induced
phase difference OR will be considered in reference to
Figures 8 and 9, the horizontal axis for the curve 80 has
been relabeled as A to indicate that the total phase
difference is being considered, rather than only the
rotationally induced phase difference, as in Figure 6.
Referring now to Figure 8, the effect of the phase
modulation Awl (curve 94) upon the intensity IT of the
optical output signal will be discussed. Curve 80
represents the relationship between the intensity of the
optical output signal resulting from two interfering
coherent waves to the phase difference between the
waves. When the relative phase angle between them is
zero, as illustrated at 93, the resultant intensity of the
combined wave is a maximum, as illustrated at 95. When
the relative phase between the waves Wl and W2 is non-
zero, the combined optical signal will have a lower
intensity depending upon the magnitude of the phase
difference I. The intensity continues to decrease with
increasing until the relative phase difference is
either plus or minus 180, as illustrated at 97 and 99
respectively. At a phase difference of plus or minus
180, the two counter-propagating waves completely
destructively interfere, and the resultant intensity is
zero as illustrated at 97 and 99.
In Figure 8, it is assumed that the loop 14 is at
rest, and thus, the optical signal is not affected by the
Sagnac effect. Specifically, it may be seen that the
modulation induced phase difference curve 94 causes the
optical output signal to vary as illustrated by the curve
96. The curve 96 is obtained by translating the points on
~3~S~:
-25-
the curve 94, representing the instantaneous phase
difference Al between Wl and W2 onto the curve 80
representing the resultant optical intensity for a phase
difference of that magnitude. When all the points on the
S curve 94 are translated onto the curve 80, and the
corresponding intensities are plotted, the curve 96
results. The translation of the curve 94 through the
curve B0 is symmetrical about the vertical axis of the
curve 80, so that the optical intensity measured by the
detector 30 varies periodically at a frequency equal to
the second harmonic of the modulating frequency, as shown
by the curve 96.
Since, as discussed above, the lock-in amplifier 46 is
tuned by the reference signal at the modulation frequency
fm from the signal generator 40 (Figure l), the lock-in
amplifier synchronously detects only the detector output
signal at the modulation frequency fm~ i.e., first
harmonic, of the modulator 38. But since the detector
output signal is at the second harmonic of the modulation
frequency, as shown by the curve 96, the output signal
from the amplifier 46 will be zero and the display 47 will
indicate a rotation rate of zero.
It should be noted that even if birefringence induced
amplitude fluctuations occur in the optical output signal,
as discussed in reference to the curve 84 of Figure 6, the
curve 96 of Figure 8 will remain at a second harmonic
frequencyO Thus, such birefringence induced amplitude
fluctuations will not affect the amplifier 46 output
signal. The detection system thus far described therefore
provides a substantially more stable operating point that
is insensitive to changes in birefringence. -
When the loop 14 is rotated, the counter-propagating
waves Wl, W2 are shifted in phase, as discussed above, in
accordance with the Sagnac effect. The Sagnac phase shift
provides a constant phase difference OR for a constant
rotational velocity. This Sagnac phase shift adds to the
2q~ f
6-
phase difference l created by the modulator 38, so that
the entire curve 94 is translated in phase from the
position shown in Figure 8, by an amount equal to ~R~ as
shown in Figure 9. This causes the optical output signal
to vary nonsymmetrically along the curve 80 between the
points 99 and 101. This causes an optical output signal
as illustrated by curve 96.
The points on the curve 96 are derived as follows.
The combined phase difference, illustrated at 103 on curve
94, translates through the point 101 on the curve 80 to
the point 105 on the curve 96. The point 107 on the curve
94 translates through the point 109 on the curve 80 to a
point 111 on the curve 96. Likewise, the point 113
translates through the point 99 to the point 115, and the
point 117 translates through the point 109 to the point
119. Finally, the point 121 translates through the point
101 to the point 123.
The optical output signal 96 has a first harmonic
component as illustrated in phantom lines of the
sinusoidal curve 98. The peak amplitude of the first
harmonic component 98 need not, however, exactly match the
amplitude of the optical output signal at point 115
although it might in some cases.
It will be seen subsequently that the RMS value of
this sinusoidal curve 98 is proportional to the sine of
the rotationally induced Sagnac phase difference OR.
Since the amplifier 46 synchronously detects signals
having the fundamental frequency of the modu-lator 38, the
amplifier 46 will output a signal that is proportional to
the RMS value of the curve 98. This signal can be used to
indicate the rotation rate of the loop.
The drawings of Figure 9 illustrate-the intensity
waveform of the optical output signal for one direction of
rotation (e.g., clockwise) of the loop 14. However, it
will be understood that, if the loop 14 is rotated in the
opposite direction (e.g., counter-clockwise) at an equal
~3~
-27-
velocity, the intensity waveform 96 of the optical output
signal will be exactly the same as illustrated in Figure
9, except that it will be translated so that the curve 98
is shifted 180 from the position shown in Figure 9.
The lock-in amplifier 46 detects this 180 phase
difference for the curve 98, by comparing the phase of the
first harmonic 98 with the phase of the reference signal
from the signal generator 40, to determine whether the
rotation of the loop is clockwise or counter-clockwise.
Depending on the direction of rotation, the amplifier 46
outputs either a positive or negative signal to the
display 47. however, regardless of the direction of
rotation, the magnitude of the signal is the same for
equal rates of rotation of the loop l
the waveform of the amplifier output signal is shown
in Figure 10 as the curve 100. It will be seen that this
curve 100 is sinusoidal and varies positively or
negatively from the zero rotation rate output voltage,
illustrated at 125, depending on whether the rotation of
the loop 14 is clockwise or counter-clockwise. Further,
the curve 100 has a substantially linear portion 102 which
varies symmetrically about the origin and provides a
relatively wide operating range for measuring rotation.
Moreover, the slope of the curve 100 provides excellent
sensitivity through its linear operating range 102 to
small Sagnac phase shifts.
Thus, by utilizing the synchronous detection system,
the above-described problems of nonlinearity,
insensitivity to small Sagnac phase shifts, and
birefringence induced amplitude fluctuations are reduced
or eliminated for rotation rates of the loop 14 which keep
the points 99 and 101 in Figure 9 somewhere on the curve
80 between the points 97 and 95.
A further advantage of the detection system thus far
disclosed relates to the fact that state of the art phase
modulators, such as the modulator 38, induce amplitude
~L~3~2~
-2~-
modulation in the optical output signal, either directly
or indirectly, through polarization modulation, i.e., the
phase modulator also shifts some of the light passing
therethrough to the unselected polarization mode.
However, it will be recalled from the discussion in
reference to Equation (3) that, by operating at a specific
or "proper" frequency at which the phase difference
between the modulation of the waves Wl and W2 is 180, the
odd harmonic frequency components of this amplitude
modulation, that are induced in each of the counter-
propagating waves Wl, W2 by the modulator 3~, cancel each
other when the waves are superposed to form the optical
output signal. Thus, since the above-described detection
system detects only an odd harmonic, i.e., the fundamental
frequency, of the optical output signal, the effects of
the undesired amplitude modulation are eliminated.
Therefore, by operating at the specific frequency defined
by Equation (3), and by detecting only an odd harmonic of
the optical output signal, the rotation sensor of the
present invention may operate independently of modulator
induced amplitude and polarization modulation.
A further benefit of operating at the proper frequency
is that even harmonics of the phase modulation, induced by
the modulator 38 in each of the counter-propagating phase
Wl, W2, cancel when these waves are superposed to form the
optical output signal. Since these even harmonics may, by
superposition, produce spurious odd harmonics in the
optical signal which might otherwise be detected by the
detection system, their elimination improves the accuracy
of rotation sensing.
In addition to operating the phase modulator 38 at the
frequency defined by Equation (3), it is aiso preferable
to adjust the magnitude of the phase modulation so that
the amplitude of the detected first harmonic of the
optical output signal intensity is maximized, since this
provides improved rotation sensing sensitivity and
~3~
-29-
accuracy. It has been found that the first harmonic of
the optical output signal intensity is at the maximum, for
a given rotation rate, when the amplitude of the modulator
induced phase difference Al between the waves Wl, W2,
indicated by the dimension labeled Z in Figures 7, 8, and
9, is 1.84 radians. This may be understood more fully
through reference to the following equation for the total
intensity (IT) of two superposed waves having individual
intensities of Il and I2, respectively, with a phase
difference therebetween.
IT = Il + I2 + 2 ~IlI2 co ( I)
where:
R + Al (6)
and
l = Z Sin(2~fmt).
Thus,
OR + Z Sin (2~fmt~ (8)
The Fourier expansion of cosine (~) is:
( OR) {J9(Z) + 2~n=lJ2n(æ)cos[2~(2nf t)]}
( OR) ~2~n=l J2n_l(Z)sin[2~(2n-l~f t]}
where Jn(Z) is the nth Bessel function of the variable z,
and z is the peak amplitude of the modulator induced phase
difference between the waves Wl, W2.
3~ ~J~
-30-
Therefore, detecting only the first harmonic of IT
yields:
IT(l) = 4./IlI2 Jl(z)sin(~R) sin(27~fmt) (10)
Thus, the amplitude of the first harmonic of the
optical output signal intensity is dependent upon the
value of the first Bessel function Jl(Z)~ Since Jl(Z) is
a maximum when z equals lo84 radians, the amplitude of the
phase modulation should preferably be selected so that the
magnitude (z) of the modulator induced phase
difference Q~l between the waves Wl, W2 is 1.84 radians.
Reducing the Effects of Backscatter
As is well known, present state-of-the-art optical
fibers are not optically perfect, but have imperfections
such as density fluctuations in the basic material of the
fiber. These imperfections cause variations in the
refractive index of the fiber which causes scattering of
small amounts of light. This phenomena is commonly
referred to as Rayleigh scattering. Although such
scattering causes some light to be lost from the fiber,
the amount of such loss is relatively small, and
therefore, is not a major concern.
The principal problem associated with Rayleigh
scattering relates not to scattered light which is lost,
but rather to light which is reflected so that it
propagatés through the fiber in a direction opposite to
its original direction of propagation. This is commonly
referred to as "backscattered" light. Since such
backscattered light is coherent with the light comprising
the counter-propagating waves Wl, W2, it can
constructively or destructively interfere with such
propagating waves, and thereby cause variation in the
intensity of the optical output signal, as measured by the
detector 30.
~3~
The portion of backscattered light from one wave which
will be coherent with the counter-propagating wave is that
which is scattered within a coherence length of the center
of the loop 14. Thus, by reducing the coherence length of
the source, the coherence between the backscattered light
and the counter-propagating waves is reduced. The
remaining portion of the backscattered light will be
incoherent with the counter-propagating wave, and thus,
the interference therebetween will vary randomly so that
0 it is averaged. Therefore, this incoherent portion of the
backscattered light will be of substantially constant
intensity, and consequently, it will not cause significant
variations in the intensity of the optical output
signal.
Accordingly, in the present invention, the effects of
backscatter are reduced by utilizing as the light source
10, a laser having a relatively short coherence length,
for example, one meter or less. By way of specific
example, the light source 10 may comprise the model GO-DIP
laser diode, commercially available from General Optronics
Corp., as mentioned above.
An alternative method of prohibiting destructive or
constructive interference between the backscattered waves
and the propagating waves involves the inclusion of an
additional phase modulator in the system at the center of
the fiber loop 14. This phase modulator is not
synchronized with the modulator 38.
The propagating waves will pass through this
additional phase modulator one time only, on their travel
around the loop. For backscatter which occurs from a
propagating wave before the wave reaches the additional
modulator, the backscatter will not be phase modulated by
this additional modulator, since neither its source
propagating wave nor the backscatter itself has passed
through the additional modulator.
~3~2~;~
-32-
On the other hand, for backscatter which occurs from a
propagating wave after the wave passes through this
additional phase modulator, the backscatter will be
effectively twice phase modulated, once when the
5propagating wave passed through the additional phase
modulator, and once when the backscatter passed through
the additional modulator.
Thus, if the additional phase modulator introduces a
phase shift of I, the backscattered wave originating at
10any point except at the center of the loop 14 will have a
phase shift of either zero, or (t), either of which is
time varying with respect to the I phase shift for the
propagating wave. This time varying interference will
average out over time, effectively eliminating the effects
15of the backscatter.
In yet another alternative method of prohibiting
destructive or constructive interference from backscatter,
the additional phase modulator, not synchronized with the
modulator 38, may be introduced at the output of the light
20source 10.
In this case, backscatter occurring at any point other
than the center of the loop 14 will have a different
optical path length from the light source 10 to the
detector 30 than does the propagating wave from which the
25backscatter originated.
Thus, the propagating wave will traverse the loop 14
one time, while the backscattered wave and the propagating
wave from which it originated will have traversed a
portion of the loop 14 twice. If this portion is not one-
30half of the loop, the path lengths differ.
Because the path lengths differ, a propagating wave
which reaches the detector 30 will have bee-n generated at
the source 10 at a different time than a backscattered
wave which reaches the detector 30 simultaneously
35The phase shift introduced by the additional phase
modulator at the source 10 introduced a phase shift I
~3~L2~
-33
relative to the propagating wave, but a phase shift of
~(t+K) to the backscattered wave, where K is the time
difference between the passage of the waves through the
modulator. Since ~(t~K) is time varying with respect to
I, the backscattered interference will average out over
time, effectively eliminating the effects of the
backscatter.
extended D~namic_Rar~e Detection System Usin~_A Gated Wave
The detection system described above with reference to
Figures 1-10 is a very effective rotation sensing system
within a certain range of rotational velocities for the
loop 14. However, the dynamic range is limited by certain
phenomena. Referring to Figure 9, it can be seen that the
curve 80 is periodic. Therefore, if a large rotation rate
causes a large enough AIR to move the curve 94 past
either the point 97 or the point 95, then the function 96
could repeat itself for a second, higher rotation rate.
This second rotation rate would be substantially greater
than the rotation rate which caused the Sagnac phase
shift ~bR depicted in Figure 9, but would be
indistinguishable from the lower velocity using the output
optical signal 96. That is, if the OR from some larger
rotational velocity were sufficiently large to move the
curve 9~ so as to operate between two new points 99' and
101' on the second lobe of the curve 80, then the output
optical signal 96 would be indistinguishable in such a
case from the case shown where the curve 94 operates
between the points 99 and 101.
The present invention comprises a novel method, and
associated apparatus, for extending the range of detection
of optical fiber gyroscopes. In performing this method,
the optical fiber gyroscope described above-is modified to
include modulation of the counter-propagating light waves
at an additional frequency level (fm) which is much lower
than the "proper" frequency or bias frequency (fb)
described above by Equation 3.
~3~
-34-
With the reciprocal phase modulator located
asymmetrically in the sensing loop, the application of a
signal to that modulator can produce a differential shift
Q~c between the phases of the two counter-propagating
waves in the loop. This a is time varying at the
modulation frequency lo and contains no DC term because
the phase shift produced by the modulator in one half of
its modulation cycle is cancelled by that produced in the
next half cycle.
In contrast, the differential phase shift OR which is
caused by rotation can be a DC quantity and, thus, a
cannot be used to directly null out OR. however, if the
gyroscope is gated off during every other half cycle of
the modulation waveform, the average a produced in the
remaining half cycles can be used to directly null out the
rotation produced signal in those same half cycles. By
monitoring the amplitude of the signal which produces the
a during the gated-on half cycles, it is possible to
determine the rotation rate of the sensor.
With a bias frequency fb for biasing the operating
point, as described above, by imposing an additional
modulation frequency fm which is much lower than the bias
phase modulation frequency, and then by gating the gyro
off during every other half cycle of the fm waveform, a
phase difference modulation waveform is produced whose
time average value has a net DC level. By adjusting the
amplitude of the second phase modulation at frequency fm~
this time average DC value of the phase difference
modulation may be adjusted to effectively null out the OR
produced in those same half cycles. The technique
described above functions to effectively null out the
effects of rotation on the output signal since no rotation
is identified during the period of time in which the gated
signal is off, and the effects of OR are cancelled by the
phase modulation at frequency fm when the gated signal is
on. Since the amount of rotation is proportional to the
~3~%
-35-
amplitude of phase difference modulation at fm which was
necessary in order to null out the influence of ~R~ the
rotation rate may be determined by monitoring the
amplitude of the second modulation signal. This method
will be described in more detail below, in conjunction
with a description of the apparatus utilized in practicing
the method.
Referring to Figure 11, one preferred embodiment of a
device is seen which, when used in conjunction with the
method described herein, provides a significant increase
in the range of detection, as well as an improvement in
the reliability of the results provided by such
detection. The detection system of Figure 11 embodies
many of the components of the systern illustrated in Figure
1. Thus, for purposes of simplicity, those components of
Figures 1 and 11 which have the same structure and
function have been assigned corresponding numbers.
In the circuit of Figure 11, the optical output signal
from detector 30 is transmitted via line 48 through an
amplifier 300, where its intensity is magnified
sufficiently to be useable in the electronic circuitry.
From amplifier 300, the output signal passes on line 302
to a conventional electronic gate 304. Operation of gate
304 is controlled by a gating signal received through line
306 from an ac signal generator 308. The phase of the
signal on line 306 may be adjusted by use of conventional
phase delaying devices in line 306.
Signal generator 308 produces a second phase
modulation signal at a frequency fm which may be
arbitrarily selected, but which should be much lower than
that of the bias phase modulation which is typically set,
as described previously, at the "proper" frequency, fp.
The signal from gate 304 is synchronously gated onto
line 310 at the second phase modulation frequency fm
produced in signal generator 308. The signal is then
transmitted into a band pass filter 312 which passes onto
~3~S~
-36-
line 314 only the fb frequency component of the signal
received from line 310. In the absence of any other
signals to alter its magnitude, the signal at frequency fb
on line 314 is representative of the amount of rotation
experienced by loop 14.
As described below, the signal on line 314 is utilized
in conjunction with the lock-in amplifier 46 to produce a
feedback signal which controls the amplitude of the second
phase modulation at frequency fm. With proper amplitude
adjustment of this second phase difference modulation, a
signal may be generated which causes the phase modulator
38 to influence the counter-propagating waves in the loop
such that, on a time averaged basis, the signal at
frequency fb on line 314 is driven towards zero,
regardless of the loop rotation rate.
In order to produce the feedback signal described
above, the signal on line 314 is transmitted to lock-in
amplifier 46. In addition, the lock-in amplifier receives
a reference signal from line 316 which corresponds to the
bias modulation frequency fb produced by ac signal
generator 40. Generally, this frequency fb corresponds to
the "proper" frequency as calculated previously using
equation (3).
In response to the signals received from lines 314 and
316, lock-in amplifier 46 generates an "error signal"
which is proportional to the amplitude of the input signal
from line 314 and which matches the frequency of the
reference signal from line 316. This error signal will
lie somewhere on the curve 100 of Figure lO. In this
particular case, the error signal will be some DC level on
the curve 100 for a fixed rotation rate resulting in a
fixed amplitude of the first harmonic component on the
input line 48. If the amplitude of the first harmonic
component changes, the DC level of the error signal will
change as the operating point shifts along the curve lO0.
~3~
-37-
s explained previously, without the second phase
modulation at frequency fm, the curve 100 is periodic
because the curve 80 in Figure 9 is periodic. Therefore,
the magnitude of the fb frequency component of the optical
output signal 96 will vary periodically as increasing
Sagnac phase shifts push the total phase shift curve 94
out into other lobes of the curve 80. That is, the point
134 (Figure 10) on the curve 100 represents a situation
where the Sagnac phase shift has pushed the curve 94 out
far enough so that maxima and minima of the total
resultant phase shift curve translate through
symmetrically balanced points on the second lobe of the
curve 80. The resultant output waveform 96 would look
like the output optical signal 96 depicted in Figure 8 for
the zero rotation rate case and would have no first
harmonic component. Because the waveform 96 has no first
harmonic component in this situation, the output of the
lock-in amplifier would be zero despite the fact that the
rotation rate is non-zero.
The detection system of the present invention solves
this problem through use of the feed back error signal, by
adjusting the amplitude of the second phase modulation
signal at frequency fm in response to changes in the first
harmonic signal on line 314. The adjusted second phase
modulation signal is then utilized, as described below, to
adjust the phase modulation of the counter propagating
waves in the loop so that the signal at frequency fb on
line 314 is effectively cancelled. As a result, even
though the rotation is such that the Sagnac phase shift is
pushed to the point 134 on curve 100, Figure 10, the
amplitude of the second phase modulation signal provides a
ready indication of the actual rotation rate at high
velocities which, without such feedback, would place the
curve 94 beyond the point represented by 134 of Figure 10.
The function of adjusting the amplitude of the second
phase modulation signal in response to the feedback error
~L~23~;25~:
-38-
signal is performed by the error correction modulator
130. To accomplish this, the error correction modulator
130 receives an error signal from lock-in amplifier 46 via
line 318 and also receives the second modulation signal
from signal generator 308 on line 320. Preferably, the
second modulation signal defines a sinusoidal waveform.
Upon receiving a non-zero error signal on line 318,
the error correction modulator 130 increases or decreases
the amplitude of the second phase modulation signal in
response to the magnitude and sign of the error signal in
order to reduce the magnitude of the error signal on the
line 318 to zero, or to within a predetermined range of
zero. When the predetermined level for the error signal
on line 318 is reached, the modulator 130 maintains the
amplitude of the second phase modulation signal until the
error signal again changes.
Upon detecting a change in the error signal, the
modulator 130 again changes the amplitude of the second
phase modulation signal until the error signal on the line
318 is again reduced to zero or to within a predetermined
range of zero. The adjusted second phase modulation
signal is transmitted from the error correction modulator
130 onto line 322. The feedback approach described herein
can also be applied to other types of gyroscopes, such as
ones which are made of high birefringent fiber.
The adjusted second phase modulation signal on line
322 is combined with the bias modulation signal from
signal generator 40 on line 324. This combined signal
from line 324 is applied to phase modulator 38 so as to
influence the counter propagating waves and, consequently,
the output signal from detector 30, in accordance with the
method described above. Thus t the second phase modulation
signal functions to bias the phase difference of the
counter-propagating light waves to substantially null the
phase shift produced in the counter-propagating light wave
phase difference by the rotation rate. In this context,
~3~2
39-
the bias applied by the second phase modulation signal
does not merely serve to compensate for the component of
the output signal at frequency fb caused by the rotation
rate, but it effectively nulls the phase difference signal
produced by that rotation rate, thereby removing that
related component from the output signal.
The rotation velocity may be determined by use of
output display 208 which is connected through a band pass
filter 326 to line 324. Specifically, the modulation
signal from line 324 is connected by line 330 to filter
326 which allows only the signal at the second modulation
frequency fm to pass. The signal from filter 326 passes
on line 332 to the output display 208. The signal on
display 208 corresponds to the amplitude of the second
modulation signal at frequency fm and, thus, may be used
to determine the rotation velocity. Display 208 and
related circuitry for determining rotation velocity will
be described in detail hereafter.
y reverence to Figure 12, it is possible to
graphically describe the resulting relative phase shift
experienced between the counter propagating waves as a
result of loop rotation and phase modulation in the
apparatus illustrated in Figure 11. In Figure 12 it can
be seen that the optical output signal (not shown) taken
at the photodetector 30 comprises the resultant or total
phase shift curve 350 which represents the sum of the
Sagnac phase shift OR (represented by the constant bias
352 for constant rotational velocity) and the sinusoidally
time varying, second phase difference modulation signal
Arm (cos ~mt) represented by the curve 354, and the
sinusoidally time varying, bias phase difference
modulation difference signal ~b (cos ~bt). The resultant
phase shift is thus defined as:
b cos ~bt) + (em cos ~mt) + OR (11)
~3~
--40--
The time average value of can be adjusted to a
value of approximately zero by gating off a portion of the
signal. Thus, as illustrated in Figure 12, every other
half cycle of the second phase difference modulation at
frequency fm 354 is gated off. 8y adjusting the amplitude
of the second phase difference modulation 354 in this
situation, the portion of the bias modulation signal 350
which is gated on can be positioned about vertical axis
355.
In the circuit illustrated in Figure 11, gate 304 is
turned on and off in synchronism with the second phase
modulation signal by use of a gating signal from signal
generator 308. Thus, with the gating signal on line 306
synchronized to switch gate 304 at each half cycle of the
~5 second phase modulation signal frequency fm~ the waveform
of Figure 12 may be produced. It will be appreciated that
during the time that the signals are gated off, as
indicated in Figure 12, the value of zero will be present
on the output of detector 30 (Figure 11).
The output signal at frequency fb which is produced as
a result of the conditions described above is illustrated
at 360 of Figure 13. It is noted that line 360 is, for
purposes of illustration, not drawn to scale with respect
to the second phase modulation waveform 354. Thus, it can
be seen that by adjusting the amplitude of the second
phase modulation signal 354 until the time average value
of the gated portion of the output signal at the frequency
fb equals zero, it is possible to determine the rotational
velocity of the loop. Specifically, the rotation velocity
is determined by observing the amplitude of the second
phase modulation signal which caused the zero error
signal.
In the absence of the modulation signal, the detector
output amplitude Ib at the bias modulation frequency fb
may be described mathematically as
3L23~52
-41-
Ib = CPOJ~ b)sin~ (12)
Where C is a constant;
P0 is the optical power incident on the detector;
~b is the amplitude of the phase difference
modulation between the counter propagating waves;
Jl is the first order bessel function of the first
kind; and
is the phase difference between the counter
propagating waves in the sensing coil.
When the second phase modulation signal is
additionally applied at a frequency fm much lower than the
bias modulation frequency fb, the waveform of the phase
difference modulation in the presence of rotation induced
non-reciprocal phase shift ~R~ is as illustrated in
Figure 12. When the signal from the photodetector 30 is
switched off during fifty percent of each cycle of phase
modulation at frequency fmr the demodulated output power
at the bias modulation frequency fb is illustrated in
Figure 13. Under the condition that the lock-in amplifier
integrates the signal over many cycles of phase modulation
at frequency fmt the demodulated output power can be made
zero by adjusting the amplitude of the phase difference
mOdulation em- This means that the rotation induced
non-reciprocal phase shift can be canceled on the time
average by the phase modulation with gating. The
demodulated output power is illustrated at 360 in Figure
13~ The time average of this output signal 360 is
30described as:
. .
T/4
b ( / ) 0 1( ~b) J T/ 4 ( R em Sum ) (13)
~3~2,
-42-
where T = l/fm;
em = 2~fm; and
Q~m is the amplitude of the phase difference modulation at
frequency fm
The relationship between the Sagnac phase shift air
and the magnitude Q~m of the second modulation signal at
the frequency fm to null the demodulated power to zero can
be obtained from the relation:
tanQ~ = 4 1 1 J (Q~ ) (14)
Where: Jn is the n-th order Bessell function.
The relationship of the amplitude of the second phase
difference modulation to the value of Q~R, described by
equation 14 is graphically illustrated in Figure 14. The
curve 370 of Figure 14 represents the response of the
sensor to rotation when the gyro is operated in an
electronically closed loop configuration. Curve 370
graphically illustrates the transfer function or scale
factor which describes the amplitude of the second phase
difference modulation Q~m which is necessary to
substantially null out the Sagnac phase shift (Q~R) in the
gated apparatus illustrated in Figure 11.
It will be seen that the scale factor of Figure 14 has
a monotonic behavior which provides for the dynamic range
for gyroscope operation which is limited only by that of
the phase modulator used. The small deviation of the
scale factor curve 370 from complete linearity results
from the fact that the net non-reciprocal phase shift is
averaged to zero using a time varying phase shift instead
of a DC phase shift. Thus, the invention provides a means
to eliminate the ambiguity in the detector output signal
for higher rotation rates where prior art sensors would
~3~S;~
not know which of several possible rotation rates was
causing the detector output of that particular
characteristic.
Because the frequency of the second phase modulation
signal at frequency fm is arbitrary, that frequency and
phase needs to have no fixed relationship wlth the bias
phase modulation operated at the Proper frequency. As a
result, less stability is required of the components which
generate and control the two excitation signals. In
addition, this lack of frequency and phase relationship
between two modulations permits the electrical combining
of the two excitation signals and their application to a
single phase modulator without compromising the rotation
sensors sensitivity.
Several of the other components of the apparatus of
Figure 11 are described in more detail below.
Figure 15 shows one embodiment of the error correction
modulator 130. In this embodiment, the error signal on
the line 318 is coupled to the inverting input of an
operational amplifier connected as an integrator. The
exact structural details of practical integrators are well
known to those skilled in the art and no further
discussion of those details will be given here.
As is well known in the art of operational amplifiers,
the negative feedback voltage developed across the
capacitor tends to keep the point 170 at a virtual
ground. That is, the voltage at the point 170 is held at
or near zero volts by the negative feedback.- However, no
current flows to ground through this virtual short. The
input current iin to the operational amplifier 169 through
the output impedance of the lock-in amplifier 46,
represented by the impedance Rol72, is equal to the output
error voltage of the lock-in amplifier 46 divided by its
output impedance Row since the impedance to ground from
the point 170 is zero. But since no current flows to
ground from the node 170, the input current iin flows
~23~2S~
--44--
through the capacitor 168 and an output voltaye V0
relative to ground, builds up on the line 174 as a
function of time. The expression for the output voltage
V0 as a function of time is:
V0 C riindt (15
where C is the value of the capacitor 168.
Referring to Figure 16, the response characteristics
for the operational amplifier integrator 169 as shown.
Figure 16(A) shows a hypothetical error signal on the line
318. The output voltage V0 of the integrator on the line
174 is plotted in Figure 16(B).
It can be seen from Figure 16(B) that for zero error
signals, the output voltage curve has zero slope and for
increasing magnitudes of non-zero error signals, the
magnitude of the slope of the output voltage curve for V0
increases. That is, the sign of the slope depends upon
whether the error signal is positive or negative, and the
steepness of the slope at any instant in time depends upon
the magnitude of the error signal at that instant in time.
As the error signal increases from the origin to the
point 176, the integrator output signal V0 increases to
the point 176B. Referring again to Figure 15, a
conventional balanced modulator such as an -MCL496L,
manufactured by Motorola, and associated circuits converts
this input voltage V0 on the line 174 to corresponding
changes in the envelope of the driving signal on the line
322. That is, the modulator 188 amplitude modulates the
fixed amplitude signal on the line 320 with the signal on
the line 174. This driving signal on the line 322 is then
transmitted to line 324 where it is combined with the bias
modulation signal from generator 40 and applied to the
phase modulator 38.
23~S~
--45--
As the amplitude of the driving signal on the line 322
increases the amplitude of the low frequency component in
the optical output signal begins to rise. When it rises
far enough, the time average value of the gated signal
tends to cancel the first harmonic component caused by the
rotation. This tends to reduce the error signal as shown
between the points 176 and 177 in Figure 16(A). The
decreasing error signal changes the steepness of the slope
of the integrator output voltage V0 in Figure 16(B) as
shown between the points 1 76B and 177B. At the point 177
in Figure 16(A), the magnitude of the driving signal is
just enough to cause cancellation of all of the rotation
caused first harmonic component in the optical output, and
thus the error signal will be zero. This is reflected by
a flat non-zero portion of the integrator output voltage
curve for V0 between the points 177B and 178B.
At the time 178 in this hypothetical situation, the
rotation rate of the loop 14 changes such that the error
signal changes sign and begins to increase in magnitude as
shown between 178 and 180 in Figure 16(A). This causes a
decrease in the output voltage V0 because the current iin
changes directions and the voltage on the capacitor 168
begins to change. This is shown between the points 178B
and 180B in Figure 16(B). The effect is to decrease the
amplitude of the driving signal which causes the error
signal to trend back toward zero as seen between the
points 180 and 182 in Figure 16(A).
At the time 182 in the hypothetical situation, the
rotation of the loop 14 again changes such that more first
harmonic component is generated by the Sagnac phase shift
so as to flatten the error signal curve as illustrated
between the points 182 and 184. This causes the
integrator output voltage to ramp downward at a constant
slope to decrease the amplitude of the second or low
frequency phase modulation signal between the points 182B
and 184B.
~3~
-46-
At the time 184~ the rotation rate of the loop again
changes but the error signal is still negative and non-
zero. The non-zero error signal causes the integrator
output voltage V0 to continue to decrease, thereby
changing the amplitude of the driving signal and causing
the error signal to move toward zero as shown between the
points 184 and 186.
Once the error signal reaches zero, the integrator
output voltage holds steady at whatever amplitude caused
the cancellation of all or substantially all of the Sagnac
generated first harmonic component. The situation at the
time 186 represents a non-zero constant rotation rate in
the loop 14 where the amplitude of the driving signal on
the line 140 has been adjusted to the proper level to just
cause cancellation of the Sagnac-generated first harmonic
component in the optical output signal.
Those skilled in the art will appreciate that if
rotation continues accelerating in one direction, the
output voltage V0 could rise above safe levels and cause
component failures in, for example, the amplitude
modulator 188 for the circuit of Figure 15. To prevent
such occurrences, voltage limiting devices should be
coupled to the integrator to limit the maximum positive
and negative voltage excursions of V0.
Referring to Figure 17, there is shown the preferred
embodiment for a portion of the error-correction modulator
circuit 130 to replace the integrator 190 in Figure 15.
In this embodiment, a differential amplifier 192 has its
inverting input coupled to the error signal on the line
318 and has its output is coupled to the amplitude
modulator 188 by the line 174.
The manner in which the system depicted in Figure 17
works is better understood with reference to Figure 18,
which depicts the overall rotation sensor in schematic
terms with the components in the sensor represented by a
three-port network 196 coupled to the differential
~l23~Z~2
-47-
amplifier 192. The optical portion and most of the
electronic components of the sensor have been represented
by the voltage divider impedance network 196 which has two
inputs coupled to either end of the two impedances Zl and
Z2 The midpoint of this divider is coupled to the
inverting input of the differential amplifier 192.
When a rotation is applied to the loop, a rotation
signal tSymbolic) will be applied to the second input of
the three port network 196 which results in an error
signal being applied to the line 318 coupled to the
inverting input of the differential amplifier 192. The
difference between this input error signal and the
reference signal on the line 133, which in this case is
ground potential, is amplified by the differential
amplifier 192 and the inverted, amplified difference
signal is applied to the output line 194. This output
line is also coupled to the first input of the network 196
such that negative feedback occurs through the impedance
Zl tending to cancel the voltage at the point 198 caused
by the rotation signal.
The signal on the line 194 then tends to minimize the
voltage swings at the point 198. The point 198 physically
represents the output of the lock-in amplifier 46 in
Figure 11. The impedances Zl and Z2 are virtual
impedances representing the overall transfer function and
loop gain of the optical and electronic portions of the
system.
The time response, phase margin, bandwidth and
sensitivity of the system are matters of design choice
depending upon the application and standard feedback
system analysis can be used to establish system
parameters.
The effect of the feedback through the impedance Zl is
to restrict the swings in the error signal on the output
line 318 of the lock-in amplifier to a small range
represented by the box 200 in Figure 10. The range is a
3~2
-48-
matter of design choice and depends upon the gain of the
differential amplifier 192. Higher gain results in a
smaller range of variation of the input signal, i.e., a
smaller box but less stability.
Any structure which reacts to non-zero error signals
so as to reduce the error signal to zero or substantially
zero by increasing or decreasing the magnitude of the
second phase modulation driving signal on the line 322
will suffice for purposes of the invention. For some
tO embodiments it will be desirable to maintain the level of
the second phase modulation driving signal at the
cancellation amplitude which reduces the error signal to
zero or near zero. The exact circuit used to accomplish
this function is not critical to the invention.
An alternative circuit which could be used for the
error correction modulator is as shown in Figure 19. In
this embodiment, the error signal on the line 318 is
coupled to the input of a comparison processor 201. The
comparison processor has a reference voltage applied to
its reference input 203 which is ground potential in this
case. The comparison processor compares the error signal
on the line 318 with the reference signal on the line 203
and generates one of three outputs. If the error signal
is positive and non-zero, the output line 205 is activated
as with a logic one level. If the error signal is
negative and non-zero, the line 207 is activated.
Finally, if the error signal is equal to the reference
signal, the = line 205 is activated.
An up-down counter 211 has its up input coupled to the
line 205 and begins counting up from zero when the line
205 is active. The binary count is continually changing
the digital pattern on the output bus 213 as the count
progresses where the data on the bus 213 at any moment
represents the binary representation of the count.
A digital to analog converter continuously or
periodically samples the value of the binary count on the
~.q~3~5~
--49--
bus 213 and converts the digital data to an analog output
signal on the line 174. This analog signal is used by the
conventional amplitude modulator 188 to amplitude modulate
the second phase modulation driving signal on the line 320
and apply it to the line 322.
The changing amplitude of the second phase modulation
driving signal is reflected in a changing error signal on
the line 318. That is the error signal will be trending
toward the reference signal voltage.
When the error signal reaches the reference voltage,
the comparator processor 201 activates the line 209 which
is coupled to the stop input of the counter 211, thereby
stopping the count. The D/A converter then holds the
amplitude level of the second harmonic driving signal
steady at the then existing level until the error signal
changes again.
When the error signal becomes negative and non-zero,
the process repeats itself but the counter 215 starts
counting down from zero or from the then existing positive
count. If the count was zero when the line 207 was
activated, a decoder 217 activates a change sign fire 219
which causes the D/A converter to change the sign of the
analog output voltage on the line 174. If the count was
not zero when the line 207 was activated, the decoder 217
does not activate the line 219, and the D/A converter
leaves the analog signal on the line 174 in the same sign
as when the line 205 was activated but begins to lower the
amplitude as the count decreases. This process continues
until the line 209 is activated.
Because the transfer function is non linear in some
regions, linear elements used to translate the a~nplitude
of the second harmonic driving signal to the magnitude of
the Sagnac phase shift introduce errors. A device may be
used at the output to store the transfer function or to
solve the transfer function for the rotation rate or
Sagnac phase shift given the cancellation amplitude of the
~L~3~
-50-
second harmonic driving signal. That is, it is
advantageous to convert from the amplitude of the driving
signal on the line 322 which cancels the first harmonic
component in the output due to the Sagnac phase shift to
the rotation rate or Sagnac phase shift itself. Such is
the purpose of the output display circuit 208 in Figure
11 .
Figure 20 shows the preferred circuit for the output
display 208. The first harmonic of the driving signal as
passed through band pass filter 326 onto line 322 is
coupled to the input of a lock-in amplifier 210. The
lock-in amplifier is tuned to the driving signal/ i.e., it
has as its reference signal the unmodulated signal on the
line 320 from the signal generator 308 in Figure 11. The
purpose of the lock-in amplifier 210 is to filter out all
noise on the line 332 which clutters the desired
waveform. This noise can result from noise on the power
lines, electromagnetic disturbances, cross talk with the
driving signal on the line 324 and other miscellaneous
Sources.
The output signal on the line 212 is proportional to
the amplitude of the filtered driving signal at the output
212 of the lock-in amplifier, and is coupled to an analog
to digital (A/D) converter 214 where it is converted to
digital data. This data is used by a microprocessor or
computer 216 to address a look-up table in a memory 218
which stores digital data regarding the rotation rate
which corresponds to each amplitude of the driving signal
as determined by the transfer function of Equation (15).
The digital data at the output 217 of the A/D
converter 214 is used by the microprocessor 216 to access
the proper address in the ROM 218 which stoves the digital
data indicating the corresponding Sagnac phase shift or
rotation rate for that particular amplitude of the driving
signal on the line 332. The program for the
microprocessor 216 to perform this addressing function
~3~
--51--
will be apparent to those skilled in the art and any
program to perform this function will suffice. The
digital data output from the ROM can then be converted to
analog form by a digital to analog converter 220 or it can
be used in its digital form.
In other embodiments, the microprocessor 216 could be
programmed to solve the transfer function of Equation ~14)
by using the data from the A/D converter 214 as the
variable em. In these embodiments, the ROM 218 would
contain the program for performing the calculation
required in equation (14). The exact program used to
perform this calculation is not critical, and programs
will be known to those skilled in the art to perform this
calculation. Any program which can perform this
calculation will be adequate for purposes of the
invention.
Other embodiments might use an R.M.S. voltmeter
instead of the lock-in amplifier 210, but such a structure
would lead to errors since any noise on the line 332 might
be averaged in and misinterpreted as false amplitude of
the driving signal. The R.M.S. voltmeter has its input at
the midpoint of a voltage divider as shown in Figure 21.
The driving signal is applied to the node 221 of a voltage
divider comprised of the resistors Rl and R2. The
resistors Rl and R2 are selected to reflect the slope of
the transfer function in the linear region such that for a
given amplitude of the driving signal at the node 221 a
signal having an amplitude proportional to the rotation
rate will be developed at the node 222. This signal is
coupled to the input of an R.M.S. voltmeter to be read as
3 the Sagnac phase shift or rotation rate.
Further, an oscilloscope could also be used instead of
an R.M.S. voltmeter, as shown in Figure 23, to detect the
amplitude of the driving signal. Again a linear scaling
network comprised of the resistors R3 and R4 to scale the
input to the oscilloscope. The embodiments of Figures 21
~3~Z~2
-52
and 22 are most accurate in the linear regions of the
transfer function.
Any other device capable of measuring waveforms at the
lower modulation frequency could also be used for the
output display circuit 208. For example, analog curve
matching devices could be used to compensate for the
transfer function curve and give an output proportional to
the rotation rate. Further, the ROM look-up table and
microprocessor of Figure 20 could be dispensed in the
approximately linear regions of the transfer function
curve such that a simplified Figure 20 embodiment could
also be used in the approximately linear region for an
approximate result.
Another preferred embodiment of a method and apparatus
for sensing rotation with a generally linear scale factor,
over an extended dynamic range, may be described wit,h
reference to Figures 23-29.
In a device such as that illustrated in Figure'l,
introduction of a time-varying signal through the
~0 asymmetrically positioned phase modulator 38 causes' a
phase difference between counter-propagating waves ,when
measured at the output of detector 30. This induced
differential phase shift I is defined as:
I = I - i ) (16)
;:
Where I is the phase shift produced by the phase
modulator at time t; and
is the time difference between interfering waves passing
through the phase modulator 38.
Referring to Figure 23, it is seen that a DC phase
difference between counter-propagating waves at a given
time I may be achieved by applying a linear phase ramp
such as that indicated at 400 to the counter-propagating
waves through phase modulator 38. Specifically, linear
~3~2.~;2
-53-
phase ramp 400 represents the influence of the ramp signal
input through modulator 38 on the wave propagating
counter-clockwise in the sensing loop. The influence of
the same input signal on the clockwise propagating signal
is illustrated by line 402. The amount of difference
between ramps 400 and 402 is dependent upon the asymmetric
location of the phase modulator 38 in the sensing loop.
The phase difference signal A between the
counter-clockwise and the clockwise propagating waves is
indicated at 404. Of partlcular interest is the fact that
this phase difference is a DC value whose magnitude may be
varied by adjusting the slope of the ramp signal. Thus,
it becornes apparent that the ramp signal may be applied
through phase modulator 38 to produce a DC phase
difference magnitude which can be adjusted so as to
effectively null out the rotation induced Sagnac phase
shift.
One means of producing such a ramp function would be
to utilize a frequency shifter located at an asymmetric
position in the sensing loop. In this case would be
defined as
A = 2~f (l7)
Where of is the amount of frequency shift. The use of a
frequency shifter would provide an additional advantage of
permitting frequency output to be utilized as a measure of
rotation rate. However, a frequency shifter in a fiber
form suitable for a gyroscope application has not been
reported
Commonly used fiber-optic phase modulators, such as
modulator 38 which modulates fiber length, cannot provide
a continuous phase ramp to produce the DC differential
phase shift between the counter-propagating waves. Thus,
to utilize a phase modulator in this application requires
the simulation of a phase ramp.
~23~
-54~
Figure 24 illustrates one waveform which may be
utilized to simulate a phase ramp. Specifically, line 406
in Figure 24(A) illustrates the application of a saw-tooth
wave to a counterclockwise propagating signal in the
sensing loop. Line 408 indicates the influence of the
same sa~-tooth wave shape, applied from an asymmetrically
positioned phase modulator, to a clockwise propagating
signal in the sensing loop. Line 410 in Figure 24(B)
represents the phase difference signal i produced by
the phase difference between the interfering waves
illustrated in Figure 24(A).
As can be seen from the waveform represented by line
410, the phase difference cannot be constant at all times
due to the resetting process and reciprocity of the two
optical paths. However, during those periods indicated at
412 when line 410 defines a DC value, the DC Sagnac phase
shift can be nulled out by adjusting the amplitude or
frequency of the phase modulation. Thus, by applying the
substantially DC phase bias to the phase difference of the
counter-propagating light waves, the Sagnac phase shift
experienced by the counter-propagating light wave phase
difference is substantially nulled. It is further noted
that, during the periods not included in the segments
labeled 412, the zero Sagnac phase shift can be simulated
by turning off the rotation signal received from detector
30 of Figure 1.
us a result, the rotation induced Sagnac phase shift
can be effectively nulled by a phase modulation induced
phase difference for part of the time, and by turning off
the signal at the light source 10 or at or after the
detector 30 for the rest of the time. The slope of the
ramp, which determines the differential phase shift, can
be controlled by adjusting the amplitude of the modulation
signal.
Of course, it will be appreciated that other waveforms
having a ramp type configuration could also be utilized to
~3~
produce a similar effect. For example, a triangle
waveform phase modulation could be utilized, with the
understanding that the production of a DC phase modulation
output signal would require that the signal be turned off
for a longer period than with the saw-tooth wave due to
the shorter ramp length in the triangle wave shape.
One of the most commonly used fiber optic phase
modulators is a piezo-electric cylinder with several turns
of fiber wrapped around it, as described previously.
Unfortunately, the frequency response of this device is
not uniform over a wide frequency range. As a result, it
is almost impossible to achieve a saw-tooth wave phase
modulation of the type illustrated in Figure 24, unless
the amplitudes and phases of each Fourier component of the
waveform are controlled.
One method for overcoming the problem of
non-uniformity described above is to produce the saw-tooth
or triangle waveform in an approximate manner by combining
sinusoidal phase modulations in the all fiber optic
rotation sensor. For example, a saw-tooth waveform may ye
simulated by combining the phase difference modulation at
one frequency with the second harmonic of that frequency,
with the amplitude of the second harmonic and the phase
relationship of the waves properly adjusted. Likewise,
the triangle waveform may be produced by combining the
phase difference modulation at one frequency with the
third harmonic of the frequency, which has been properly
adjusted for amplitude and phase relationship.
Figure 25 illustrates one preferred collection of
waveforms which may be utilized in the all fiber optic
gyroscope to simulate a saw-tooth waveform. Specifically,
the first phase modulation signal for simulating the
saw-tooth wave comprises a sine wave 450 of Figure 25(A),
which defines Al. The line 450 is illustrative of the
effect of the sinusoidal phase modulation signal on the
counterclockwise propagating wave in the sensing loop, and
~3~
-56-
line 452 illustrates the influence of this same sinusoidal
modulation signal on the clockwise propagating wave.
In Figure 25(B) line 454 describes the influence on
the counterclockwise propagating wave of a second phase
modulation signal which is at the the second harmonic
frequency of the sinusoidal modulation signal 450. This
second harmonic phase modulation signal is referred to as
(t). Line 456 of Figure 25(B) illustrates the influence
of the second harmonic phase modulation signal on the
clockwise propagating wave.
Figure 25(C) illustrates the waveforms comprising the
sum of the modulation signals of Figures 25(A) and
25(B). Specifically, the saw-tooth type waveform
indicated at 458 comprises the summation of waveforms 450
and 454, and illustrates the response of the
counterclockwise propagating wave to this modulation
signal. Likewise, the saw-tooth type waveform illustrated
at 460 describes the sum of the waveforms 452 and 456, and
illustrates the effect of this waveform on the clockwise
propagating waves in the rotation sensor.
Figure 25(D) illustrates the phase difference
modulation with respect to time. This signal, indicated
at 462, thus comprises the difference between the waveform
458 i and waveform 460 i ), where is the time
difference between interfering waves passing through the
phase modulator. The waveform of Figure 25(D) may be
described as
= cos wmt + 0.3 cos 2 wmt (18)
As described with respect to Figure 24, it will by
noted that the waveform 462(~(t)) includes portions
indicated at 464 which are generally linear. By gating
the phase difference signal as described earlier, it is
possible to utilize these generally linear or DC portions
.2S~
of the phase difference modulation 462 to effectively null
the rotation induced Sagnac phase shift. As with the
saw-tooth waveform of Figure 24, the amplitude of the DC
portion 464 can be controlled by adjusting the amplitude
or frequency of phase modulation. Thus, the DC-like
sections of phase difference modulation 464 can be used to
null out Sagnac phase shift AIR, and signal turn Hoff
during the periods not included in the 464 sections can be
used to simulate zero R for the rest of the time.
Figure 26 graphically illustrates the combined
influence of the phase modulations which can exist if the
saw-tooth waveform 458 of Figure 25(C) were introduced as
a second modulation signal at a lower frequency (fm) in
the rotation sensor of Figure 11. Figure 26 also
illustrates the output signal which would be detected as a
result of phase modulation under those circumstances.
Specifically, the DC value for the phase shift
resulting from the Sagnac phase shift at a fixed rotation
rate is illustrated at 352. The phase modulation signal
which is produced by the saw-tooth second modulation
signal is illustrated at 354. In addition, the phase
modulation produced by the bias modulation signal (fb) is
illustrated at 350. It is noted that, as with the
sinusoidal modulation waveform utilized in the embodiment
of Figure 11, the saw-tooth modulation signal should be at
a frequency which is much lower than the bias modulation
freqUency fb-
It is seen in Figure 26 that the phase modulation
signals described above oscillate about the DC phase shift
352 which is Q~ R. It is also noted that th.e amplitude of
the lower frequency, second phase modulation 354 has been
adjusted so that the generally flat or DC portions of that
line 354 are positioned on the vertical axis 355. Thus,
by gating either the output of detector 30 or the light
source 10 of the apparatus of Figure 11, it is possible to
output only those portions of the resulting output signal
, .
~3~
-58-
which are produced during the DC segment of the lower
frequency modulation signal 354 as indicated at 464.
During this gated period 464, resulting signals oscillate
about the vertical axis 355. During the remaining
periods, the output signal equals zero, thus simulating a
situation where the Sagnac phase shiEt is nulled out.
The output resulting from gating the rotation sensor
as described above and during the periods indicated at 464
of Figure 26 produce an output signal having a waveform
which is approximated by the waveform indicated at 466 of
Figure 26.
Of particular interest is the fact that the output
signal 466 includes no first harmonic, indicating that the
Sagnac phase shift OR has been substantially nulled
during the gated periods, and is not monitored during the
off periods. Thus, by monitoring the amplitude of the
second phase modulation signal, it is possible to
determine the amount of rotation experienced by the
gyroscope, even in extended dynamic conditions of high
rotation. Preferred circuits for detecting this signal
amplitude and determining the rotation rate were described
previously with respect to the sensor illustrated in
Figure 11.
Figure 27 illustrates one preferred embodiment -of a
rotation sensor which may be used for monitoring rotation
through use of a simulated ramp modulation signal. It is
noted that many of the components of the apparatus
illustrated in Figure 27 correspond both in construction
and operation to elements contained in the apparatus of
Figure 11. Therefore, corresponding elements are
identified with corresponding numbers.
Based on its construction, it becomes apparent that
the rotation sensor illustrated in Figure 27 functions in
a manner which is substantially identical to the sensor of
Figure 11. However, the sensor illustrated in Figure 27
replaces the sinusoidal- second modulation signal with a
~'~3~2S~
-S9-
low frequency modulation signal which is generally
configurated like a saw-tooth wave. In order to produce
the saw-tooth modulation signal, the signal generator 308
transmits a sinusoidal waveform onto line 500. This
sinusoidal waveform may be substantially identical to the
waveform transmitted to line 320 from generator 308 in
Figure 11. In addition, the sinusoidal waveform from
signal generator 308 is also transmitted on line 502 to a
frequency multiplier 504 which receives the sinusoidal
modulation signal at frequency fm and doubles its
frequency to produce a second harmonic at frequency 2fm
which is transmitted to an amplitude adjustment device
506.
Device 506 may comprise any conventional means for
adjusting the amplitude of a signal, such as a
potentiometer. From the amplitude adjust device 506, the
signal is transmitted to the phase shift circuit 136 where
its phase is shifted relative to the first harmonic phase
modulation signal from the generator 308 in the
relationship which generally corresponds to that between
the waveforms illustrated in Figure 25(A) and 25(B). The
amplitude adjust circuit 506 and the phase shift circuit
508 may be manually set by a one time adjustment so long
as the sinusoidal modulation waveform praduced by signal
generator 308 is maintained at a constant frequency fm.
The second harmonic waveform from phase shift circuit
508 is transmitted onto line 510 which connects with line
500. Thus, the first harmonic signal on line 500 and the
second harmonic signal on line 510 are combined to produce
a phase modulation waveform having a generally saw-tooth
configuration such as that illustrated in Figure 25(C).
The signals from lines 500 and 510 are combined and
transmitted through line 320 to the error correction
modulator 130, where the combined signal is processed in
the manner which was described with reference to the
rotation sensor illustrated in Figure 11.
-60-
As was explained above, the rotation sensor of Figure
27 functions to null out the DC influence of the Sagnac
effect, by gating the output signal so as to detect only
that portion of the output which results from phase
modulation produced by the ramped portion of the saw-tooth
wave. As a result, the gating signal on line 306 from
signal generator 308 must be adjusted so that the gate 304
is turned on only during the ramped portion of the
saw-tooth wave. It has been found that the gating signal
from signal generator 308 should be set to gate
approximately 30% of each period of the modulation signal
on line 320. The portion of the waveform of line 320
which is gated may be identified by merely extrapolating
upwardly the gated period identified at 464 in Figure
25(D).
By reference to Figure 28, it is seen that the
transfer function or a scale factor which results from the
use of the rotation sensor of Figure 27 is substantially
linear. This result is obtained because of the fact that
the Sagnac phase shift (OR) is being nulled out by the
phase difference modulation (em) which defines a
substantially DC signal. Thus, as is indicated by the
graph of Figure 28, any increase in the magnitude of phase
difference modulation produced by the Sagnac effect can be
effectively nulled out by the corresponding increase in
the magnitude of the phase difference modulation produced
by the ramp portion of the saw-tooth wave modulation
signal.
As with the rotation sensor of Figure ll, the band
pass filter 326 passes the signal at frequency fm from
line 330 to an output display 208 which may be utilized to
determine the rotation velocity by identifying the
amplitude of the phase modulation signal which is
necessary to cancel out the Sagnac phase shift.
The linearity of the scale factor illustrated in
Figure 28 practically eliminates the source wave length
~3~;2
-61-
dependence of the gyroscope scale factor. This is
possible because the amplitude of the phase difference
modulation has the same wavelength dependence to the
applied signal as the Sagnac phase shift has to the
rotation rate ( I-). Considering the fact that the
wavelength of a light source is difficult to control, this
phase modulation approach can improve the stability of the
scale factor. The stability of the system is further
improved if the feedback modulation frequencies fm and 2fm
do not coincide with the resonance frequency of the phase
modulator. In addition, if harmonic frequencies of fm do
not coincide with the bias modulation frequency fb, then
additional offset or noise in the rotation signal is also
eliminated.
In the rotation sensor of Figure 27, the gating time
interval and relative amplitudes of the two frequency
components can be adjusted to provide a linearity of the
scale factor on the order of 10~5 up to 20 radians of
Sagnac phase shift assuming a linear response of the phase
modulator to the applied signal (erg., when
a (cos ~mt) + 0.4 cos (I mt))~
In both the rotation sensor of Figure 11 and that of
Figure 27, the gating process introduces a possibility of
loss of the optical power, and loss of rotation
information during the time that the sensor is gated
off. The device of Figure ll(A), typically involves loss
of half of the optical power since the device is gated off
for approximately half the time. In the device of Figure
27, with gating of approximately 30% of the waveform, the
loss of optical output could occur during approximately
70% of the time. This information loss can result in an
error in measured rotation angle, I, when a sudden change
in angle occurs within a gated-out time interval. Take as
an example the case of a full cycle of square wave angular
acceleration using an acceleration rate of i /dt2¦
1,000/sec2, which is a value used to represent maximum
~3~%~2
--62--
expected acceleration in many applications. For a typical
gating frequency fm of 15 kHz, and with gating occurring
during half of the time, an acceleration of the above
amount within the first half of a gated out time interval
followed by a deceleration of the same magnitude within
the second half of the interval, leads to an error in of
about 2.8x10-7 degrees. Thus, it becomes apparent that
the reliability of the phase sensing devices described
herein is very good, with the influence of the gating
arrangement causing only a very small likelihood of error
in the measurement of the rotation velocity.
Figure 29 illustrates another embodiment of the
rotation sensor utilizing the saw-tooth waveform. In this
embodiment, the signal generator 308 produces a modulation
signal at the frequency fm which comprises a train of
square wave pulses. These square wave pulses contain
harmonics of frequency fm~ including 2fm~ These square
wave pulses are transmitted via line 320 to the error
correction modulator 130 and are processed in the manner
described previously with respect to the sensors
illustrated in Figures 11 and 27.
The square wave signal produced by modulator 130 is
transmitted via line 530 to a low pass filter 532. Filter
532 eliminates all but the first and second harmonics of
the signal transmitted from error correction modulator
130. The filtered signal is then transmitted via line 534
to a phase adjust circuit 536. One particular embodiment
of phase adjust circuit 536 comprises a tunable band pass
filter which is utilized to modify the phase of the second
harmonic with respect to the first harmonic, so as to
produce the desired saw-tooth waveform for the phase
modulation.
The saw-tooth wave modulation signal from phase adjust
536 is transmitted onto line 538, where it is combined
with the sinusoidal modulation frequency fb produced by
signal generator 40 on line 324. The resulting signal is
~3~25~
-63-
applied to the phase modulator 38 as the modulation
signal. In all other respects, the sensor of Figure 29
functions in a manner identical to the sensor of Figure
27.
5One particular embodiment of the rotation sensor
illustrated in Figure 29 is constructed and evaluated as
follows. The fiber length and radius of the sensing coil
is about 580 meters, and 7 centimeters, respectively. The
wave length of light source utilized is about 830
10nanometers. The phase modulator 38 comprises a
piezoelectric hollow cylinder with several turns of fiber
wrapped around it. The first resonance frequency of the
piezoelectric cylinder is about 20 khz. The bias
modulation frequency fb produced by signal generator 40 is
1~2 khz, producing an amplitude of phase difference
modulation (~b) is approximately equal to 1.8 rad.
The saw-tooth waveform frequency modulation may be
produced as follows. A train of square wave pulses is
generated by the signal generator 308 which comprises a
20pulse generator, at a repetition frequency fm of 15 khz.
The frequency spectrum of this signal contains harmonics
of the fundamental frequency fm. A low pass electric
filter 532 suppresses all the frequency component leaving
only the first and second harmonics of fm The relative
25amplitude of these frequency components (15 khz a`nd 30
khz) may be adjusted by varying the width of square pulses
from the pulse generator. A variable band pass filter
comprises the phase adjust circuit 536, which is utilized
to adjust the relative phase of the two frequency
30components. This signal, combined with the bias
modulation signal from generator 40 is applied to the
phase modulator 38.
The electric signal from the silicon photo detector 30
is gated with an electric switch or gate 304 by a
35synchronizing signal from the pulse generator 308,
transmitted on line 306. The phase of gating may be
~3~
-64-
adjusted by adjusting the pulse delay of the trigger
signal. Approximately 303 of the signal from detector 30
is allowed to pass throuyh the gate 304 to obtain a
linearized scale factor. The signal from gate 304 is
transmitted across line 310 and through band pass filter
312, which allows passage only on the bias modulation
frequency fb. This signal is then measured in the lock-in
amplifier 46, as compared with the reference signal at the
fb frequency, from signal generator 40. The comparison of
the signal from filter 312 against the reference signal
produce the error signal from lock in amplifier 46, which
is transmitted to the error correction modulator 130 as
was described previously in the specification. The actual
scale factor which results from operation of the circuit
of Figure 29 corresponds to the scale factor illustrated
at 520 in Figure 28.
Although the rotation sensors described herein
illustrate use of a single phase modulator, it will be
appreciated by those skilled in the art that separate
phase modulators could be utilized for the bias phase
modulation and the lower frequency second phase
modulation. Furthermore, it will be recognized that other
waveforms could be utilized in conjunction with the gating
arrangement described herein, with acceptable results.
Such alternate embodiments are considered to be within the
scope of the invention as described and claimed herein.
In summary, not only does the invention described
herein comprise a significant improvement over the prior
art in extending the dynamic range for rotation sensing
over a very broad range of rotation velocities, but it
also overcomes other long existent problems in the
industry by (1) providing a means for obtaining extended
dynamic rotation sensing while optionally utilizing only a
single phase modulator; (2) providing for such rotation
sensing with greatly improved stability by substantially
suppressing the source wavelenyth dependence of the scale
2~
-65-
factor; and . (3) providiny a rotation sensor with
significantly increased accuracy and reliability by
linearizing the scale factor or transfer function and,.
thereby, siynificantly simpli.fying the signal processing
required in the sensing device.
