Abstract

A frequency-locking loop affects the bandwidth and output of the resonator integrated optic gyro (RIOG). A low-delay, high-bandwidth frequency-locking loop is implemented on a single field-programmable gate array with triangular phase modulation. The signal processing delay is reduced to less than 1 μs. The loop model is set up, and the influences of loop parameters on the bandwidth and unit step response are analyzed; the bandwidth of 10 kHz is obtained with the optimized loop parameters. As a result, the accuracy of the frequency-locking loop is reduced to 1.37 Hz (10 s integrated time). It is equivalent to a rotation rate of 0.005deg/s, which is close to the ultimate sensitivity of the RIOG. Moreover, the bias stability of the RIOG is improved to 0.45deg/s (10 s integrated time) based on the frequency-locking loop.

© 2013 Optical Society of America

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    [CrossRef]
  8. F. Dell’Olio, C. Ciminelli, and M. N. Armenise, “Theoretical investigation of InP buried ring resonators for new angular velocity sensors,” Opt. Eng. 52, 024601 (2013).
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  19. X. Yu, H. Ma, and Z. Jin, “Improving thermal stability of a resonator fiber optic gyro employing a polarizing resonator,” Opt. Express 21, 358–369 (2013).
    [CrossRef]
  20. Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
    [CrossRef]
  21. H. Ma, X. Lu, L. Yao, X. Yu, and Z. Jin, “Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro,” Appl. Opt. 51, 5178–5185 (2012).
    [CrossRef]
  22. H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
    [CrossRef]
  23. K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro-optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000).
    [CrossRef]
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    [CrossRef]
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  27. G. A. Massey, M. K. Oshman, and R. Targ, “Generation of single-frequency light using the FM laser,” Appl. Phys. Lett. 6, 10–11 (1965).
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  28. Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).
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    [CrossRef]
  30. L. K. Strandiord and G. A. Sanders, “Resonator optic gyro employing a polarization rotating resonator,” Proc. SPIE 1585, 163–172 (1991).
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    [CrossRef]
  32. L. Feng, M. Lei, H. Liu, Y. Zhi, and J. Wang, “Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology,” Appl. Opt. 52, 1668–1675 (2013).
    [CrossRef]
  33. C. H. Lefevre, The Fiber-Optic Gyroscope (Artech, 1993), pp. 157–167.
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    [CrossRef]

2013 (7)

F. Dell’Olio, C. Ciminelli, and M. N. Armenise, “Theoretical investigation of InP buried ring resonators for new angular velocity sensors,” Opt. Eng. 52, 024601 (2013).
[CrossRef]

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
[CrossRef]

M. Lei, L. Feng, Y. Zhi, and H. Liu, “Effect of intensity variation of laser in resonator, integrated optic gyro,” Appl. Opt. 52, 1–7 (2013).
[CrossRef]

X. Yu, H. Ma, and Z. Jin, “Improving thermal stability of a resonator fiber optic gyro employing a polarizing resonator,” Opt. Express 21, 358–369 (2013).
[CrossRef]

C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, “High performance InP ring resonator for new generation monolithically integrated optical gyroscopes,” Opt. Express 21, 556–564 (2013).
[CrossRef]

L. Feng, M. Lei, H. Liu, Y. Zhi, and J. Wang, “Suppression of backreflection noise in a resonator integrated optic gyro by hybrid phase-modulation technology,” Appl. Opt. 52, 1668–1675 (2013).
[CrossRef]

2012 (2)

H. Ma, X. Lu, L. Yao, X. Yu, and Z. Jin, “Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro,” Appl. Opt. 51, 5178–5185 (2012).
[CrossRef]

C. Ciminelli, F. Dell’Olio, and M. N. Armenise, “High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation,” IEEE Photon. J. 4, 1844–1854 (2012).
[CrossRef]

2011 (4)

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
[CrossRef]

L. Hong, C. Zhang, and L. Feng, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50, 094404 (2011).
[CrossRef]

H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

2007 (2)

G. Galzerano and P. Laporta, “Single-frequency diode-pumped Yb:KYF4 laser around 1030 nm,” Opt. Express 15, 3257–3264 (2007).

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photon. Technol. Lett. 19, 1685–1687 (2007).
[CrossRef]

2006 (1)

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

2000 (2)

1991 (2)

L. K. Strandiord and G. A. Sanders, “Resonator optic gyro employing a polarization rotating resonator,” Proc. SPIE 1585, 163–172 (1991).

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring-resonator gyro with a 90 polarization-axis rotation in the polarization-maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

1989 (1)

K. Iwatsuki, M. Saruwatari, M. Kawachi, and H. Yamazaki, “Waveguide-type optical passive ring-resonator gyro using time division detection scheme,” Electron. Lett. 25, 688–689 (1989).
[CrossRef]

1986 (2)

1984 (1)

1981 (2)

1977 (2)

E. I. Moses and C. L. Tang, “High-sensitivity laser wavelength-regulation spectroscopy,” Opt. Lett. 1, 115–117 (1977).
[CrossRef]

S. Ezekiel and S. R. Balsamo, “Passive ring resonator gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

1965 (1)

G. A. Massey, M. K. Oshman, and R. Targ, “Generation of single-frequency light using the FM laser,” Appl. Phys. Lett. 6, 10–11 (1965).
[CrossRef]

Arditty, H. J.

Armenise, M. N.

C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, “High performance InP ring resonator for new generation monolithically integrated optical gyroscopes,” Opt. Express 21, 556–564 (2013).
[CrossRef]

F. Dell’Olio, C. Ciminelli, and M. N. Armenise, “Theoretical investigation of InP buried ring resonators for new angular velocity sensors,” Opt. Eng. 52, 024601 (2013).
[CrossRef]

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

C. Ciminelli, F. Dell’Olio, and M. N. Armenise, “High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation,” IEEE Photon. J. 4, 1844–1854 (2012).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Numerical and experimental investigation of an optical high-Q spiral resonator gyroscope,” in ICTON (IEEE Photonics Society, 2012), paper Th.A4.5.

Balsamo, S. R.

S. Ezekiel and S. R. Balsamo, “Passive ring resonator gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Barbour, N. M.

N. M. Barbour, “Inertial navigation sensors,” (2011).

Blondel, M.

Campanella, C.

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

Campanella, C. E.

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Numerical and experimental investigation of an optical high-Q spiral resonator gyroscope,” in ICTON (IEEE Photonics Society, 2012), paper Th.A4.5.

Chen, Y.

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
[CrossRef]

Ciminelli, C.

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

F. Dell’Olio, C. Ciminelli, and M. N. Armenise, “Theoretical investigation of InP buried ring resonators for new angular velocity sensors,” Opt. Eng. 52, 024601 (2013).
[CrossRef]

C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, “High performance InP ring resonator for new generation monolithically integrated optical gyroscopes,” Opt. Express 21, 556–564 (2013).
[CrossRef]

C. Ciminelli, F. Dell’Olio, and M. N. Armenise, “High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation,” IEEE Photon. J. 4, 1844–1854 (2012).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Numerical and experimental investigation of an optical high-Q spiral resonator gyroscope,” in ICTON (IEEE Photonics Society, 2012), paper Th.A4.5.

Dell’Olio, F.

C. Ciminelli, C. E. Campanella, F. Dell’Olio, C. Campanella, and M. N. Armenise, “Theoretical investigation on the scale factor of a triple ring cavity to be used in frequency sensitive resonant gyroscopes,” J. Eur. Opt. Soc. 8, 13050 (2013).

F. Dell’Olio, C. Ciminelli, and M. N. Armenise, “Theoretical investigation of InP buried ring resonators for new angular velocity sensors,” Opt. Eng. 52, 024601 (2013).
[CrossRef]

C. Ciminelli, F. Dell’Olio, M. N. Armenise, F. M. Soares, and W. Passenberg, “High performance InP ring resonator for new generation monolithically integrated optical gyroscopes,” Opt. Express 21, 556–564 (2013).
[CrossRef]

C. Ciminelli, F. Dell’Olio, and M. N. Armenise, “High-Q spiral resonator for optical gyroscope applications: numerical and experimental investigation,” IEEE Photon. J. 4, 1844–1854 (2012).
[CrossRef]

C. Ciminelli, F. Dell’Olio, C. E. Campanella, and M. N. Armenise, “Numerical and experimental investigation of an optical high-Q spiral resonator gyroscope,” in ICTON (IEEE Photonics Society, 2012), paper Th.A4.5.

Deparis, O.

Donati, S.

S. Donati, Electro-optical Instrumentation Sensing and Measuring with Lasers (Prentice-Hall, 2004), pp. 187–233.

Ezekiel, S.

F. Zarinetchi and S. Ezekiel, “Observation of lock-in behavior in a passive resonator gyroscope,” Opt. Lett. 11, 401–403 (1986).
[CrossRef]

S. Ezekiel and S. R. Balsamo, “Passive ring resonator gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Feng, L.

Galzerano, G.

Gavrielides, A.

Hasebe, K.

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

He, Z.

Higashiguchi, M.

Hong, L.

L. Hong, C. Zhang, and L. Feng, “Effect of phase modulation nonlinearity in resonator micro-optic gyro,” Opt. Eng. 50, 094404 (2011).
[CrossRef]

Hotate, K.

Iwatsuki, K.

Jin, Z.

X. Yu, H. Ma, and Z. Jin, “Improving thermal stability of a resonator fiber optic gyro employing a polarizing resonator,” Opt. Express 21, 358–369 (2013).
[CrossRef]

H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
[CrossRef]

H. Ma, X. Lu, L. Yao, X. Yu, and Z. Jin, “Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro,” Appl. Opt. 51, 5178–5185 (2012).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
[CrossRef]

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photon. Technol. Lett. 19, 1685–1687 (2007).
[CrossRef]

Kawachi, M.

K. Iwatsuki, M. Saruwatari, M. Kawachi, and H. Yamazaki, “Waveguide-type optical passive ring-resonator gyro using time division detection scheme,” Electron. Lett. 25, 688–689 (1989).
[CrossRef]

Kurosaki, Y.

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

Laporta, P.

Lefevre, C. H.

C. H. Lefevre, The Fiber-Optic Gyroscope (Artech, 1993), pp. 157–167.

Lefovre, H. C.

Lei, M.

Liu, H.

Lu, X.

Ma, H.

X. Yu, H. Ma, and Z. Jin, “Improving thermal stability of a resonator fiber optic gyro employing a polarizing resonator,” Opt. Express 21, 358–369 (2013).
[CrossRef]

H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
[CrossRef]

H. Ma, X. Lu, L. Yao, X. Yu, and Z. Jin, “Full investigation of the resonant frequency servo loop for resonator fiber-optic gyro,” Appl. Opt. 51, 5178–5185 (2012).
[CrossRef]

H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
[CrossRef]

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photon. Technol. Lett. 19, 1685–1687 (2007).
[CrossRef]

Maehar, S.

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

Mao, H.

Massey, G. A.

G. A. Massey, M. K. Oshman, and R. Targ, “Generation of single-frequency light using the FM laser,” Appl. Phys. Lett. 6, 10–11 (1965).
[CrossRef]

Mégret, P.

Moses, E. I.

Ogata, K.

K. Ogata, Modern Control Engineering, 5th ed. (Prentice-Hall, 2010), pp. 320–485.

Ohkawa, M.

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

Ohtaa, Y.

Y. Ohtaa, S. Maehar, K. Hasebe, Y. Kurosaki, and M. Ohkawa, “Frequency stabilization of a semiconductor laser using the Rb saturated absorption spectroscopy,” Proc. SPIE 6115, 1–10 (2006).

Oshman, M. K.

G. A. Massey, M. K. Oshman, and R. Targ, “Generation of single-frequency light using the FM laser,” Appl. Phys. Lett. 6, 10–11 (1965).
[CrossRef]

Passenberg, W.

Quiring, V.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Ren, Y.

H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
[CrossRef]

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonance frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C. 12, 942–950 (2011).
[CrossRef]

Reza, S.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Ricken, R.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Rogister, F.

Sanders, G. A.

L. K. Strandiord and G. A. Sanders, “Resonator optic gyro employing a polarization rotating resonator,” Proc. SPIE 1585, 163–172 (1991).

Saruwatari, M.

K. Iwatsuki, M. Saruwatari, M. Kawachi, and H. Yamazaki, “Waveguide-type optical passive ring-resonator gyro using time division detection scheme,” Electron. Lett. 25, 688–689 (1989).
[CrossRef]

Shupe, D. M.

Soares, F. M.

Sohler, W.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Strandiord, L. K.

L. K. Strandiord and G. A. Sanders, “Resonator optic gyro employing a polarization rotating resonator,” Proc. SPIE 1585, 163–172 (1991).

Suche, H.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Sukow, D. W.

Suzuki, K.

Takiguchi, K.

K. Suzuki, K. Takiguchi, and K. Hotate, “Monolithically integrated resonator micro-optic gyro on silica planar lightwave circuit,” J. Lightwave Technol. 18, 66–72 (2000).
[CrossRef]

K. Takiguchi and K. Hotate, “Evaluation of the output error in an optical passive ring-resonator gyro with a 90 polarization-axis rotation in the polarization-maintaining fiber resonator,” IEEE Photon. Technol. Lett. 3, 88–90 (1991).
[CrossRef]

Tang, C. L.

Targ, R.

G. A. Massey, M. K. Oshman, and R. Targ, “Generation of single-frequency light using the FM laser,” Appl. Phys. Lett. 6, 10–11 (1965).
[CrossRef]

Vannahme, C.

C. Vannahme, H. Suche, S. Reza, R. Ricken, V. Quiring, and W. Sohler, “Integrated optical Ti:LiNbO3 ring resonator for zero bias stability,” ECIO, Copenhagen, Denmark (2007).

Wang, J.

Wang, W.

H. Ma, W. Wang, Y. Ren, and Z. Jin, “Low-noise low-delay digital signal processor for resonant micro optic gyro,” IEEE Photon. Tech. L. 25, 198–201 (2013).
[CrossRef]

Yamazaki, H.

K. Iwatsuki, M. Saruwatari, M. Kawachi, and H. Yamazaki, “Waveguide-type optical passive ring-resonator gyro using time division detection scheme,” Electron. Lett. 25, 688–689 (1989).
[CrossRef]

Yang, Z.

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photon. Technol. Lett. 19, 1685–1687 (2007).
[CrossRef]

Yao, L.

Ying, D.

Z. Jin, Z. Yang, H. Ma, and D. Ying, “Open-loop experiments in a resonator fiber-optic gyro using digital triangle wave phase modulation,” IEEE Photon. Technol. Lett. 19, 1685–1687 (2007).
[CrossRef]

Yu, X.

Zarinetchi, F.

Zhang, C.

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Figures (10)

Fig. 1.
Fig. 1.

Schematic illustration of the RIOG based on triangular phase modulation. DFB-FL: distributed feedback fiber laser; ISO: isolator; IOR: integrated optical resonator; SG1, SG2: signal generators; C1, C2, C3: couplers; PD1, PD2: photodetectors.

Fig. 2.
Fig. 2.

Principle illustration of triangular phase modulation. (a) Resonance curve detected at PD2 induced by DFB-FL frequency sweep. (b) Triangular phase modulation corresponds to square wave frequency modulation. (c) Resonance curve and demodulation curve with triangular phase modulation. (d) Output of PD1 and PD2 when the gyro is at rotation state.

Fig. 3.
Fig. 3.

Schematic illustration of the signal processing scheme. (a) Signal processing scheme of the frequency-locking loop. (b) Signal processing procedure corresponds to the sample count.

Fig. 4.
Fig. 4.

Schematic model of the frequency-locking loop.

Fig. 5.
Fig. 5.

S-domain model of the frequency-locking loop.

Fig. 6.
Fig. 6.

Bandwidth influenced by the loop parameters. (a)–(d) are amplitude-frequency responses of the closed-loop transfer function when K, Ti, τl, and τd take different values, respectively.

Fig. 7.
Fig. 7.

Unit step response influenced by the loop parameters. (a)–(d) are unit step responses of the closed-loop transfer function when K, Ti, τl, and τd take different values, respectively.

Fig. 8.
Fig. 8.

Amplitude-frequency response and unit step response with the optimized parameters. (a) Amplitude-frequency response of the closed-loop transfer function. (b) Unit step response of the closed-loop transfer function.

Fig. 9.
Fig. 9.

Frequency-locking process of the RIOG.

Fig. 10.
Fig. 10.

Experiment results of the frequency-locking error and gyro output. (a) Equivalent frequency-locking error. (b) Output of the RIOG.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

f=12πd(ϕ(t))d(t).
Iout=kΔf,
{Igyro=k(fcwflaser)flaser=fccw+ferror,
Igyro=Ioutkferror.
H(s)=K11+τls(1+1Tis)eτds.
Φ(s)=H(s)1+H(s)=K(1+Tis)eτds(1+τls)Tis+K(1+Tis)eτds
Φe(s)=11+H(s)=(1+τls)Tis(1+τls)Tis+K(1+Tis)eτds.
ess=lims0sΦe(s)1s=lims0(1+τls)Tis(1+τls)Tis+AF(1+Tis)eτds=0.

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