Synthetic heterodyne detection in a fiber-optic ring ... - Fiber Optics Lab

81

1, 1993 / Vol. 18, No. 1 / OPTICS LETTERS

January

Synthetic heterodyne detection in a fiber-optic ring-laser gyro S. Huang, P.-A. Nicati, K. Toyama, B. Y. Kim, and H. J. Shaw Edward L. Ginzton Laboratory,Stanford University,Stanford, California 94305 Received September 3, 1992

rotation rate and direction A synthetic heterodyne detection scheme for ring-laser gyros to sense both technique for phase-modulation push-pull sinusoidal the with is presented. This scheme is compatible ring-laser Brillouin fiber-optic a in suppressing frequency locking. The good experimental results achieved gyro show the potential

of this detection scheme in applications.

In a ring-laser gyro, the rotation rate is given by the frequency difference between the two counterpropagating laser waves in the laser cavity. The simplest way to measure the frequency difference is to combine

the two beams and observe the beats between them. However, the beats do not tell the rotation direction. rate One type of readout that can sense both rotation 2 For detection." quadrature spatial is direction and an all-fiber ring-laser gyro, however, this method does not seem appealing. In order to get spatial quadrature signals, we have to extract both lasers through optical fiber couplers before the two lasers combine

and then obtain the interference pattern of the two sampled laser beams by4 using some bulk-optics components. One scheme', used in Brillouin fiber-optic gyros does not have the problem of sensing rotation direction, in which a large constant frequency bias is introduced between the two counterpropagating lasers. However, this method may have difficulties with stability of the constant bias and lack of optical reciprocity. Here we describe a simple detection scheme-synthetic heterodyne detection-for fiber-

D through C1, leading to a combined at detector 6 by detector current I(t) = -o[1 2

+ cos(± m sin wmt + fQbt

+ Jo)] I

(1)

where IO/2 is the intensity of each of the counterpropagating Stokes waves at the detector, Womand (Dmare the modulation angular frequency and index, respectively, ko is the initial phase, and fb = f 1 cw - f 1ccw is the gyro angular beat frequency induced by rotation, with ficw and fQccwthe frequencies of the clockwise (CW) and counterclockwise

(CCW)

Stokes waves in the absence of the phase modulation. Therefore positive and negative values of fQb correspond to the CCW and CW rotation directions, respectively. With this sign convention and the arrangement of Fig. 1, the plus or minus in Eq. (1) corresponds, respectively, to the location of coupler C2 in region I or II. Equation (1) can be expanded into modulation sidebands as in Eq. (2):

I(t) = I2( 2 1 + JO(4Dm)COS(flbt

+ ko)

+ f£b)t + '00] - COS[(Wm- flb)t - 00k]} ± Ji(DPm){COS[(Wm + fQb)t

+ 00]

+

COS[(2c.m J 2 (DFm){

±

J3((D.m){cos[(3om + flb)t +

+ cos[(2a)m-

flb)t

-

00]}

0o]- cos[(3cm- Qb)t - ko]} + **..) * (2)

optic ring-laser gyros based on sinusoidal phase modulation within the cavity, which senses both rotation to an approach used rate and direction. It is related 5 with interferometric gyros. We describe this detection system in connection

with push-pull

sinusoidal phase modulation in a

laser cavity in which two phase modulators (PM1 and PM2), located symmetrically as in Fig. 1, are driven

with antiphase excitations. This system,6which has favorable properties for lock-in reduction,

also pro-

duces a position-independent phase modulation that is suitable for the synthetic heterodyne detection scheme. Clockwise and counterclockwise laser outputs extracted from the cavity by coupler C2 are 0146-9592/93/010081-03$5.00/0

(D.s inot

Fig. 1. Schematic of a fiber-optic ring-laser gyro with two antiphased phase modulators in the ring cavity. S, light source; D, detector; C's, optical fiber couplers; PM's, phase modulators. © 1993 Optical Society of America

82

OPTICS LETTERS / Vol. 18, No. 1 / January

1, 1993

push-pull modulation index E:Fm= 2.4 rad, so that aJi(2.4) - 1/2J 2 (2.4) = 0. Then the output of the mixer, S(t), can be obtained as

Qb> 0:

co 0

(Cm

20Om

3CO,

+ other harmonics}i.

4(Om

Qb< 0:

J M211 t 0

4 | I~~~~~~I

0)m

--

t,

as *

|

20Jm

30

S) = Io2{0.4318 cos[(wm + flb)t + 'ko]

. v-

I

CO

*

40)m

Fig. 2. Frequency spectra of the final output signals from the gyro, for two opposite rotation directions, when (IAm= 2.4 rad and the coupler C2 is in region I.

(3)

The sideband at Wm - Qb is absent after the above processing. The remaining single sideband cWm+ f 1 b can be easily picked up by a bandpass filter around (Din. Figure 4 illustrates the spectra of the output signals from the filter for both Db > 0 and fQb < 0One can see that the location of this single sideband gives the rotation rate and sense at the same time. This location, i.e., the frequency readout after the processing, fro, is easy to measure by means of a spectrum analyzer or a frequency counter (Fig. 3). This scheme has been tested in a Brillouin fiberoptic ring-laser gyro operated at 1.3-/Lmwavelength and having the basic circuit of Fig. 1 together with polarization controllers and cavity stabilization circuitry.6 The push-pull modulation frequency and index used were fE =

= 11 kHz

Wom/27r

!Qb Qb> 0: A(t) Generator

_'I

,

:

…-_________I

co

Qb < ° ReadoutFrequency

0).

fmv

Fig. 3. Synthetic heterodyne signal processing circuit. D is the detector at the gyro output shown in Fig. 1.

Fig. 4. Frequency spectra after the gyro outputs (Fig, 2) pass through the signal processing.

For best suppression of the central lock-in dead band,

4Dm is chosen to be 2.4 rad.6 The dc sideband at fQb then vanishes, and the rotation-induced beat frequency flb will be read at the first and/or higher

harmonics. Figure 2 illustrates the frequency spectra of I(t) for both rotation directions, fQb > 0 and Qb < 0, when ¢Dm= 2.4 rad and coupler C is located 2 in region I. When £kb > 0, the right sidebands of all harmonics, i.e., nw. + Qb (n = 1, 2, 3 .... ), have the same sign, whereas the left sidebands, i.e., nor. - fib, change signs alternately. For the case of fb < 0, the right and left sideband behavior is reversed. The synthetic heterodyne detection scheme is based on these spectral characteristics. The synthetic heterodyne signal processing circuit is shown in Fig. 3. The output of the ring-laser gyro with sinusoidal push-pull modulation, I(t) of Eq. (2), is ac coupled to a mixer.

Through the mixer,

the ac part of I(t) is multiplied by a signal A(t) = C(a + cos cot), where C is an arbitrary real number. The dc weight, a, is chosen to be 0.4158, while the

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.

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TI 1 T

. 11, .

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I. .1..

i

i

-I

'-1

I11VI 1\

I.

i -120 daV-t

l...

.

I

1

*

.-

i

NI

VA

m 1 V ' 'V

l

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!

i

iI

.

11W

I I I

,i

i

I

1l

1

IIl I

II

-

l II ,A

. .. l

Ab 3 1l

A:

I ' - ___ Il

I I

I

iA

11 I I

Il

.

dev-

1

I

.~~~~~~~~~~~~~

; it

-

__.

A,

_e

w.

1

l . l

1P

l

i 1. -1httX

I I l?

-

I,1

2kH.z

i~~~~~~~~

11V `1IlVn ]

A"

V l

1 4- 2hH.

Fig. 5. Measured spectra of the output signals after the signal processing through a fast-Fourier-transform spectrum analyzer (in log scale). Upper trace, CW rotation; lower trace, CCW rotation.

16

z

Ad,.......

15 14

_ ..

c

12

0

11

(U 4' a: 41

10 9

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.

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.

..........

. .....

SK*,

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.

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_.j-.......... ...*

~~~~..... 16 15

S_W. ...

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14 F

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13 12

CUS

11

Z0

10

83

CW and CCW rotations can show reversed sideband configurations. Note that the adjustment for all parameters in the A(t) generator is not critical as long as we can obtain enough sideband discrimination. The suppressed sidebands shown in Fig. 5 are approximately 10-20 dB lower than the remaining sidebands, which is adequate for the proper readout of the gyroscope. A better sideband suppression can be achieved by a finer adjustment of the synthetic heterodyne signalprocessing parameters. In addition, an unexpected frequency peak can be seen at the modulation frequency of 11 kHz, which is caused by the imperfect mixer. Two measured curves of readout frequency fro versus rotation rate Qb are given in Fig. 6. These two curves are of good linearity but with opposite slopes because they correspond to phase delays, in the A(t) generator of Fig. 3, that have a 180° difference. As can be seen from Fig. 6, the readout frequency at zero rotation is not 11 kHz; instead, there is a positive or negative frequency bias depending on the slope of the curve. It has been verified that this bias is induced

... .... .......-----

13

1, 1993 / Vol. 18, No. 1 / OPTICS LETTERS

..... January

by the Kerr effect, which is due to a power unbalance

9 8

7 6 -6

C4

R

Z

CCWRotaton

0 CWRotation

RotationrMt[degsecl

Fig. 6. Measured curves of readout frequency fro versus rotation rate Qb for phase delays in the A(t) generator with a 1800difference. The push-pull phase-modulation frequency used was 11 kHz.

and 4Dm= 2.4 rad, respectively. Figure 5 gives the measured spectra through a fast-Fourier-transform spectrum analyzer for CW and CCW rotations, respectively, on a log scale.

Note that whether CW

between the two counterpropagating lasers in the resonant cavity. The power unbalance in our present system induces a bias equivalent to a CCW rotation; therefore both curves show a shift toward the CCW rotation direction. In summary, we have demonstrated a novel synthetic heterodyne detection scheme for sensing rotation rate and direction in a fiber-optic Brillouin ring-laser gyro, which is compatible with the sinusoidal push-pull phase modulation technique for suppressing frequency locking. In this scheme, only simple signal processing is needed, and the beat frequency readout is shifted to a high-frequency range that is advantageous for reducing electronic noise. Experimental results are in good agreement with the theory. This research was supported by Litton Systems, Inc.

rotation (or CCW rotation) corresponds to a right sideband

(fo > fin) or to a left sideband

(fro < fi)

is determined by two factors. First, it depends on which region of the cavity the coupler C2 is located in. If coupler C2 is located in region II instead of region I (equivalent to interchanging the modulation signals on the two phase modulators), the spectra in Figs. 2 and 4 will change:

all left and right sidebands will

exchange with each other. Second, if the phase delay in the A(t) generator

(Fig. 3) is shifted by 1800, we

will have A(t) = C(a - cos o)wt) instead of A(t) = C(a + cos wst). Then the surviving single sideband will be Wn,- Qb instead of Wm+ Qb, and hence the spectra

of flb > 0 and fQb < 0 in Fig. 4 will

be exchanged. Therefore, under different conditions,

References 1. F. Aronowitz, Laser Applications (Academic, New York, 1971), Vol. 1, p. 148. 2. W. W. Chow, J. Gea-Banacloche, L. M. Pedrotti, V. E.

Sanders, W. Schleich, and M. 0. Scully, Rev. Mod.

Phys. 57, 61 (1985). 3. R. K. Kadiwar and I. P. Giles, Electron. Lett. 25, 1729 (1989).

4. F. Zarinetchi, S. P. Smith, and S. Ezekiel, Opt. Lett. 16, 229 (1991). 5. B. Y. Kim and H. J. Shaw, Opt. Lett. 9, 378 (1984). 6. S. Huang, K. Toyama, B. Y. Kim, and H. J. Shaw, "Lock-

in reduction technique for fiber-optic ring-laser gyros," Opt. Lett. (to be published).