Performance parameters of the designed IFOG prototype (analog closed-loop configuration).
A depolarized fiber optic gyroscope (DFOG) prototype with closed-loop configuration, sinusoidal-bias, and serrodyne-feedback electrooptic phase modulations was designed. A complete optoelectronic design is realized by using computational simulation tools (optical subsystem: Synopsys®-Optsim™ software and electronic subsystem: National Instruments®-MultiSim™ software). The design presented here includes both optical and electronic circuits, being the main innovation, is the use of an analogical integrator provided with reset and placed in the feedback of the electrooptic phase-modulation chain that produces a serrodyne-shaped voltage ramp signal for obtaining the interferometric signal phase cancellation. The performance obtained for this model (threshold sensitivity ≤0.052°/h; dynamic range = ± 78.19°/s) does reach the IFOG intermediate grade (tactical and industrial applications) and does demonstrate the suitability and reliability of simulation-based software tools for this kind of optoelectronic design.
- interferometric-fiber-optic-gyroscope (IFOG)
- depolarized-fiber-optic-gyroscope (DFOG)
- super-luminescent-laser-diode (SLD)
- single-mode-fiber (SMF)
- phase-modulator (PM)
- closed-loop configuration
- bias phase-modulation
- feedback phase-modulation
- IFOG intermediate grade
- IFOG navigation grade
- phase-sensitive-demodulator (PSD)
- Lyot depolarizer
In all the electro-optical engineering areas, particularly in the design of high-cost devices like IFOGs, the computational simulation resources can provide a powerful and inestimable advance. It stems from the rapidity, the reproducibility, and the reliability of this kind of hardware to obtain the ultimate design of a preconceived model. Furthermore, it is possible to obtain substantial cost savings in components and time consuming for the model assembly in optical bench. Only after having obtained an ideal design so much for the performance characteristics all that for the adaptation to a specific application, it is suitable to initiate the laboratory manufacture stage for the prototype designed previously. In this article, it is shown to the reader an aspect that is not usually in the literature, namely: how to realize the simulation of a classical IFOG system without having to make the real model in the laboratory. For this proposal, three classical electrooptic simulation tools: Synopsys™ OptSim®, National Instruments™ MultiSim® and MathWorks™ Matlab-Simulink® will be used. In the present decade, the design trends on interferometric fiber optic gyroscope (IFOG) are focused on devices with very high performance (navigation-grade, sensitivity ≤0.001°/h), mainly targeting aeronautics and spacecraft applications. Nevertheless, it is also possible to realize designs for certain applications that do not need such a high grade of performance (intermediate-grade, sensitivity ≤0.01°/h or industrial-grade, sensitivity ≤1°/h). The latter mentioned will constitute the objective of the model presented. What continues next is a brief overview of the basis of IFOG performance.
The nonreciprocal phase shift between the two waves in counter-propagation (clockwise and counterclockwise) induced by rotation when both propagate across the sensing coil of optical-fiber, also known as Sagnac effect, is usually given by the expression (see, for instance, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]):
2. Sensor design
2.1. Design of the optical system
The components of the optical system of this gyroscope are depicted in Figure 1. The light source is a 1310 nm superluminescent diode (SLD) with a Gaussian low ripple spectral profile. For this unit, the commercial reference SLD1024S of Thorlabs was used, with DIL-14 pin assembly package, with FC/APC fiber pigtailing and realized in standard single-mode optical fiber. This unit provides an adjustable optical power up to 22 mW maximum level, although only 5 mW maximum level is needed for the present model. This unit takes an integrated thermistor to perform the temperature control, so that it is possible to obtain the stabilization of the power source on the spectral range. Accordingly with the temperature stabilization, the chip package must not exceed a maximum temperature of 65°C. The directional optical coupler is four ports (2 × 2 configuration), with 50/50 output ratio, realized with fiber-optic side-polished technique, and an insertion loss of 0.60 dB. The linear polarizer placed at the output of the directional input-output coupler is featured in polarization-maintaining fiber (PMF) with a 2.50 m length, insertion loss of 0.1dB, and a polarization extinction ratio (PER) > 50 dB. The integrated optical circuit IOC (integrated optical chip) performs the function of optical directional coupler at the input of the sensing fiber-optic coil (Y-Junction) and also the function of electro-optic phase modulator (PM). In a more advanced design, the linear fiber-optic polarizer can be replaced by an integrated approach, so that the former remains joined at the input of the IOC wave-guide . This way, the bulk optic polarizer is avoided, which is one important contribution to reduce the whole space occupied by the optical system of the gyroscope.
The chosen PM is electro-optical class. Its electrodes remain parallel to the wave-guide channels obtained by diffusion of Ti on a lithium-niobate (LiNbO3) substrate. The PM zone of the IOC includes two pairs of electrodes placed symmetrically with regard to the central axis of the integrated block. The output ports of the IOC remain connected, respectively, to the heads of the two Lyot depolarizers (both made on PM-fiber), with lengths L1 and L2, respectively. These Lyot depolarizers are realized in polarization-maintaining optical fiber (PMF), connecting two segments appropriate lengths, so that the axes of birefringence of both form angles of 45°.
Calculations of Lyot depolarizer lengths are shown next. Calculated lengths L1 and L2 of the Lyot depolarizers summarize 26.20 and 52.40 cm, respectively.
These calculations were realized taking into account a 26.20 μm value for the coherence length of a broadband light source (emitting at 1310 nm wavelength) and a 13.10 mm value for the beat length of optical fiber. The two optical waves CW (clockwise) and CCW (counterclockwise) coming from the sensing coil gather together on the Y-Junction placed at the input of the IOC. The sensing coil consists of 300 m of optical standard single-mode fiber (commercial type SMF28), made by quadrupolar winding on a spool of 8 cm average-diameter, which provides 1194 turns. This optical fiber presents the following structural characteristics: step refractive index, basis material = fused-silica, external coating = acrylate, core diameter = 8.2 μm, cladding diameter = 125 ± 0.7 μm, and external coating diameter = 245 ± 5 μm, with the following optical parameters: ncore = 1.467, ncladding = 1.460, NA = 0.143, maximum attenuation = 0.35 dB/km at 1310 nm, h-parameter = 2×10−6 m−1, dispersion coefficient ≤ 18.0 ps/(nm × km) at 1550 nm, polarization dispersion coefficient ≤ 0.2 ps/km½, birefringence: B = 1.0×10−6.
The chosen PM is electro-optical class. Its electrodes remain parallel to the wave-guide channels obtained by diffusion of Ti on a lithium-niobate (LiNbO3) substrate. The PM zone of the IOC includes two pairs of electrodes placed symmetrically with regard to the central axis of the integrated block. The output ports of the IOC remain connected, respectively, to the heads of the two Lyot depolarizers (both made on PM-fiber), with lengths L1 and L2, respectively. These Lyot depolarizers are realized in polarization-maintaining optical fiber (PMF), connecting two segments of appropriate lengths, so that the axes of birefringence of both form angles of 45°.
2.2. Design of the electronic system
In absence of rotation (Ω = 0 rad/s), the transit-time of the two counter-propagated waves across the sensing coil is seconds, being its value:
With the values of parameters adopted previously for the model design, assuming 1467 for ncore value and using 1194 turns of optical-fiber wrapped on standard fiber-optic coil, the resultant value for the transit time is
resulting, for the present design in a calculated value of 340.83 kHz. Equation (3) comes from the condition of maximum amplitude of the bias phase-difference modulation for the optical wave, which is possible to formulate by the following expression:
The condition of maximum amplitude needs the 2π
However, and this is the novelty, it has been changed the structure of feedback chain, adding now a new design of analogical integrator which incorporates one FET transistor (2N3848) as it is depicted in Figure 3. The function of this transistor is realizing periodically the shortcut of the capacitor therefore nulling instantaneously the voltage on feedback branch of integrator OPAMP. The time period for shortcut FET transistor is driving by the value of
Referring to Figure 3, block #7 generates a linear ramp voltage
In accordance with the interference principle, the light intensity at the photodetector optical input presents the following form (for sinusoidal phase-modulation):
This way, the time variation of the voltage signal V
Therefore, the output signal of the phase modulator will be the sum of the phase-difference signals associated with the
3. Calculations and estimations
This design has been simulated using Matlab-Simulink™ The MathWorks® and MultiSim™ National Instruments®. (Note that Synopsys® OptSim™ original version software only allows implementing APD-type photodetectors on optical circuit design, consequently an APD-PIN equivalent current-conversion will be necessary for connecting the simulation results to IFOG prototype designed in this article, which owes PIN photodetector). The open-loop scale factor K0 can be calculated (being c ≈ 3 × 108 m/s the speed of light in vacuum) as:
The parameters of the model were chosen as fiber coil length L = 300 m, fiber coil diameter D = 80 mm, number of turns in the coil N = 1194, and light source wavelength λ = 1310 nm. The average optical-power at detector optical-input is
The threshold sensitivity considers the SNR at photodetector optical input provided by the optical simulation, and the dynamic range and scale factor are determined by the sine function nonlinearity (assuming the maximum value ). In the formulae,
4. Simulation results
Three different kinds of computer simulations have been realized. First, the control system simulation has been realized using Matlab-Simulink™ for determining the 2% settling-time
Figure 7 represents the parametric model of IFOG´ electro-optical system. It is depicted as a parameterized block diagram corresponding to electro-optical system equivalent to the gyroscopic sensor. Here, it is taking into account the values of the parameters identified on its optical and electronics circuits. The system’s step-response curve (obtained with Matlab-Simulink®) is shown in Figure 8. A settling time
Considering an input value of 210 μW as the average optical power value providing by light source, 145.61 μW were obtained at the optical input of photodetector, which means a power loss of −9.837808 dBm. Calculation of photon-shot-noise photocurrent at photodetector, taking into account 100 μA for average real value of photocurrent at its electrical output, is the following:
Note that lower the photon-shot-noise photocurrent value, lower is the threshold sensitivity of IFOG sensor and therefore also higher is its accuracy. On the other hand, it is needed to say that for low level of optical power coupled into photodetector, the main optical noise source of IFOG-sensor is photon shot noise (excess RIN can be neglected). This way, in accordance with photon-shot-noise photocurrent above calculated, the threshold sensitivity of gyro sensor (that is to say, the minimum rotation-rate which is able to measure) can be calculated as shown next (this value is collected in Table 1):
Figures 12–14 represents the electrical interferometric signal (in APD photo-current form, after electrical BP filtering,
The results of electronic circuits’ simulation (realized by MultiSim™ software) collect the waveforms voltage on the following test-point voltage:
The expansion of Eq. (5) with only the contribution of first two time-component harmonics allows obtaining an approximate value for detected photo-current. The result of this approximation is:
being the maximum value of detected photo-current and the amplitude of differential phase-modulation. Assuming the value, this value corresponding to the maximum value of function , the following Bessel functions calculations are obtained:
then, taking into account 100 μA as the DC average detected photodetector-current and after some numerical adjusts, Eq. (9) yields the following analytical value:
This analytical expression allows to calculate for every rotation-rate Ω value (i.e., Sagnac phase shift) the DC term and the first and second harmonics terms. These terms can later be introduced as current DC and AC generators on MultiSim™ circuit simulation program (block 1 on Figure 4). By this means,
Table 3 shows data obtained for 0 to ±10 [°/s] dynamic range with a step of 1°/s, and Figure 22 shows the corresponding VΩ versus Ω graphical representation. Table 4 shows data obtained for 0 to ±1 [°/s] dynamic range with a step of 0. 10°/s, and Figure 23 shows the corresponding VΩ versus Ω graph. Tables 2
from correlation values of both curves (output data curve and linear fitting curve), it can be determined the non-linearity percentage coefficient of the SF, defined as the percentage of the standard deviation, which can be calculated by the following expression:
so that in our case, for full dynamic range with N = 17 and taking the values obtained from Table 2, this expression yields a value of 4.386%. For Table 3 Eq. (12) reaches the value of 0.838% and for Table 4 its value is 0.0%. This values agree with these obtained for commercial IFOG units of similar characteristics.
5. Discussion of simulation results
The results obtained for the performance parameters of the gyroscope model designed in this article (threshold sensibility = 0.052°/h, dynamic range = ±78.19°/s, scale factor nonlinearity = 4.836%) are sufficient for intermediate grade gyroscopic applications, such as stabilization, pointing, and positioning of mobile platforms or inertial-navigation systems for terrestrial robots and automotive vehicles [31, 32, 33, 34, 35, 36].
The effects of the different types of optical noise [37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50] which take place are not critical in the specific design of this sensor, since its operation works in a medium level of optical-power and the signal-to-noise-ratio (SNR) is relatively high at photodetector’s optical-input (SNR > 100 dB). The most important type of optical-noise for this sensor is photon-shot-noise on photodetector, with a 3.31 pA noise-equivalent-current value, this value being much less than 100 μA that is the average photocurrent value for photodetector electrical output signal, in zero rotation-rate conditions. This type of noise is not susceptible of correction, since it owes to intrinsic quantum-mechanical mechanism of photoconductivity (electron–hole production by photonic shoot).
The relative intensity noise (RIN) is an important issue in this design, since it works at a medium-level of average optical-power coupled to photodetector optical-input (145.61 μW average optical-power value). This type of noise stems from two causes: (1) the two interfering optical waves do not come to photodetector with the same optical power level, due to polarization crosstalk between the two orthogonal polarizations states along the entire length of sensing fiber-coil (due to fiber-birefringence phenomenon), and (2) the light source is low-coherence (broadband source), thereby producing several beat wavelengths, which add at photodetector optical-input, causing a variation in relative intensity on every point of photodetector’s response-curve. This noise can be minimized by reducing the optical power emitted by light source. But a very large reduction in optical power also lowers the SNR at the photodetector, so that to maintain it at a high level, the optical power emitted by light source cannot be reduced greatly.
The noise associated with the fiber nonlinear Kerr effect is based on the electro-optical phenomenon which consists in changes experienced by refractive index of the optical fiber caused when it is excited by an optical wave that varies in amplitude. This occurs by the fluctuation of the optical power level of light source. In the case of the gyroscopic system, this optical power variation coupled to the fiber coil causes changes on its refractive index, which results in a phase change in the optical wave propagated along the length of the optical fiber coil. This change can be evaluated as a phase-equivalent noise and could be diminished efficiently using a low coherence light source (broadband source). Another important aspect is providing the light source with a thermal stabilization system to achieve a constant level of optical power emission.
The Shupe thermal effect is due to local temperature gradients along the fiber coil length. These temperature gradients induce phase changes in the optical waves traveling through the fiber. This effect can be minimized performing an appropriate winding of fiber-coil, so that a uniform temperature distribution is achieved throughout its entire length. The quadrupolar winding (number of turns in each layer of coil equal to an integer multiple of four) fulfills this condition. Other minor optical noise sources with less effect on the optical signal detected by photodetector are due to backscattering and reflections phenomena along the length of the sensing fiber-coil. A serious disadvantage for this model design is that the results of optical simulation do not allow realizing the evaluation of the main sources of optical noise.
Regarding the electrical noise generated by the electronic circuits, the most important is white noise (thermal-noise or Johnson noise), which spreads equally over all the frequencies. An appropriate way for overcoming this noise source is performing a selective filtering at the frequency of the desired signal and fitting later the gain of the amplification stages to increase the electrical SNR at the output. In the case of the designed IFOG circuits, a strict design of LPF (Low-Pass-Filter) and BPF (Band-Pass-Filter) is necessary after photodetector-amplifier. It is crucial for obtaining a good scale-factor linearity of designed IFOG-model. It is due to the fact that it depends on linearity of the obtained VΩ versus Ω graphical representation derived from signal demodulation process.
An IFOG prototype was theoretically designed by means of simulating tools. The conventional IFOG design with sinusoidal phase modulation is based on open-loop configuration. The main innovation of IFOG-design presented here is the use of a simple closed-loop electro-optical configuration, realized by means of optical and electronic cost competitive components. Furthermore, the proposed design also allows to reach substantial progress in stability and linearity of the Scale Factor (SF), dynamic range and threshold sensitivity of the gyroscope, compared to previous models proposed with the same fiber-optic coil length (L = 300 m). The cost advantage in optical subsystem is obtained by means of a design with depolarization of optical waves, by using two Lyot depolarizers, both realized in optical fiber. This allows using a sensing coil made in optical standard fiber, instead of a special polarization maintaining fiber, which is much more expensive. On the other hand, the electronic circuit subsystems (detection, demodulation, and feedback signal processing) is based on a conventional analog design, using classic electronic components which are high precision and cost competitive, so that it also contributes to achieving a reasonable cost and at the same time optimizing quality/price ratio of final device. An interesting observation regarding to cost is that if the entire volume occupied by the device does not suppose a major restriction (this condition is fulfilled in certain applications), it is possible to get an additional saving cost by means of a particular design of optical subsystem. This design can be based on a suitable selection of bulk optical components: the Integrated Optical Circuit (IOC) can be replaced with two 2 × 2 fiber optical couplers (SMF fiber), a fiber polarizer, and a fiber-based electro-optic phase modulator (PZT), since until the day the IOC is not standard-manufacture. The same way, for light source it is possible using a low-power and limited-consumption laser, as an Erbium-Doped-Fiber-Amplifier (EDFA), and for depolarization of the optical wave a new solution based on bulk optics can be adopted, such as crystal Lyot depolarizers.
Lefèvre HC. The Fiber-Optic Gyroscope. Second ed. Boston-London: Artech House; 2014
Ezekiel S, Arditty HJ. Fiber-Optic Rotation Sensors. Berlin: Springer-Verlag; 1982
Lawrence A. Modern Inertial Technology: Navigation, Guidance, and Control. 2nd ed. New-York: Springer-Verlag; 1992
Sagnac G. L’ether luminex demontre par l’effect du vent relatif d’ether dans un interferometre en rotation uniforme. Comptes Rendus de l'Académie des Sciences. 1913; 95:708-710
Sagnac G. Sur la preuve de la realité de l’ether luminex par l’experience de l'interferographe tournant. Comptes Rendus de l'Académie des Sciences. 1913; 95:1410-1413
Hariharan P. Sagnac or Michelson-Sagnac interferometer. Applied Optics. 1975; 14(10):2319-2321
Bergh RA, Lefevre HC, Shaw HJ. Overview of fiber-optic gyroscopes. IEEE Journal of Lightwave Technology. 1994; LT-2:91-107
Bergh RA, Lefevre HC, Shaw HJ. All-single-mode fiber-optic gyroscope. Optics Letters. April 1981; 6(4):198-200
Moeller RP, Burns WK, Frigo NJ. Open-loop output and scale factor stability in a fiber-optic gyroscope. Journal of Lightwave Technology. Feb. 1989; 7(2):262-269
Bohm K, Petermann K. Signal processing schemes for the fiber-optic gyroscope. Proceedings of SPIE, Fiber Optic Gyros: 10th Anniversary Conf. 1986:36
Burns WK et al. Fiber-optic gyroscopes with depolarized light. Journal of Lightwave Technology. 1992; 10(7):992-998
Szafraniec B et al. Theory of polarization evolution in Interferometric fiber-optic depolarized gyros. Journal of Lightwave Technology. 1999; 17(4):579-590
Kintner EC. Polarization control in optical-fiber gyroscopes. Optics Letters. 1981; 6(3):154-156
Sanders GA, Szafraniec B. Progress in fiber-optic gyroscope applications II with emphasis on the theory of depolarized gyros. AGARD/NATO Conf. Report on Optical Gyros and Their Applications, AGARDougraph. 1999; 339:11/1-1142
Pavlath GA. Productionization of fiber gyros at Litton guidance and control systems. SPIE Proceedings. 1991; 1585:2-5
Sanders GA, Szafraniec B, Liu R-Y, Laskoskie C, Strandjord L. Fiber optic gyros for space, marine and aviation applications. SPIE Proceedings. 1996; 2837:61-71
Patterson RA, Goldner EL, Rozelle DM, Dahlen NJ, Caylor TL. IFOG technology for embedded GPS/INS applications. SPIE Proceedings. 1996; 2837:113-123
Lefèvre HC et al. Integrated Optics: a Practical Solution For The Fiber-Optic Gyroscope. Proc. SPIE 0719, Fiber Optic Gyros: 10th Anniversary Conf. 101, March 11, 1987. 101-112. DOI: 10.1117/12.937545
Kim BY et al. Response Of Fiber Gyros To Signals Introduced At The Second Harmonic Of The Bias Modulation Frequency. Proc. SPIE 0425, Single Mode Optical Fibers, 86, November 08 1983. DOI: 10.1117/12.936218
Kim BY et al. Gated phase-modulation feedback approach to fiber gyroscopes. Optics Letters. 1984; 9(6):263-265
Kim BY et al. Gated phase-modulation feedback approach to fiber gyroscopes with linearized scale factor. Optics Letters. 1984; 9:375-377
Kim BY et al. Phase reading all-fiber-optic gyroscope. Optics Letters. 1984; 9:378-380
Böhm K et al. Signal processing schemes for the fiber-optic gyroscope. Proc. SPIE 0719, Fiber Optic Gyros: 10th Anniversary Conf. 101, March 11 1987. DOI: 10.1117/12.937536
Moeller RP et al. Open-loop output and scale-factor stability in a fiber-optic-gyroscope. Journal of Lightwave Technology. 1989; 7(2):262-269
Ebberg A et al. Closed-loop fiber-optic gyroscope with a Sawtooth phase-modulated feedback. Optics Letters. 1985; 10(6):300-302
Kay CJ et al. Serrodyne modulator in a fibre-optic gyroscope. Optoelectronics, IEEE Proceedings Journal. 1985; 132(5):259-264
Yahalom R et al. Low-Cost, Compact Fiber-Optic Gyroscope For Super-Stable Line-Of-Sight Stabilization. Proceedings of the IEEE/ION Position Location and Navigation Symposium (PLANS), Indian Wells, CA(USA). May 2010. DOI: 10.1109/PLANS.2010.5507131
Çelikel O et al. Establishment of all digital closed-loop Interferometric fiber-optic-gyroscope and scale factor comparison for open-loop and all digital closed-loop configurations. IEEE Sensors Journal. 2009; 9(2):176-186
Sandoval-Romero GE et al. Límite de Detección de Un Giroscopio de Fibra Óptica Usando Una Fuente de Radiación Superluminiscente. Rev. Mexicana de Física. 2002; 49(2):155-165
Medjadba H et al. Low-Cost Technique For Improving Open-Loop Fiber Optic Gyroscope Scale Factor Linearity. Proceedings of the International Conference on Information and Communication Technologies, 2006 (ICTTA’06), 2, Damascus (Syria). 1684718, 2057–2060, April 24–28, 2006. DOI: 10.1109/ICTTA.2006
Bennett S et al. Fiber optic gyros for robotics. Service Robot: An International Journal. 1996; 2(4)
Emge S et al. Reduced Minimum Configuration Fiber Optic Gyro for Land Navigation Applications. Proc. SPIE 2837, Fiber Optic Gyros: 20th Anniversary Conf., Denver CO(USA), August 04, 1996
Bennett SM et al. Fiber optic gyroscopes for vehicular use. Proceedings of the IEEE Conf. on Intelligent Transportation System (ITSC’97), Boston MA (USA), Nov. 9-12, 1997, 1053-1057. DOI: 10.1109/ITSC.1997.660619
Cordova A, Patterson R, Rahu J, Lam L, Rozelle D. Progress in navigation grade FOG performance. SPIE Proceedings. 1996; 2837:2017-2217
Pavlath G. The LN200 fiber gyro based tactical grade IMU. Proc. Guidance, Navigation and Control, AIAA, pp. 898-904, 1993
Kamagai T et al. Fiber optic gyroscopes for vehicle navigation systems. Fiber Optic Laser Sensors XI, Proceedings of SPIE. Sept. 1993; 2070:181-191
Hotate K, Tabe K. Drift of an optical fiber gyroscope caused by the faraday effect: Influence of the earth’s magnetic field. Applied Optics. 1986; 25:1086-1092
Bohm K, Petermann K, Weidel E. Sensitivity of a fiber optic gyroscope to environmental magnetic fields. Optics Letters. 1982; 6:180-182
Blake JN. Magnetic field sensitivity of depolarized fiber optic gyros. SPIE Proc., 1367, Fiber Optic and Laser Sensors VIII. pp. 81-86, 1990
Bergh RA, Lefevre HC, Shaw HJ. Compensation of the optical Kerr effect in fiber-optic gyroscopes. Optics Letters. June 1982; 7:282-284
Takiguchi K, Hotate K. Method to reduce the optical Kerr-effect-induced bias in an optical passive ring-resonator gyro. IEEE Photonics Technology Letters. Feb. 1992; 4:2
Bergh RA, Culshaw B, Cutler CC, Lefevre HC, Shaw HJ. Source statistics and the Kerr effect in fiber-optic gyroscopes. Optics Letters. 1982; 7:563-565
Shupe DM. Thermally induced nonreciprocity in the fiber-optic interferometer. Applied Optics. 1980; 19(5):654-665
Ruffin PB, Lofts CM, Sung CC, Page JL. Reduction of nonreciprocity in wound fiber optic interferometers. Optical Engineering. 1994; 33(8):2675-2679
Lofts CM, Ruffin PB, Parker M, Sung CC. Investigation of effects of temporal thermal gradients in fiber optic gyroscope sensing coils. Optical Engineering. Oct. 1995; 34(10):2853-2863
Sawyer J, Ruffin PB, Sung CC. Investigation of effects of temporal thermal gradients in fiber optic gyroscope sensing coils, part II. Optical Engineering. Jan. 1997; 36(1):29-34
Ruffin PB, Sung CC, Morgan R. Analysis of temperature and stress effects in fiber optic gyroscopes. Fiber Optic Gyros, Proceedings of SPIE. Sept. 1991; 1585:283-299
Frigo NJ. Compensation of linear sources of non-reciprocity in Sagnac interferometers. Fiber Optic Laser Sensors I, SPIE Proceedings. 1983; 412:268-271
Ruffin PB, Baeder JS, Sung CC. Study of ultraminiature sensing coils and the performance of a depolarized interferometric fiber optic gyroscope. Optical Engineering. Apr. 2001; 40(4):605-611
Lefevre HC, Bergh RA, Shaw HJ. All-fiber gyroscope with inertial navigation short-term sensitivity. Optics Letters. 1982; 7:454-456