FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

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The generation of nonreciprocal phase modulation by the frequency method will now be described (see Refs. 11 and 18, Subsection 5.4.20). In this scheme fcw is made different from fccw so that: @ Cw -0 Ccw = (2nnL/c)(fcw - fccw) (5.56) A simple way of implementing this method is by employing two acoustooptic (A/0) frequency shifters placed symmetrically on either side of the beamsplitter within the interferometer. By driving the A/O with independent oscillators it is possible to generate both nonreciprocal phaae modulation as well as fixed nonreciprocal phase shifts. For example, In a 1 km fiber a frequency difference fcw - f ccw of 50 kHz generates a nonreciprocal phase shift of T/2. Related frequency methods have also been investigated (see Refs. 19 and 20, Subsection 5.4.20). 5.4.14 Open Loop and Closed Loop Operation The open loop sensor system is shown in Fig. 5.58 where a nonreciprocal phase modulator (NRPM) is placed near one fiber end and driven at fm. The output of the photodetector is then demodulated at fm in a phase senaitive demodulator. After low pass filtering the demodulator output is a sinusoidal function of At as illustrated in Fig. 5.58. For any given A$, a d.c. voltage output is obtained which is proportional to A$. The disadvantages of the open loop system include (a) the calibration of the demodulator output since this depends on the gains of the various amplifiers that precede it as well as on the intensity of the light source and (b) the nonlinear behavior of the demodu~ator output with A$. 1, T II NRPT LIGHT NRPM I 1. — A II I w fm l--cl ~ETEcToRL A — Fig. 5.59 I / NULL DEMOD OUTPUT -u Smo * Closed-loop nonreciprocal phase modulation in a fiberoptic rotation-rate sensor. ‘She advantages of the closed loop system over the open loop system include (a) the output is independent of light source intensity variations since the system ia always operated at null (the modulation frequency must be high enough to reach the photon shot noise); (b) the output is independent of the gains of individual components in the measurement system as long as a very high open-loop gain is maintained; and (c) the output linearity and stability depends only on the NRPT. The NRPT could, for example, be a Faraday effect device or an acoustooptic frequency shifter. If a Faraday device is used, then the stability depends on the stability of the length of the fiber and the atability of the magnetic-field/phase-shift transfer function. However, if the NRPT is an acoustooptic crystal, then a frequency difference Af = fcw - fccw is generated to offset a A$ = (21TLD/loC)n caused by a rotation. Therefore: A+ LIGHT SOURCE DETECTOR OUTPUT I wAIP which implies that: A+ = 2rAfnL/c = (21TLD/aoC)il (5.57) Af = (D/nAo)!2 (5.58) Eq. (5.58) indicates that the scale factor stability depends on the coil diameter D, n, and ~. If the numerator and denominator of Eq. (5.58) is multiplied by nD/4, then: Fig. 5.58 Open-loop nonreciprocal phase modulation in a fiberoptic rotation-rate sensor. In the closed loop system (see Refs. 11 and 18, Subsection 5.4.20), shown in Fig. 5.59, the output of the demodulator is passed through a servo amplifier which then drives a nonreciprocal phase transducer (NRPT) placed within the fiber interferometer. In this way, the sensor is always operated at null, i.e., at A+ = O by generating a suitable nonreciprocal phase shift in the NRPT that is equal to but opposite in sign to that generated by a rotation 0. The output of the system ia then the output of the NRFT. Therefore, the NRFT becomes a critical element. Af = [(nD2/4)/(nlomD/4)]~ = (4A/XoP)fl (5.59) where P is the optical perimeter = nTD of the fiber coil. It should be noted that Eq. (5.59) is identical with Eq. (5.44) for either the ring laser or the passive reaonator approach. 5.4.15 Problems in Fiberoptic Rotation Sensors So far the basic principles of fiber rotationrate sensors with emphasis on the measurement of small nonreciprocal phase shift in a multiturn fiber interferometer have been described. A number of error aources that can influence the performance of the fiber gyro will now be described briefly. 5-21
Fig. 5.60 lists several sources of error that must be dealt with in order to achieve the predicted performance. Perhapa the major source of noise is backscattering within the fiber (see Ref. 21, Subsection 5.4.20) and at interfaces, particularly in a setup that employs discrete components. To overcome this problem, researchers have used broadband lasers (see Ref. 17 and 22, Subjection 5.4.20), frequency jittered lasers (see Ref. 18, Subsection 5.4.20), phase modulators, (see Ref. 23, Subsection 5.4.20), and even light-emitting diodes (LED) (see Ref. 24, Subsection 5.4.20). By destroying the temporal coherence of the light source the detection system becomes sensitive only to the interference be- 5.4.16 Integrated Fiber “Gyros” Although the early investigation of fiberoptic “gyros” employed (see Refs. 19, 30, 32 and 33, Subsection 5.4.20) discrete optical components for convenience, it is clear that if fiber gyros are to make a large impact an integrated (see Ref. 34, Subsection 5.4.20) optical system (Fig. 5.61) with a semiconductor laser/LED as a light source must be uaed. Beamsplitters can be replaced by either waveguide or fiber 3-dB couplers (see Ref. 17, Subsection 5.4.20). Nonreciprocal RAYLEIGH SCAITERING IN FIBER SCAITERING FROM INTERFACES POLARIZATION EFFECTS PRESENCE OF HIGHER ORDER MODES TEMPERATURE GRADIENTS NONIDEAL MODULATORS NONIDEAL POLARIZERS INTENSITY DEPENDENT NONRECIPROCITY LIGHT SOURCE PROBLEMS MEASUREMENT SYSTEM PROBLEMS STRESS INDUCED EFFECTS MAGNETIC FIELD EFFECT Fig. 5.60 Sources of noise and errors that must be considered in the design of a fiberoptic rotation-rate sensor. tween waves that followed identical counter-propagating paths. Thus, interference due to backacattering will, in principle, average to zero. The problem that has received much attention both theoretically (see Refs. 25 and 26, Subsection 5.4.20) and experimentally (see Ref. 17, Subsection 5.4.20) is the error due to the polarization behavior of the optical fiber. By uaing polarizers to establish the axis of polarization (see Ref. 26, Subsection 5.4.20) in the long-fiber interferometer, it has been possible to reduce polarization-dependent errors. The use of the now available single-mode polarization-preserving fibers (see Ref. 27, Subsection 5.4.20) may turn out to be a convenient solution. 4I Fig. 5.61 I Q=POuTpuT f~ NR MODULATOR An open-loop integrated fiberoptic rotation-rate sensor employing a phase transducer. phase modulators may employ a short length of fiber wound around a PZT, the Faraday ef feet, an integrated Bragg cell, or other features. Integrated polarizers (see Ref. 17, Subsection 5.4. 20) and polarization controllers (see Ref. 17, Subsection 5.4. 20) are also feasible. In the closed loop approach shown in Fig. 5.62 the nonreciprocal phaae transducer could be a Bragg cell, a Faraday effect device, or other device. In other words various possibilities exist for constructing a solid-state fiber gyro. An all-optical-fiber open-loop system has already been demonstrated with a very promising performance (see Ref. 17, Subsection 5.4.20). All the fiber gyros under study so far have used single mode fibers. Care has to be taken to insure that higher order transverse modes are highly attenuated. A number of error sources are related to temperature gradients, (see Ref. 28, Subsection 5.4.20) non-ideal polarizers, (see Ref. 29, Subsection 5.4.20) non-ideal modulators, stress induced effects, external magnetic field effects (see Ref. 30, Subsection 5.4.20) and electronics problems in the measurement system. A very basic source of nonreciprocal phase shift has been uncovered, namely that due to unequal intensities propagating along opposite directions in the fiber (see Ref. 31, Subsection 5.4.20). This is a nonlinear optical effect based on four-wave mixing that takes place in a fiber having a third order nonlinear susceptibility. Such an intensity-induced nonreciprocity may be reduced by maintaining equal intensities in the counterpropagating beam. 5-22 Fig. 5.62 I SERVO DETECTOR f~ A closed-loop integrated fiberoptic rotaa tion-rate sensor employing phase transducer.
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FIBEROPTIC SENSOR TECHNOLOGY HANDBO
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FOREWORD THE FIBEROPTIC SENSOR TECH
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4.2 Phase 4.2.1 4.2.2 4.2.3 4.2.4 4
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CHAPTER 1 INTRODUCTION 1.1 BACKGROU
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CHAPTER 2 FIBEROPTIC SENSOR COMPONE
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fleeted each time it is incident on
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6=0 REFERENCE PLANE that propagate
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in the right center of Fig. 2.13. T
Page 17 and 18:
The vertical height of the various
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60 40 20 10.C ~8 x z 6 n u 4 % c 62
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: 1.5 z o GeOz 0 ~ =1.49 u w > ~1.4
Page 23 and 24: tension it collapses to eliminate t
Page 25 and 26: MAXIMUM TENSILE STRENGTH (GN/m2 = l
Page 27 and 28: mately a 0.5 electron-volt increase
Page 29 and 30: I in one portion of the recombinati
Page 31 and 32: crated electron-hole paira that are
Page 33 and 34: sink fiber. Likewise angular misali
Page 35 and 36: fused together. The ends are bent a
Page 37 and 38: A laboratory beam splitter set-up u
Page 39 and 40: aged multichannel unit. High-streng
Page 41 and 42: CHAPTER 4 LIGHTWAVES IN FIBEROPTIC
Page 43 and 44: tor addition indefinitely, as indic
Page 45 and 46: modes. Since at point (a) the two e
Page 47 and 48: as a number of wavelengths. An expr
Page 49 and 50: 100 meters of fiber, length changes
Page 51 and 52: the aingle-sideband phaae noiae int
Page 53 and 54: sets up periodic spatial fluctuatio
Page 55 and 56: ient configuration in the lower rig
Page 57 and 58: sors or a pressure gradient sensor.
Page 59 and 60: nickel H. = 3.6 oersteds and for a
Page 61 and 62: optical source of constant intensit
Page 63 and 64: in a straight section of the fiber
Page 65 and 66: A simplified design of the cladding
Page 67 and 68: Referring once more to Fig. 5.35, i
Page 69 and 70: The path length AL traveled by ligh
Page 71 and 72: 5.4.9 Fiberoptic Rotation-Rate Sens
Page 73: a modulation scheme, the output of
Page 77 and 78: CHAPTER 6 FIBEROPTIC SENSOR ARRAYS
Page 79 and 80: method of sensor energization will
Page 81 and 82: 1 The preceding discussion applied
Page 83 and 84: SIMPLEX FIBEROPTIC TRANSMITTER FIBE
Page 85 and 86: MAXIMUM ALLOWABLE RISETIME = 0.7/RN
Page 87 and 88: PROCESSING STATION TRANSMISSION wAV
Page 89 and 90: fiberoptic cable (optical cable), a
Page 91 and 92: angstrom. A unit of length equal to
Page 93 and 94: core. The central primary light-con
Page 95 and 96: diffraction. 1. The procesa by whic
Page 97 and 98: fiberoptic. Pertaining to optical f
Page 99 and 100: methods of coupling power outside t
Page 101 and 102: M Mach-Zehnder interferometer. An i
Page 103 and 104: N nanometer. One thousandth of a mi
Page 105 and 106: velocity is also the velocity at wh
Page 107 and 108: where nl and n2 are the reciprocals
Page 109 and 110: slab dielectric optical waveguide.
Page 111 and 112: v vacancy defect. In the somewhat o
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