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. 1. V. Vali and R. W. Shorthill, Appl. Opt. 15, 1099 2. R. A. Bergh, H. C. Lefevre, and H. J. Shaw, Opt. 502 (1981). 3. H. C. Lefevre, R. A. Bergh, and H. J. Shaw, Opt. 454 (1982). 4. W. K. Burns, R. P. Moeller, C. A. Villarruel, and M. 5. J. L. Davis and S. Ezekiel, Opt. Lett. 6, 505 (1981). 6. W. C. Davis, W. L. Pondrom, and D. E. Thompson, in FiberOpticRotationSensorsand RelatedTechnologies, 7. 8. 9. 10. S. Ezekiel and H. J. Arditty, eds. (Springer-Verlag, Berlin, 1982), p. 308. B. Y. Kim, H. C. Lefevre, R. A. Bergh, and H. J. Shaw, Proc. Soc. Photo-Opt. Instrum. Eng. 425, 86 (1983). B. Y. Kim and H. J. Shaw, Opt. Lett. 9,263 (1984). B. Y. Kim and H. J. Shaw, Opt. Lett. 9, 275 (1984). K. B13hm, P. Marten, E. Weidel, and K. Petermann, Electron. Lett. 19, 997 (1983). D. Eberhard and E. Voges, Opt. Lett. 9, 22 (1984). J. H. Cole, B. A. Danver, and J. A. Bucaro, IEEE J. 11. 12. theoretical prediction. QE-18,1639 (1982). 14. R. Ulrich, Opt. Lett. 5, 173 (1980). A good linearity over a wide Lett. 7, Abebe, in Technical Digest of 1983 International Conference on Integrated Optics and Optical Fiber Communication (Institute of Electronics and Communication Engineers of Japan, Tokyo, 1983), paper 28C3-2. Figure 4 shows the measured phase shift in the filter output signal induced by rotation of the gyroscope. The experimental results show good agreement with dynamic range is obtained. (1976). Lett. 6, Quantum Electron. QE-18, 694 (1982). 13. E. L. Green and P. G. Cable, IEEE J. Quantum Electron.
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