FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

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detect displacements of the movable mirror as small as 10-13 m. l%is configuration has the advantage that little or no light is fed directly back into the laser. This is in contrast to the Michelson configuration. A more detailed description of how such feedback can lead to laser instability and noise is contained in Section 4.2. It should be noted that there are two other beams not shown explicitly in Fig. 4.2, that travel upward from the second beam splitter, i.e. a reflected portion of the upper horizontal beam and a transmitted portion of the righthand vertical beam. These could be fed to another optical detector to yield a second output signal , which may be employed to advantage in certain applications. 4.1.1.4 The Sagnac Interferometer Fig. 4.4 — 1 FIXED t MOVABLE MIRROR MIRROR TRANSDUCER The principle of the Fabry-Perot interferometer. The shown in Fig. Sagnac interferometric configuration is sive mirrors. The reflectivity of these mirrors usually is quite high, e.g. 95% or even higher. Assuming 4.3. With this arrangement, the two porthat the reflectivity (reflection coefficient) is 95%, at any instant 95% of the output light from the laser source will be reflected back toward the laser and 5% will be transmitted into the Interferometer cavity. When this portion of the incident light reaches the right-hand mirror, 95% of it will be reflected back toward the left-hand mirror and 5% will be transmitted through to the detector. This will combine with light that has been reflected back and forth successively an increasing number of times between the two mirrors. Neglecting losses other than the 5% transmission (at each interface), each successive output beam intensity will be reduced from the previous one by the factor II II (0.95)2 = 0.9025. Assuming that the laser has a coher- ) 1 11/ I A ence lenzth manv times the distance between the two mirrors, the optical signal intensity incident on the LASER I Fig. 4.3 The principle of the Sagnac interferometer. tions of the laser’s output beam are sent in opposite directions around the closed path formed by the beam splitter and the two mirrors. They are then recombined to be sent on to the photodetector and also back toward the laser. If any of the mirrors is displaced perpendicular to its reflecting surface, both path lengths would be changed by the same amount and there should be no detectable change in the interference process at the photodetector. On the other hand, if the table on which the interferometer is mounted were set into, say clockwise, rotation about an axis perpendicular to the plane of the beams, the beam traveling clockwiae, i.e. In the direction of rotation, would be delayed with respect to the counterclockwise traveling beam. The clockwise beam has to “catch up” to the end moving in the same direction. The counterclockwise beam runs into the end moving in the opposite direction. Thus, the Sagnac interferometer may be employed as a sensitive rotation detector and, in principal, it is the basis for the design of the ring laser gyroscope currently in use in a number of inertial guidance systems. 4.1. tion 4.4. .5 The Fabry-Perot Interferometer The fourth type of inter ferometric conf igurathe Fabry-Perot interferometer, is shown In Fig. It consists of two parallel, partially transmis- 4-2 detector may be found by forming the vector sum of the electric fields of the various transmitted beams. 4.1.1.6 Interferometer Sensitivity The sensitivity of various interferometers is shown graphically in Fig. 4.5. Consider first, what occurs in the first three type of interferometers that were considered earlier. For the Michelson, Mach-Zehnder, and Sagnac configurations, two separate optical beams are combined at the sensitive interface of the photodetector. As indicated in the upper left, the wo electrical fields are represented by the vectors ~1 and 22 which are assumed to be of equal magnitude and linearly polarized in the same direction. The optical intensit is proportional to the square of their vector sum, E z ( 8 ), which is at its maximum when the temporal and spatial relative phase angle between the two vectors is zero. If the length of one of the interferometer paths changes the phase angle varies, and E2( e ) and the intensity vary as indicated in the graph in the upper right in Fig. 4.5. , i.e. , the intensity drops to zero as 13 increases from O to n radians, varying as cos e. For further increases in e, E2( e) oscillates from zero to its maximum and back to zero again each time 13 varies by 2T radians. The corresponding diagrams for the Fabry- Perot interferometer are shown in the lower portion of Fig. 4.5. As pointed out earlier in this case, there is a set of electrical field vectors, in principle infinite in number, each successive one down from the previous by a factor R2, where R is the amplitude reflection coefficient. When the mirror separation is some integral number of half wavelengths, all of these vectors are in phase and the output intensity is at a maximum. When the separation is increased slightly, each successive vector is shifted with respect to the previous one by the same angle. By continuing the vec -
tor addition indefinitely, as indicated in the lower left, one can easily show that E2(13) in this case is a sharply peaked function with maxims at = O, Zm, 411,... and s. forth; E2(e) rapidly decreases and remains CIOSe to zero for values of f3 only slightly different from O, 2n, 41r,... etc., as indicated in the vector diagram at the lower center in Fig. 4.5c. Thus, in the vicinity of its maxima, the Fabry-Perot interferometer is an extremely sensitive position and length measuring device. It is in fact, one of the most sensitive displacement measuring devices available to modern science. that are currently available, it is already possible to construct relatively small-sized, highly-stable, and quite rugged interferometric fiberoptic sensors that are capable of withstanding the rigors of many fieldtype applications. Sketches outlining “all fiber” configurations of the four different types of interferometers are shown in Fig. 4.6. In the Mach-Zehnder fiberoptic in- A) MICHELSON A) MICHELSON, MACH-ZEHNDER AND SAGNAC 3dB COUPLER B) FA6Ry-pEROT El > ~ A RELATIVE PHASE SHIFT (RADIANS) =;:’’:;s RTRANSDUCER B) MACH-ZEHNDER E’[@), r 5’=i!4._-!=-!’=f \ DISPLACEMENT- O.25 05 0.75 I MICRON C) SAGNAC LASER El DETECTOR Fig. 4.5 4.1.2 The sensitivity of various typea of interferometers as a function of relative phase difference between two interfering lightwavea. Fiberoptic Intenaity Interferometer Up to this point, the various interferometers have been depicted aa they exist in the typical optics laboratory, with air paths and lumped optical devices such as beam splitters and mirrora. Their extremely high displacement sensitivity has been used to measure atrain and streas. In addition, they also have a very high dynamic range. This will be brought out in more detail in later discussion. If the many advantages of the use of fiberoptic, electrooptics, and integrat - ed-optics are added, one can conceive of configurations and systems that are capable of revolutionizing sensor technology. By employing single-mode optical fibers for the interferometer paths, the rather stringent limitation on their length is immediately removed. Path lengths of the order of a kilometer are easy to achieve and are being used in practice. Extremely small, longlife, solid-state laaers and detectors that are capable of being used in hostile environments are becoming available. Elements such as etched or lapped fiber-tofiber couplers and their integrated-optic counterpart are being developed and tested. By incorporating items D) FABRY-PEROT LASER - 1 !- DETECTOR a \: ‘/ PARTIAL TRANSMITTING MIRRORS Fig. 4.6 The configuration of various types of fiberoptic interferometera. terferometer shown in Fig. 4.6b, the two beam splitters are replaced with two etched or lapped 3-db couplers that divide the laser output beam into two equal portions and they also recombine the light that haa traversed the two optical paths. It is possible to buttcouple the laser output beam directly into the fiber and to similarly couple the output fibers directly into the two photodetectors. Thus, between aource and detectors, the interferometera consiats only of fiber elementa. By combining integrated circuit techniques with current electrooptic capabilities, all of the other elements, including the laser, detectors, and signal processor, could be packaged in a single miniature chip to which the fibers will be butt-coupled. Though the device is not an off-the-shelf item today, there is little doubt that they will be readily available in the not too distant future. 4-3 4.1.3 Polarization in Fiberoptic Sensors Earlier in this discussion of interferometers it was mentioned, but not especially emphasized, that
Page 1 and 2: FIBEROPTIC SENSOR TECHNOLOGY HANDBO
Page 3 and 4: FOREWORD THE FIBEROPTIC SENSOR TECH
Page 5 and 6: 4.2 Phase 4.2.1 4.2.2 4.2.3 4.2.4 4
Page 7 and 8: CHAPTER 1 INTRODUCTION 1.1 BACKGROU
Page 9 and 10: CHAPTER 2 FIBEROPTIC SENSOR COMPONE
Page 11 and 12: fleeted each time it is incident on
Page 13 and 14: 6=0 REFERENCE PLANE that propagate
Page 15 and 16: 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: CHAPTER 4 LIGHTWAVES IN FIBEROPTIC
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 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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