FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

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1 1 I where P is the optical perimater of tha path. In the active resonator (i.e., ring laser) approach the cw and ccw outputs of the laser have a frequency difference Af which IS auto~tically generated when the laser is JIL subjected to a rotation. In the case of the passive resonator, Af has to be measured by means of lasers external to the cavity (see Refs. 8 and 9, Subsection 5.4.20). SAGNAC EFFECT I 1 I I ACTIVE APPROACH PASSIVE APPROACH [ r { RING LASER RESONATOR II INTERFEROMETER PHOTON SHOT NOISE c ~0/2 ‘jf]MFG= LD ~ ~ Fig. 5.48 Photon shot-noise computation for a multiturn fiberoptic gyroscope utilizing the Sagnac effect. fcw H Fig. 5.46 fccw I-7 d ( AL=!$N,, &@=bA N,, A. & - AL Methods of measuring the change in effective optical length ( Sagnac ef feet). 5.4.8 Fundamental Limits in Optical Rotation Sensors Figs. 5.47 and 5.48 show a comparison without derivation of the quantum noise limit for all three cases. For the ring laser (RL) , the quantum limit comes from spontaneous emission in the gain (see Ref. 10, Subsection 5.4. 20) medium and gives an uncertainty 6!l in the measurement of Sl given by: where r. is the linewidth of the ring laser cavity with no gain; nph Is the number of photons/see in the laser beam and T is the averaging time. For the passive resonator (PR) case the limit is determined by photon shot noise and is given by: 6nPR = (kop/4A)(rc/(nphTl~T )1’2) (5.46) where q D is the quantum efficiency of the photodetector. As can be seen, the passive and active resonator approaches give approximately the same limit. For the multiturn fiberoptic (FO) interferometer ( see Ref. 11, Subsection 5.4. 20) the photon shot noise limit is given by: M-lFo = (c/LD) (ko/2(nph~JjT )1/2) (5.47) where nph is a number of photons/see leaving the interf erometer. Al these limits are compare -# in Fig. 5.49 for A = 100 cm i ; P = 60 cm; 10 = 6 x 10 =3X 1015 photons/see corresponding to 1 mW; L =c~bOn~h(i. e. , N = L/P = 1000); rc = 300 kHz; IID = O. 3; and T = 1 sec. We notice tha the uncertainty d~ in this example is about 5 x 10 -t ,E or O. 008°/hr for all three cases. 6% x oioP/4A)(rc/(nphT) l’2) (5.45) RING LASER PASSIVE RESONATOR FIBER ● RING LASER GYRO J-------+ 1 I 1 ! SPONTANEOUS EMISSION , \-~:;.+.w- fccw i fcw ● PASSIVE RESONATOR GYRO t+ +- + ~+ 4 4 I fccw fcw ,\cJ P I ‘~ ,)!! x — — RLG 4A ~ ~2 EXAMPLE: A = 77 P = To L = NP = 100 cm 2 ; Ao= 6x1O cm c AOI 2 LD j= = 40 cm ; n ~h = 3x1015Isec = lmW = 400 m ; T * 1 sec rc x 300 kHz 70 = 0.3 El PHOTON SHOT NOISE -t Fig. 5.47 I Computation of quantum noise limits in fiberoptic rotation-rate sensors. I Fig. 5.49 &f)= 4.10–4QE 7XI0 “QE 5X1O–4 f)E 0.006 “/hr 0.01 “Ihr 0.008 O/hr Computation and comparison of the shot-noise limits for various types of rotation-rate sensors utilizing the Sagnac ef feet. 5-17
5.4.9 Fiberoptic Rotation-Rate Sensors A simple configuration of a multiturn fiberoptic rotation-rate aensor (see Ref. 7, Subsection 5.4.20) is shown in Fig. 5.50. Light from a laser or some other suitable light source ia divided into two beams by a 50-50 (3 dB) beamsplitter and then coupled into the two ends of a multiturn (multlloop) singlemode fiber coil. The light emerging from the two fiber ends is combined by the beamsplitter and detected in a photodetector. In the abaence of rotation, the two emerging beams interfere either destructively or constructively depending on the type of beamsplitter used. For a 50-50 (3 dB) lossless beamsplitter the emerging beams, as shown in Fig. 5.50, interfere destructively. Fig. 5.50 d DETECTOR L –L~cw=~NQ Cw c n e,g. N=1000:A=100cm2: Q=f)E =AL~16gcm -5A =2X1O A$=8mANQs10-4 RAD Aoc NTURNS Computation of the phaae change for a multiturn fiberoptic interferometric rotationrate sensor. However, the emerging beams that return back to the light source interfere constructively, i.e., at the peak of a fringe. In the presence of a rotation rate $2, a AL will be generated given by: Typically, for a fiber attenuation rate of 1 dB/km, the optimum length is several km. 5.4.10 Photon Shot-Noise Limit Earlier a proof was given of a comparison of the basic limits to the rotation measurement using the three techniques outlined in Fig. 5.46. In this section we will derive an approximate formula for the limit in a fiberoptic rotation-rate sensor. Fig. 5.51 shows a plot of intensity I or detector output current iD versus nonreciprocal phase shift A+ . In this case, the peak intensity, due to constructive interference, is shown centered on A$ = O for a zero rotation rate. In the presence of a rotation, A+ shifts from zero and therefore a change in detection current iD occurs. The greatest change in iD for a given small change in A$ clearly occurs at the point on the fringe with the maximum slope, i.e., where A$ = + ~12. Therefore, by applying a fixed nonreciprocal bia~ of T/2, the operating point can be maintained where the sensitivity to rotation is a maximum. In this way, an applied rotation causes a A$ which in turn generates a change in the light intensity at the detector that is proportional to the rotation. A problem arises when the 1 &I D ,) ;1 ,1 i ,1 ,1 INTENSITY NOISE -w OY?$7 ) A+ 8(A+) - PHOTON / SHOT NOISE N O I S E - - 8( AIP)s-= — iD/~ - iD/IT T 7r *LS .— SIN iDm m *OC ~=87AN BUT A@=* —Q AOC AL = Lcw - Lccw = (4Atf/c)n = (LDIc)Q (5.48) where A, N, L, D have been defined earlier. This AL will therefore cause a fringe shift Az given by: or a phase shift of: AZ = (LD/ioC)n (5.49) A$ = (21TWaoC) (5.50) For A = ~D2/4 = 100 cm2 and N = L/rD = 1000 (i.e., D ‘11.3 cm and Lx 355 meters) and if i. = 0.63 ~m and n= 1.5, we get a phase shift of 3.0 rad for a rotation rate of 1 rad/sec. Therefore, to detect the full earth rotation, we must measure a phase shift of 9.1 x 10-5 radians and for typical navigation applicat ons (10-3 ~) the phase ahift reduces to about 10 -{ radians. For a given size sensor, i.e., a fixed coil diameter D, the sensitivity may be enhanced by increasing the length of the fiber L by adding more turns. Unfortunately L cannot be increased indefinitely because of the finite attenuation of optical power in the fiber. Fig. 5.51 The optical intensity (power) or photodetector output current as a function of phase change and photon shot-noise computation in a fiberoptic rotation-rate sensor. intensity of the light source varies since this cannot be distinguished from a change in intensity due to a rotation. Therefore, the uncertainty in the measurement of a given rotation rate, i.e., a given A$, must be influenced by the intensity noise in the light. M- though there are many ways of compensating for intensity variations of the light source, it is not, however, possible to reduce the effect of photon shot noise (see Ref. 12, Subsection 5.4.20) because it is a random proceas. Therefore under ideal conditions the uncertainty in the measurement of A$ ia limited only by the photon ahot noise (see Ref. 12, Subsection 5.4.20). This uncertainty 6(A$) is therefore given by: 6(A$) = (photon shot noise)/(fringe alope) (5.51) 5-18
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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
Page 19 and 20: 60 40 20 10.C ~8 x z 6 n u 4 % c 62
Page 21 and 22: : 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: The path length AL traveled by ligh
Page 73 and 74: a modulation scheme, the output of
Page 75 and 76: Fig. 5.60 lists several sources 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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