Phase-reading, all-fiber-optic gyroscope

378
OPTICS LETTERS / Vol. 9, No. 8 / August 1984
Phase-reading, all-fiber-optic gyroscope
B. Y. Kim and H. J. Shaw
Edward L. Ginzton Laboratory, W. W. Hansen Laboratories of Physics, Stanford University, Stanford, California 94305
Received April 5, 1984; accepted May 17, 1984
An open-loop, all-fiber-optic gyroscope with wide dynamic range and linear scale factor is described.
This novel
approach converts the Sagnac phase shift into a phase shift in a low-frequency electronic signal by using optical
phase modulation followedby amplitude modulation of the electronic signal. Preliminary experimental results
verify the theoretical predictions.
Since the first demonstration of an optical-fiber Sagnac interferometerl considerable effort has been devoted to fiber-optic gyroscopes. Some of the reported
gyroscopes showed high sensitivity and good stability
near zero rotation rate. 2 4 Others have closed-loop
configurations to overcome the limited dynamic range
that stems from the nonlinear response of the interferometer to the rotation rate. 5' 6 However, problems
in designing suitable electronic/optical feedback devices
have made it difficult to achieve the high sensitivity
shown in Refs. 2-4 in a closed-loop form.
Recently, we reported a series of simple, closed-loop
approaches to large dynamic range using phase modulators as feedback devices.7 -9 One advantage of these
approaches is the availability of an in-line fiber-optic
phase modulator that does not compromise the established high rotation sensitivity reported in Refs. 2 and
3. Also, a linearized scale factor with suppression of the
source wavelength dependence, which is a problem with
achieved.9
other approaches, is
However, the output
is in analog form, and digital readout over the full dynamic range with high resolution has not been demon-
strated.
Other approaches to the dynamic-range problem
include electronic signal processing1 0 and single-sideband detection1 applied to open-loop gyroscopes. In
the former case, dynamic range and resolution are
limited by the analog-to-digital converter available,
whereas the single-sideband approach requires a
wideband phase modulator, which is not available in
fiber-optic form at present.
In this Letter, we report an alternative signal-processing approach applied to an open-loop gyroscope,
requiring no new components and capable of digital
readout over unlimited linear dynamic range. Compared to so-called synthetic heterodyne demodulation
procedures for two-beam interferometers, which have
been described,12' 1 3 the amplitude modulation used in
the present scheme provides a simpler mechanism for
achieving the desired form of output signal. It also
provides a complementary pair of output signals, permitting direct demodulation by means of a standard
time-interval counter, giving digital readout with essentially unlimited dynamic range.
Rotation introduces a nonreciprocal phase shift
0146-9592/84/080378-03$2.00/0
(AOR) between the counterpropagating waves in an
optical-fiber Sagnac interferometer. In most cases, this
phase information is converted into intensity information through an optical interference process. Although the differential phase shift (AOR) is linearly
proportional to the rotation rate, the intensity output
is a nonlinear (periodic) function of rotation rate. The
key to obtaining a wide, linear dynamic range is to recover the original optical phase information.
The detector output I from a phase-modulated,
open-loop gyroscope'4 contains frequency components
at the phase-modulation frequency fm and its har-
monics:
I(t) = C[1+ cos(Ak\(msin wCmt=C
f1+
[JO(AObm) +
2
E
n=1
AIR)]
J2 n(A'km) cOs2ncmtj
X COS(AOR)
+ r2
E
J 2 n-i(A .m)sin(2n -1)wmtI
X sin(AOR)J
(1)
Here C is a constant, Jn denotes the nth-order Bessel
function, Aom is the amplitude of the phase difference
between the counterpropagating waves produced by the
modulation, and wm = 2 irfm. Note that if we have two
sinusoidal signals at the same frequency nfwmwhose
amplitudes are cos AOR and sin AOR, respectively, and
whose phases are in quadrature, we can add them directly to obtain a single sinusoidal signal whose phase
is AIR. We see from Eq. (1) that the detector current
contains terms of the above kinds, lacking only in that
the cos AOR and sin AkR terms are of different
frequencies. If the current I is amplitude modulated
at the difference frequency wm between adjacent harmonics, each harmonic component becomes partially
translated into the frequencies of its nearest neighbors.
The result is that all harmonics then contain terms in
both cos AIR and sin AkR such that the nth harmonic
has a term cos(nwm+ AbR). Here the Sagnac optical
phase shift AIR has been transposed to a low-frequency
electronic phase shift, which can be measured directly
by standard means.
One simple way to realize the above approach is de© 1984, Optical Society of America
August 1984 / Vol. 9, No. 8 / OPTICS LETTERS
K 1 = K3
379
a J2(AO.)
K 2 = -K 4 - (8/7T)E (-1)nJ 2 n_1 (Akm)/
n=1
(2n - 3)(2n + 1).
(3)
If K1 = K 2 = K, Eqs. (3) become
I, = K Cos(2Wmt-AR)
I2 = K cos(2wmt+ AtkR).
Fig.
1.
Schematic of the phase-reading, all-fiber gyro-
scope.
a6m
0
K
/rN\
OFF
I
r
.
ON
with the phase-modulation signal. Spurious signals
resulting from switching transients are smaller at the
even harmonics of the detector current than at the odd
harmonics. For this reason we chose to operate at the
second harmonic of the detector output, corresponding
to Eqs. (4). Signals at 26 kHz were selected from
channels 1 and 2 by using two bandpass filters and sent
to a digital time-interval counter, which measured the
time difference between zero crossings in the two
channels.
Fig. 2.
1
I
|
CH. 2
(b)
OFF |
Modulation signals:
coil used as a reference.
electronic switch was operated at 13 kHz in synchronism
(a)
ON
]
Here a measurement of the phase difference between
I, and 12 yields 2A4R. This method, which requires a
double pole switch, has advantages in terms of stability
over the simpler procedure of using a single detector
channel modulated by a standard gate and measuring
the phase of the first harmonic (n = 1) against that of
the signal applied to the phase modulator in the sensing
An experiment has been performed using an all-fiber
gyroscope described earlier,3 as depicted in Fig. 1. An
in-line phase modulator, which is a piezoelectric cylinder with several turns of fiber wrapped around it, was
driven by a sinusoidal electronic signal at 13 kHz. An
SWITCH
CH. I
(4)
(a) sinusoidal phase-difference
The condition K 1 = K 2 in Eqs. (3) was achieved ex-
modulation produced by phase modulator in sensing coil; (b)
switching sequences for detector channels I and 2.
picted in Fig. L A phase modulator in the sensing coil
generates a sinusoidal phase-difference modulation
Ak(t) at frequencyf t , as shown in Fig. 2(a). Amplitude
modulation of the detector output is accomplished by
an electronic switch, which transmits this output alternately to channels 1 and 2 at frequency fin. The
signals in channels 1 and 2 are thus square-wave modulated at this frequency, 180 deg out of phase with each
other. The phase of the switching is set with reference
to the phase of Ak(t), with switching transitions oc-
(a)
(b)
(c)
(d)
curring at the peaks of AO(t), as shown in Fig. 2(b).
One harmonic component nfwm of the signals in each of
channels 1 and 2 is selected by bandpass filters.
The filtered signals from the two channels, I, and 12,
are as follows:
Channel 1: I, = K1 cos(A4R) cos(nw,,t)
+ K2 sin(AkR) sin(nCmt),
Channel 2: I2
=
K3 coS(AqR) cos(ncomt)
+ K 4 sin(Aq5R) sin(nflmt),
Fig. 3. Signals from the gyroscope. Upper traces, channel
1. Lower traces, channel 2. Horizontal scale, 20 gsec/divi-
(2)
where K1 -K 4 are constants determined by Acm and n.
For the case n = 2, which is of particular interest for the
experiments described below, the coefficients are
sion. Waveforms in (a) and (c) are inverted because of the
switching circuit. (a) Switched signals when Q = 0 deg/sec.
(b) Bandpass-filter output when Q = 0 deg/sec. (c) Switched
signal when Q = 40 deg/sec. (d) Bandpass-filter output when
Q = 40 deg/sec.
OPTICS LETTERS / Vol. 9, No. 8 / August 1984
380
n (deg/sec)
480
In summary, an approach to a wide dynamic range
has been introduced that is applied directly to a standard all-fiber gyroscope without any additional optical
elements, yielding a scale factor that is strictly linear in
principle and digital output. The stability of the scale
factor will depend on the stabilities achievable in the
phase and amplitude modulators, filters, and other
electronic components and is now under study.
-
c,, 320
-o
n 160
IIL
u)
t
0
We thank W. Hipkiss for technical assistance. This
research is supported by Litton Systems, Inc.
aY -160-I-
References
-320
-480 A
-2 D
-160
0
-80
80
160
240
SAGNAC PHASE SHIFT (deg)
Fig. 4.
Experimental results (dots) showing linear scale
factor.
perimentally by making small adjustments in the amplitude AOmof the phase-differencemodulation and the
phase of the switching such that the amplitudes of the
bandpass-filter outputs are independent of rotation
rate. Theoretically the smallest value of Akm that
satisfies this condition is about 2.8 rad for this case.
In Fig. 3, the waveforms of the switched signals and
the bandpass-filter outputs from channels 1 and 2 are
shown for rotation rates of zero and 40 deg/sec.
It is
clearly seen that the phase differences of the filtered
outputs are different for the two cases.
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