## Quadrature demodulation with synchronous difference for interferometric fiber-optic gyroscopes |

Optics Express, Vol. 20, Issue 23, pp. 25421-25431 (2012)

http://dx.doi.org/10.1364/OE.20.025421

Acrobat PDF (1674 KB)

### Abstract

We propose a novel method of quadrature demodulation with synchronous difference for suppressing noise in interferometric fiber-optic gyroscopes (IFOGs). For an IFOG with sine wave phase modulation, an in-phase result and a quadrature result are obtained simultaneously by coherent detection. Eigenfrequency modulation is used and a phase shift of 45° is set between the modulation signal and the reference signal, so that two results have the same expectation of amplitude but with opposite signs. A synchronous difference procedure is carried out for output, in which signals are added up and common noise between two results is eliminated. Theoretical analysis and experimental results show that both short term noise and long term instability of the IFOG are reduced by this method. In experimental comparison with the traditional demodulation method on the same IFOG with a 1982 m fiber coil, this method reduces the bias drift from 0.040°/h to 0.004°/h.

© 2012 OSA

## 1. Introduction

1. E. J. Post, “Sagnac effect,” Rev. Mod. Phys. **39**, 475–493 (1967). [CrossRef]

2. H. J. Arditty and H. C. Lefèvre, “Sagnac effect in fiber gyroscopes,” Opt. Lett. **6**, 401–403 (1981). [CrossRef] [PubMed]

3. R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol. **2**, 91–107 (1984). [CrossRef]

5. G. B. Malykin, “On the ultimate sensitivity of fiber-optic gyroscopes,” Tech. Phys. **54**, 415–418 (2009). [CrossRef]

6. I. A. Andronova and G. B. Malykin, “Physical problems of fiber gyroscopy based on the Sagnac effect,” Phys. Usp. **45**, 793–817 (2002). [CrossRef]

13. R. C. Rabelo, R. T. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol. **18**, 2146–2150 (2000). [CrossRef]

*et al.*first applied intensity noise substraction in the IFOG in 1991, by utilizing the unused port of source coupler as a noise reference [12

12. R. P. Moeller and W. K. Burns, “1.06-ptm all-fiber gyroscope with noise subtraction,” Opt. Lett. **16**, 1902–1904 (1991). [CrossRef] [PubMed]

*et al.*and Polynkin

*et al.*[13

13. R. C. Rabelo, R. T. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol. **18**, 2146–2150 (2000). [CrossRef]

14. P. Polynkin, J. Arruda, and J. Blake, “All-optical noise-subtraction scheme for a fiber-optic gyroscope,” Opt. Lett. **25**, 147–149 (2000). [CrossRef]

*et al.*showed that intensity noise could be relegated to the quadrature channel by adjusting the modulation depth in sine wave modulated IFOGs, thus noise in the in-phase signal was reduced [9

9. J. Blake and I. S. Kim, “Distribution of relative intensity noise in signal and quadrature channels of a fiber-optic gyroscope,” Opt. Lett. **19**, 1648–1650 (1994) [CrossRef] [PubMed]

15. R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett. **5**, 173–175 (1980). [CrossRef] [PubMed]

19. O. Çelikel and F. Sametoǧlu, “Assessment of magneto-optic Faraday effect-based drift on interferometric single-mode fiber optic gyroscope (IFOG) as a function of variable degree of polarization (DOP),” Meas. Sci. Technol. **23**, 025104 (2012). [CrossRef]

*et al.*in 2011, by subtracting two signals with different polarities at the output [10

10. X. Wang, C. He, and Z. Wang, “Method for suppressing the bias drift of interferometric all-fiber optic gyroscopes,” Opt. Lett. **36**, 1191–1193 (2011). [CrossRef] [PubMed]

9. J. Blake and I. S. Kim, “Distribution of relative intensity noise in signal and quadrature channels of a fiber-optic gyroscope,” Opt. Lett. **19**, 1648–1650 (1994) [CrossRef] [PubMed]

12. R. P. Moeller and W. K. Burns, “1.06-ptm all-fiber gyroscope with noise subtraction,” Opt. Lett. **16**, 1902–1904 (1991). [CrossRef] [PubMed]

14. P. Polynkin, J. Arruda, and J. Blake, “All-optical noise-subtraction scheme for a fiber-optic gyroscope,” Opt. Lett. **25**, 147–149 (2000). [CrossRef]

10. X. Wang, C. He, and Z. Wang, “Method for suppressing the bias drift of interferometric all-fiber optic gyroscopes,” Opt. Lett. **36**, 1191–1193 (2011). [CrossRef] [PubMed]

## 2. Theory of quadrature demodulation for the synchronous difference

3. R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol. **2**, 91–107 (1984). [CrossRef]

20. A. Lompado, J. C. Reinhardt, L. C. Heaton, J. L. Williams, and P. B. Ruffin, “Full Stokes polarimeter for characterization of fiber optic gyroscope coils,” Opt. Express **17**, 8370–8381 (2009). [CrossRef] [PubMed]

21. Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. **37**, 2841–2843 (2012). [CrossRef] [PubMed]

*V*(

_{I}*t*) =

*V*sin(

_{f}*ω*). When eigenfrequency modulation is used [3

_{m}t3. R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol. **2**, 91–107 (1984). [CrossRef]

13. R. C. Rabelo, R. T. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol. **18**, 2146–2150 (2000). [CrossRef]

*ω*=

_{m}*π*/

*τ*, and the modulation introduced phase difference as This function ensures that the in-phase signal and the quadrature signal have the same expectation of amplitude but with opposite signs. In this case, the 1

*harmonic of detected signal is changed from Eq. (26) in Appendix to where*

^{st}*I*

_{0}is the source intensity coupled to the optical circuit,

*η*is the response of the PD,

*J*is the n

_{n}*Bessel function of the first kind, and*

^{th}*V*(

_{I}*t*) =

*V*sin(

_{f}*ω*) is used as the local oscillator (LO). The quadrature LO is a cosine wave

_{m}t*V*(

_{Q}*t*) =

*V*cos(

_{f}*ω*), which has a

_{m}t*π*/2 phase difference with

*V*(

_{I}*t*). The detected signal is multiplied by two LOs respectively, with amplitude scaling as Here

*h.c.*stands for high-frequency components, which do not affect final results. After low-pass filtering (LPF), we get useful DC components

*harmonic*

^{nd}*I*

_{2H}and

*ϕ*are derived in a traditional way (see Appendix). By substituting

_{b}*ϕ*and

_{I}*ϕ*for

_{Q}*ϕ*in Eq. (21) in Appendix respectively, we get two detection results of the rotation rate with different signs as Ω

_{s}*= −Ω, and Ω*

_{I}*= Ω. As shown by Eq. (8) and Eq. (9), the factor*

_{Q}## 3. Analysis of noise reduction in the synchronous difference

10. X. Wang, C. He, and Z. Wang, “Method for suppressing the bias drift of interferometric all-fiber optic gyroscopes,” Opt. Lett. **36**, 1191–1193 (2011). [CrossRef] [PubMed]

21. Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. **37**, 2841–2843 (2012). [CrossRef] [PubMed]

*N*

_{+}(

*t*) is common noise between Ω

*and Ω*

_{I}*, and*

_{Q}*N*

_{−}(

*t*) is differential noise between them.

*N*

_{1}(

*t*) and

*N*

_{2}(

*t*) are independent random noise parts. It should be noticed here that common noise and differential noise are defined between two outputs Ω

*and Ω*

_{I}*, in spite of different signs with Ω. As Ω*

_{Q}*(*

_{Q}*t*) and Ω

*(*

_{I}*t*) are obtained simultaneously, synchronous difference is conveniently carried out in the novel method to eliminate common noise as

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*) are orthogonal detection results of the same target Ω. Two signals modulated on the light wave travel through the same circuit simultaneously, thus both short term noise and long term instability in two results have a considerable common part in

*N*

_{+}(

*t*).

*N*

_{+}(

*t*). Short term noise mainly affecting the IFOG performance includes thermal noise, shot noise, and light intensity noise as [11

11. W. K. Burns, R. P. Moeller, and A. Dandridge, “Excess noise in fiber gyroscope sources,” IEEE Photonic. Tech. Lett. **2**, 606–608 (1990). [CrossRef]

**18**, 2146–2150 (2000). [CrossRef]

*T*,

*S*, and

*I*stands for thermal, shot, and intensity, respectively.

*k*is the Boltzmann constant,

*T*is absolute temperature,

*e*is electron charge, Δ

*ν*is the source bandwidth,

*R*is detection load resistance, <

_{L}*i*> is mean electric current at the PD, and

*B*is the detection bandwidth. As optical intensity noise is proportional to the square of the light intensity, it becomes the major component of short term noise at the output when the optical power reaching the detector is more than a few tens of microwatts [13

**18**, 2146–2150 (2000). [CrossRef]

9. J. Blake and I. S. Kim, “Distribution of relative intensity noise in signal and quadrature channels of a fiber-optic gyroscope,” Opt. Lett. **19**, 1648–1650 (1994) [CrossRef] [PubMed]

**18**, 2146–2150 (2000). [CrossRef]

*n*(

_{s}*t*) is the inherent intensity noise of the light source, and

*g*(

_{Q}*t*) =

*g*[

*t*− (

*π*/4

*ω*)] is the IFOG transfer function when Eq. (1) is used as phase modulation. Here

*g*(

*t*) is the IFOG transfer function when traditional sine wave modulation is used (see Appendix). The light intensity received by the PD is given by where

*I*is the detection signal without intensity noise (see Appendix). The noise part around the 1

_{D}*harmonic of sin(*

^{st}*ωt*) in the beat signal

*n*(

_{S}*t*)

*g*(

_{Q}*t*) should be considered, which finally affects detection results. If the 45° phase shift is not set between the modulation signal and reference signal, the distribution of this part of noise in the in-phase signal and the quadrature signal will not be equal in most cases [9

**19**, 1648–1650 (1994) [CrossRef] [PubMed]

*n*(

_{I}*t*),

*n*(

_{Q}*t*) are effective intensity noise in

*I*(

_{I}*t*) and

*I*(

_{Q}*t*), and

*n*

_{1}

*(*

_{H}*t*) is the noise part around the 1

*harmonic of sin(*

^{st}*ωt*) in

*n*(

_{PD}*t*). From this point of view, two channels have a considerable common part of short term noise in

*N*

_{+}(

*t*), although signals have opposite signs.

*(*

_{I}*t*), Ω

*(*

_{Q}*t*), Ω

*(*

_{out}*t*), and Ω

*(*

_{T}*t*) have mean values of −9.287°/h, 9.161°/h, 9.224°/h, and 9.358°/h, respectively. Noise amplitudes quantified by standard deviation are 1.667°/h, 1.726°/h, 0.604°/h, and 0.623°/h for Ω

*(*

_{I}*t*), Ω

*(*

_{Q}*t*), Ω

*(*

_{out}*t*), and Ω

*(*

_{T}*t*), respectively. Here Ω

*(*

_{I}*t*) is negative in accordance with Eq. (10). The noise in Ω

*(*

_{out}*t*) is obviously reduced by the difference procedure, as its deviation is much lower than single channel results Ω

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*). The noise amplitude in Ω

*(*

_{T}*t*) is also lower than Ω

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*), for the difference noise part between

*(*

_{out}*t*) is lower than Ω

*(*

_{T}*t*), indicating that intensity noise reduction by the linear difference procedure is more effective.

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*) are close to each other in accordance with Eq. (16). Ω

*(*

_{out}*t*) has the lowest noise amplitude among the four outputs in all considered SNRs, and its curve is much lower than single channel results Ω

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*). This is a clear evidence for the reduction of noise due to the synchronous difference procedure. Furthermore, the elimination of

*N*

_{+}(

*t*) in Eq. (12) is proved more effective than the difference noise reduction in Eq. (28), as the curve for Ω

*(*

_{out}*t*) is lower than the curve for Ω

*(*

_{T}*t*). When the SNR is higher than 40 dB, the intensity noise reduction is not so obvious as low SNRs, which in practice may be submerged by other kind of noise such as phase noise induced by vibration of light circuit. In other words, performance of different demodulation methods is similar to each other when noise amplitude is very low.

*(*

_{T}*t*) perform badly in low SNRs, where large values of bias appear. Unfortunately, the amplitude of intensity noise may fluctuate over time in applications. As a result, the bias of Ω

*(*

_{T}*t*) will wave up and done,

*i.e.*, the bias stability of Ω

*(*

_{T}*t*) will get worse due to unstable intensity noise. On the other hand, biases of Ω

*(*

_{out}*t*), Ω

*(*

_{I}*t*), and Ω

*(*

_{Q}*t*) are scarcely affected by the intensity noise. As the mathematical expectation of white Gaussian noise is zero, it contribute no bias or bias instability into the output if the system is linear. In the low rotation rate case, the Sagnac phase shift

*ϕ*is very small. For instance, in the experiment detecting the Earth’s rotation rate in next section,

_{S}*ϕ*= 1.774 × 10

_{S}^{−4}rad. In quadrature demodulation procedure described from Eq. (3) to Eq. (9), the only nonlinear functions are Eq. (8) and Eq. (9), which are almost linear when

*ϕ*is small and thus arctan(

_{S}*ϕ*) ≈

_{S}*ϕ*. However, Ω

_{S}*(*

_{T}*t*) is obtained by a nonlinear function as Eq. (28), even short term noise will affect its bias and bias stability.

*(*

_{out}*t*) has the lowest noise amplitude, and its bias is robust against short term noise.

*(*

_{I}*t*) and Ω

*(*

_{Q}*t*) can be written in terms of common part

*B*

_{+}(

*t*), differential part

*B*

_{−}(

*t*), and independent parts

*B*

_{1}(

*t*) and

*B*

_{2}(

*t*). Considering only long term instability, detection results can be written as Here the eliminated common part

*B*

_{+}(

*t*) also stands for the bias component independent of the polarity of the rotation rate. In many cases of practical IFOGs,

*B*

_{+}(

*t*) is the main part of total bias [10

**36**, 1191–1193 (2011). [CrossRef] [PubMed]

*B*

_{+}(

*t*) is thus effective for bias drift reduction in these IFOGs, where the main part of bias drift is intrinsically independent of the polarity of the rotation rate.

*, due to the elimination of the common noise term*

_{out}*N*

_{+}(

*t*). In this way, gyroscope precision is enhanced. These are proved by the following experimental results.

## 4. Experimental results

23. Y. Zhao, Y. Zheng, Y. Lin, and B. Li, “Step by step improvement of measurement methods for earth’s rotary rate using fiber optic gyro,” Measurement **44**, 1177–1182 (2011). [CrossRef]

*floor of a building, where human activities might introduce additional noise.*

^{th}*is reduced notably by the synchronous difference in comparison with Ω*

_{out}*and Ω*

_{I}*, as the output data is more concentrated. In the time domain results, we should also notice that there are some high spikes due to environmental acoustic vibrations. These spikes are mainly caused by human activities near our laboratory and appear only occasionally, thus they do not contribute much to long term statistical properties. Besides the occasional spikes, there are also contentious acoustic vibrations which have similar influence with other short term noise such as intensity noise and thermal noise. All these kinds of short term noise can be treated as a whole from a mathematical perspective, and be discussed together in the comparison.*

_{Q}*and Ω*

_{I}*is illustrated in Fig. 5 as a scatter diagram, where solid curves represent fitting curves of their PDFs with a Gaussian distribution model. The scatter center is on the 135° line in accordance with Eq. (3). To quantify the short term noise reduction, we use the standard deviation of each output data to calculate the SNR improvement as [13*

_{Q}**18**, 2146–2150 (2000). [CrossRef]

*σ*= 1.048°/h,

_{I}*σ*= 1.045°/h, and

_{Q}*σ*= 0.732°/h are standard deviation values for Ω

_{out}*, Ω*

_{I}*, and Ω*

_{Q}*, respectively. The enhancement has a value of at least*

_{out}*R*=3.09 dB from a single channel result to the final output, as an evidence of short term reduction in the synchronous difference procedure.

_{dB}*is similar to Ω*

_{out}*, which has a standard deviation of*

_{T}*σ*= 0.720°/

_{T}*h*≈

*σ*. This result is consistent with theoretical analysis at high SNRs of source intensity in Fig. 3, where intensity noise difference between Ω

_{out}*and Ω*

_{out}*is small and easily emerged by other kinds of noise. To further evaluate the performance difference between Ω*

_{T}*and Ω*

_{out}*, Allan variance method is used [24*

_{T}24. F. L. Walls and D. W. Allan, “Measurements of frequency stability,” Proc. IEEE **74**, 162–168 (1986). [CrossRef]

*σ*(

*τ*) versus cluster time

*τ*. A significant phenomenon is that long term noise is notably suppressed, for the curve goes down rapidly when

*τ*becomes larger. The numerical value of bias drift is obtained by reading the bottom of the curve. The bias drift of the traditional demodulated result Ω

*is 0.040°/h, and the value is reduced to 0.004°/h by the quadrature demodulation method for the same IFOG.*

_{T}25. O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. **16**, 35–43 (2009). [CrossRef]

## 5. Conclusions

## Appendix: Traditional sinusoidal phase modulation and demodulation for IFOGs

*L*and

*D*are the length and the diameter of the fiber coil,

*c*is the speed of light in vacuum,

*λ*is the effective wave length of the light source, and Ω is the rotation rate. The interference signal received by the PD can be written as where

*I*

_{0}is the source intensity,

*η*is the response of the PD, and

*g*(

*t*) is the is the transfer function of the IFOG. For sinusoidal modulation

*ϕ*(

_{m}*t*) =

*ϕ*

_{0}sin(

*ω*), we have In this case,

_{m}t*g*(

*t*) can be expanded by Bessel functions as

*J*is the n

_{n}*Bessel function of the first kind, and*

^{th}*ϕ*= 2

_{b}*ϕ*

_{0}sin(

*ω*/2). The eigenfrequency

_{m}τ*ω*=

_{m}*π*/

*τ*is suggested for optimal detection, so that

*ϕ*= 2

_{b}*ϕ*

_{0}[3

**2**, 91–107 (1984). [CrossRef]

**18**, 2146–2150 (2000). [CrossRef]

*ϕ*is determined by

_{b}*J*

_{4}(

*ϕ*)/

_{b}*J*

_{2}(

*ϕ*) =

_{b}*I*

_{4H}/

*I*

_{2H}, and

*ϕ*is obtained by Here

_{s}*I*is the amplitude of the n

_{nH}*harmonic. It is usually assumed that the light intensity and the modulation depth are stable,*

^{th}*i.e.*,

*I*

_{0}and

*ϕ*are both constants. Then only the 1

_{b}*harmonic is used for detection as whose amplitude is denoted by*

^{st}*I*

_{1H}, and the Sagnac phase shift is determined as

*I*

_{1H}(

*t*). Here

*I*is the amplitude of the in-phase signal of the 1

_{I}*harmonic, and*

^{st}*I*is the amplitude of the quadrature signal of the 1

_{Q}*harmonic. Then the detection result is derived by Eq. (25) or Eq. (27).*

^{st}## References and links

1. | E. J. Post, “Sagnac effect,” Rev. Mod. Phys. |

2. | H. J. Arditty and H. C. Lefèvre, “Sagnac effect in fiber gyroscopes,” Opt. Lett. |

3. | R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol. |

4. | H. C. Lefèvre, |

5. | G. B. Malykin, “On the ultimate sensitivity of fiber-optic gyroscopes,” Tech. Phys. |

6. | I. A. Andronova and G. B. Malykin, “Physical problems of fiber gyroscopy based on the Sagnac effect,” Phys. Usp. |

7. | P. Y. Chien and C. L. Pan, “Triangular phase-modulation approach to an open-loop fiber-optic gyroscope,” Opt. Lett. |

8. | D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett. |

9. | J. Blake and I. S. Kim, “Distribution of relative intensity noise in signal and quadrature channels of a fiber-optic gyroscope,” Opt. Lett. |

10. | X. Wang, C. He, and Z. Wang, “Method for suppressing the bias drift of interferometric all-fiber optic gyroscopes,” Opt. Lett. |

11. | W. K. Burns, R. P. Moeller, and A. Dandridge, “Excess noise in fiber gyroscope sources,” IEEE Photonic. Tech. Lett. |

12. | R. P. Moeller and W. K. Burns, “1.06-ptm all-fiber gyroscope with noise subtraction,” Opt. Lett. |

13. | R. C. Rabelo, R. T. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol. |

14. | P. Polynkin, J. Arruda, and J. Blake, “All-optical noise-subtraction scheme for a fiber-optic gyroscope,” Opt. Lett. |

15. | R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett. |

16. | K. Bohm, P. Marten, K. Petermann, E. Weidel, and R. Ulrich, “Low-drift fiber gyro using a superluminescent diode,” Electron. Lett. |

17. | E. Jones and J. W. Parker, “Bias reduction by polarisation dispersion in the fibre-optic gyroscope,” Electron. Lett. |

18. | S. L. A. Carrara, B. Y. Kim, and H. J. Shaw, “Bias drift reduction in polarization-maintaining fiber gyroscope,” Opt. Lett. |

19. | O. Çelikel and F. Sametoǧlu, “Assessment of magneto-optic Faraday effect-based drift on interferometric single-mode fiber optic gyroscope (IFOG) as a function of variable degree of polarization (DOP),” Meas. Sci. Technol. |

20. | A. Lompado, J. C. Reinhardt, L. C. Heaton, J. L. Williams, and P. B. Ruffin, “Full Stokes polarimeter for characterization of fiber optic gyroscope coils,” Opt. Express |

21. | Y. Yang, Z. Wang, and Z. Li, “Optically compensated dual-polarization interferometric fiber-optic gyroscope,” Opt. Lett. |

22. | D. Kim and J. Kang, “Sagnac loop interferometer based on polarization maintaining photonic crystal fiber with reduced temperature sensitivity,” Opt. Express |

23. | Y. Zhao, Y. Zheng, Y. Lin, and B. Li, “Step by step improvement of measurement methods for earth’s rotary rate using fiber optic gyro,” Measurement |

24. | F. L. Walls and D. W. Allan, “Measurements of frequency stability,” Proc. IEEE |

25. | O. Çelikel and S. E. San, “Design details and characterization of all digital closed-loop interferometric fiber optic gyroscope with superluminescent light emitting diode,” Opt. Rev. |

**OCIS Codes**

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(060.2800) Fiber optics and optical communications : Gyroscopes

**ToC Category:**

Sensors

**History**

Original Manuscript: July 13, 2012

Revised Manuscript: September 14, 2012

Manuscript Accepted: October 9, 2012

Published: October 25, 2012

**Citation**

Zinan Wang, Yi Yang, Yongxiao Li, Xiaoqi Yu, Zhenrong Zhang, and Zhengbin Li, "Quadrature demodulation with synchronous difference for interferometric fiber-optic gyroscopes," Opt. Express **20**, 25421-25431 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25421

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### References

- E. J. Post, “Sagnac effect,” Rev. Mod. Phys.39, 475–493 (1967). [CrossRef]
- H. J. Arditty and H. C. Lefèvre, “Sagnac effect in fiber gyroscopes,” Opt. Lett.6, 401–403 (1981). [CrossRef] [PubMed]
- R. A. Bergh, H. C. Lefèvre, and H. J. Shaw, “An overview of fiber-optic gyroscopes,” J. Lightwave Technol.2, 91–107 (1984). [CrossRef]
- H. C. Lefèvre, The Fiber-Optic Gyroscope (Artech House, 1993).
- G. B. Malykin, “On the ultimate sensitivity of fiber-optic gyroscopes,” Tech. Phys.54, 415–418 (2009). [CrossRef]
- I. A. Andronova and G. B. Malykin, “Physical problems of fiber gyroscopy based on the Sagnac effect,” Phys. Usp.45, 793–817 (2002). [CrossRef]
- P. Y. Chien and C. L. Pan, “Triangular phase-modulation approach to an open-loop fiber-optic gyroscope,” Opt. Lett.16, 1701–1703 (1991). [CrossRef] [PubMed]
- D. A. Jackson, A. D. Kersey, and A. C. Lewin, “Fibre gyroscope with passive quadrature detection,” Electron. Lett.20, 399–401 (1984). [CrossRef]
- J. Blake and I. S. Kim, “Distribution of relative intensity noise in signal and quadrature channels of a fiber-optic gyroscope,” Opt. Lett.19, 1648–1650 (1994) [CrossRef] [PubMed]
- X. Wang, C. He, and Z. Wang, “Method for suppressing the bias drift of interferometric all-fiber optic gyroscopes,” Opt. Lett.36, 1191–1193 (2011). [CrossRef] [PubMed]
- W. K. Burns, R. P. Moeller, and A. Dandridge, “Excess noise in fiber gyroscope sources,” IEEE Photonic. Tech. Lett.2, 606–608 (1990). [CrossRef]
- R. P. Moeller and W. K. Burns, “1.06-ptm all-fiber gyroscope with noise subtraction,” Opt. Lett.16, 1902–1904 (1991). [CrossRef] [PubMed]
- R. C. Rabelo, R. T. Carvalho, and J. Blake, “SNR enhancement of intensity noise-limited FOGs,” J. Lightwave Technol.18, 2146–2150 (2000). [CrossRef]
- P. Polynkin, J. Arruda, and J. Blake, “All-optical noise-subtraction scheme for a fiber-optic gyroscope,” Opt. Lett.25, 147–149 (2000). [CrossRef]
- R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett.5, 173–175 (1980). [CrossRef] [PubMed]
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