Abstract

We present an in-depth analysis of the transient response of a resonator fiber optic gyro based on triangular wave phase modulation. Unusual effects have been observed in the process of tracking the resonant frequency of an optical fiber ring resonator (OFRR). There is a distortion phenomenon, unlike the ideally square wave or a pure DC output of the OFRR, but signal overshoot or undershoot occurs. A deep analysis of the influence of the nonideal square wave or pure DC output on gyro performance is fully developed for the first time, to the best of our knowledge. Further analysis shows that this is the transient response process after modulation by the triangular wave, and the process is related both to the parameters of the OFRR and the modulation frequency of the triangular wave. By sampling the steady-state signal of the distortion square wave, or by oversampling the distortion signal to get a number of data, and then accumulating and averaging these data to be demodulated, the distortion’s effect can be considerably decreased.

© 2010 Optical Society of America

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  1. S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
    [CrossRef]
  2. G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MA3.
  3. A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.
  4. S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MC1.
  5. G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper ME6.
  6. K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466–473 (1997).
    [CrossRef]
  7. 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 Photonics Technol. Lett. 19, 1685–1687(2007).
    [CrossRef]
  8. D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
    [CrossRef]
  9. H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
    [CrossRef]
  10. D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (2007).
  11. K. Kalli and D. A. Jackson, “Analysis of the dynamic response of a ring resonator to a time-varying input signal,” Opt. Lett. 18, 465–467 (1993).
    [CrossRef] [PubMed]
  12. L. F. Stokes, M. Chodorow, and H. J. Shaw, “All single mode fiber resonator,” Opt. Lett. 7, 288–290 (1982).
    [CrossRef] [PubMed]
  13. Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

2010 (1)

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

2008 (1)

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
[CrossRef]

2007 (2)

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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (2007).

2006 (1)

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

1997 (1)

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466–473 (1997).
[CrossRef]

1993 (1)

1982 (1)

1977 (1)

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

Balsmo, S. K.

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

Chodorow, M.

Ezekiel, S.

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

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MC1.

Harumoto, M.

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466–473 (1997).
[CrossRef]

Hotate, K.

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466–473 (1997).
[CrossRef]

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

Jackson, D. A.

Jin, Z.

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
[CrossRef]

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

Kalli, K.

Kumagai, T.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

Kurokawa, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

Li, M.

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

Ma, H.

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
[CrossRef]

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

Nakamura, S.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

Ohno, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

Pavlath, G. A.

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MA3.

Qiu, T.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper ME6.

Sanders, G. A.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper ME6.

Shaw, H. J.

Shen, Q.

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

Stokes, L. F.

Strandjord, L. K.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper ME6.

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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

Ying, D.

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
[CrossRef]

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

Yu, F.

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

Zhang, G.

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

Zheng, Y.

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (2007).

Appl. Phys. Lett. (1)

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

Chin. J. Sens. Actuators (2)

D. Ying, Y. Zheng, H. Ma, and Z. Jin, “Splitting phenomenon of resonance dips in two-frequency serrodyne modulation R-FOG,” Chin. J. Sens. Actuators 20, 1245–1248 (2007).

Q. Shen, F. Yu, H. Ma, and Z. Jin, “All digital close-loop operation of resonator fiber optic gyro,” Chin. J. Sens. Actuators 19, 810–817 (2006).

IEEE Photonics Technol. Lett. (1)

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 Photonics Technol. Lett. 19, 1685–1687(2007).
[CrossRef]

J. Lightwave Technol. (1)

K. Hotate and M. Harumoto, “Resonator fiber optic gyro using digital serrodyne modulation,” J. Lightwave Technol. 15, 466–473 (1997).
[CrossRef]

Opt. Commun. (1)

D. Ying, H. Ma, and Z. Jin, “Resonator fiber optic gyro using the triangle wave phase modulation technique,” Opt. Commun. 281, 580–586 (2008).
[CrossRef]

Opt. Lasers Eng. (1)

H. Ma, G. Zhang, M. Li, and Z. Jin, “Zero-deviation effect in a resonator optic gyroscope caused by nonideal digital ramp phase modulation,” Opt. Lasers Eng. 48, 933–939(2010).
[CrossRef]

Opt. Lett. (2)

Other (4)

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MA3.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors ConferenceOSA Technical Digest (Optical Society of America, 2006), paper MA4.

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper MC1.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference, OSA Technical Digest (Optical Society of America, 2006), paper ME6.

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Figures (9)

Fig. 1
Fig. 1

System configuration of the RFOG based on the triangular wave phase modulation. FL, fiber laser; ISO, isolator; PM1, PM2, phase modulators; CW, clockwise; CCW, counterclockwise; C1, C2, C3, C4, couplers; PD1, PD2, photodetectors; LIA1, LIA2, lock-in amplifiers; FBC, feedback circuit; SG1, SG2, signal generators; Syn, synchronized signal; OFRR, optical fiber ring resonator.

Fig. 2
Fig. 2

Measured resonant curve of the OFRR with symmetrically digital triangular wave phase modulation. (a) Splitting phenomenon of the resonance dips, (b) waveform enlarged from point A, (c) waveform enlarged from point B, and (d) waveform enlarged from point C.

Fig. 3
Fig. 3

Calculated output signals at photodetector PD1. (a) f 0 = f R , (b) f 0 = f R 40 kHz , (c) f 0 = f R + 40 kHz , (d) f 0 = f R 160 kHz , (e) f 0 = f R 320 kHz . f 0 is the central frequency of the fiber laser, f R is the resonant frequency of the OFRR, the modulation index M and the modulation frequency F of the triangular wave are 2 π and 80 kHz , respectively.

Fig. 4
Fig. 4

Calculated resonant curves of the OFRR with triangular wave phase modulation. The modulation frequency F is 80 kHz .

Fig. 5
Fig. 5

Relationships between the amplitude of the signal undershoot and overshoot and the modulation frequency F. The fractional loss of the fiber α L takes three different values of 0.05 dB , 0.01 dB , and 0.005 dB . (a) Undershoot and (b) overshoot.

Fig. 6
Fig. 6

Relationship between N m and the fractional intensity loss of the coupler α c .

Fig. 7
Fig. 7

Output signals at PD. The parameters of the OFRR take the values of a L = 0.0114 , a C = 0.088 , and k C = 0.1 for (a) and (b); a L = 0.0012 , a C = 0.03 , and k C = 0.03 for (c) and (d). The laser frequency takes the values of f 0 = f R for (a) and (c), f R + 200 kHz for (b) and (d).

Fig. 8
Fig. 8

Comparison between the ideal demodulation and the practical demodulation sampled from the steady-state data. Modulation index M is 2 π , modulation frequency F is 80 kHz . The ideal demodulation curve, which is labeled by asterisks, is the demodulation signal based on the ideal square waveform. The experimental data, labeled by open circles, is based on the steady-state signal demodulation.

Fig. 9
Fig. 9

Photodetector output signal and demodulation signals of the OFRR with modulation frequency F of 300 kHz . (a) Photodetector output when the laser frequency is equal to the resonant frequency of the OFRR, (b) photodetector output when the laser frequency takes the value of f 0 = f R + 300 kHz , and (c) demodulation signal; the solid curve is the ideal demodulation curve and the dashed curve is the demodulation signal after averaging.

Tables (1)

Tables Icon

Table 1 Relationship between the Modulation Frequency F and the Response Time t d ( = N m τ )

Equations (20)

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E laser ( t ) = E 0 exp [ i ( 2 π f 0 t + φ 0 ) ] ,
E P M 1 _ out ( t ) = ( 1 α C 1 ) ( 1 α P M 1 ) / 2 · E 0 exp { j [ 2 π f 0 t + M v ( t ) + φ 0 ] } = ( 1 α C 1 ) ( 1 α P M 1 ) / 2 · E 0 exp [ j ( 2 π f 0 t + φ 0 ) ] n = A n exp [ j ( n 2 π F t ) ] ,
A n = 1 T 1 / 2 F 1 / 2 F e j M V ( t ) · e j n 2 π F t d t = 1 T 1 / 2 F 0 e j M · 2 Ft · e j n 2 π F t d t + 1 T 0 1 / 2 F e j M · 2 Ft · e j n 2 π F t d t = 1 2 · e j ( m + n π ) 2 · sinc ( M + n π 2 π ) + 1 2 · e j ( M n π ) 2 · sinc ( M n π 2 π ) ,
E FRR _ out ( t ) = ( 1 α C 1 ) ( 1 α C 2 ) ( 1 α P M 1 ) 2 E 0 exp ( j φ 0 ) × n = A n exp ( j 2 π f n t ) h n exp ( j ϕ n ) ,
h n = ( 1 α C 4 ) { 1 ρ · ( 1 Q ) 2 ( 1 Q ) 2 + 4 Q sin 2 [ π ( Δ f + n F ) / FSR ] } ,
ρ = 1 ( T T Q R ) 2 ( 1 α C 4 ) ( 1 Q ) 2 ,
ϕ n = arctan { R sin [ 2 π ( Δ f + n F ) / FSR ] T + ( T Q + R ) Q ( 2 TQ + R ) cos [ 2 π ( Δ f + n F ) / FSR ] } ,
T = ( 1 k C 4 ) ( 1 α C 4 ) , R = k C 4 ( 1 α C 4 ) 1 α L , Q = T · 1 α L ,
V PD 1 _ out = P n = m = A n ( M ) A m * ( M ) exp [ j 2 π ( n m ) F t ] h n h m * exp [ j ( ϕ n ϕ m ) ] .
P = 1 8 ( 1 α C 1 ) ( 1 α C 2 ) ( 1 α C 3 ) ( 1 α P M 2 ) N I 0 ,
E out = E in · T e j θ + n = 0 N 1 E cross n + n = N E cross n ,
E cross 1 = n = 0 N 1 E cross n = E in · b n = 0 N 1 c n e j [ θ m + ( n N + 1 ) Δ θ ] ,
E cross 2 = n = N E cross n = E in · b n = N c n e j [ θ m - ( n - N + 1 ) Δ θ ] ,
b = R · e - j ω τ , c = Q · e - j ω τ ,
E cross 1 = b n = 0 N 1 c n e j [ θ m + ( n N + 1 ) Δ θ ] = b · e j [ θ m + ( 1 N ) Δ θ ] [ 1 ( c · e j Δ θ ) N ] 1 c · e j Δ θ ,
E cross 2 = n = N E cross n = b n = N c n e j [ θ m ( n N + 1 ) Δ θ ] = b · c N · e j ( θ m Δ θ ) 1 c · e j Δ θ .
| E 1 cross | | E 2 cross | η .
t d = N m τ .
| b · e j [ θ m + ( 1 N ) Δ θ ] [ 1 ( c e j Δ θ ) N ] 1 c e j Δ θ | | b · c N · e j ( θ m Δ θ ) 1 c · e j Δ θ | η .
| [ 1 ( c · e j Δ θ ) N ] c N | η · | 1 c · e j Δ θ 1 c · e j Δ θ | .

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