10

Physical Phenomena for Optical Fiber Sensors

Introduction

Optical fiber sensors represent a new branch of optical fiber engineer­ing that has been developing rapidly in recent years. An optical fiber sensor is a length of fiber that modulates the light passing through it when exposed to the changing environment we wish to sense. Besides the optical fiber, it has a light source such as a light-emitting diode (LED) or a laser at one end and a photodetector at the other end of the fiber to register the changes. We divide the optical fiber sensors into two types: the pure optical fiber sensor, where the fiber itself is the sensing element, and the remote sensor, in which the fibers are used only to bring light to and from a separate sensing device.

In pure fiber sensors, the measurand interacts directly with the light traveling in the fiber. The resultant light can be either intensity-, phase-, or polarization-modulated within the fiber. There generally are no optical interfaces at the modulator site. The feed and return fibers may also impose modulation of the light passing within them, however, giving misleading information or an error. Selecting a proper fiber and arranging for a suitable interaction region become important considerations in the design. A scheme of detection that favors self-canceling of these difficulties is preferred.

A remote sensor involves the use of a special sensing element that is sensitive to the environment one wishes to probe. Subjected to the environmental change, such as temperature and pressure, the sensing element modulates the light leading to and from the sensor by the 279

10. Physical Phenomena for Optical Fiber Sensors

fibers. The detection process that follows can be calibrated in accor­dance with the respective changes. The sensing element is also called a transducer, as usually a change of energy form is involved.

Intensity modulation is the most commonly used method and is easy to implement. Phase modulation is by far the most sensitive and accurate technique if used in combination with an interferometric scheme. Polarization modulation is unique, as the state of polariza­tion of the light through the fiber is affected by the environment. Other methods are also possible.

Both single-mode fibers (SMF) and multimode fibers (MMF) can be used as sensors. Multimode fibers are used for less demanding appli­cations; single-mode fibers are used when extreme sensitivity and ac­curacy are demanded. In the case of a sensor where polarization modulation is used, only SMF fiber is recommended.

In this chapter, we bring out the physical concepts and phenomena that have to be exploited for making an optical fiber into a practical fiber sensor. We defer discussion of the practical implementation of these sensors to the next chapter.

Fiber Birefringence

One important parameter that characterizes an optical fiber is the re­fractive index n. In the simple theory, n is introduced as a pure ma­terial constant that is isotropie and single-valued. This is, however, an oversimplified picture. We notice that all fibers are biréfringent. The refractive index is actually a tensor quantity. The implication of this complicated representation is that the propagation of light in this medium will have propagation constants that vary in different direc­tions. To simplify, let us illustrate a two-dimensional example. Let nx and ny be the refractive indices in the x- and y-directions, respec­tively. Then the propagation constants in the x- and y-directions be­come ßx and ßy, respectively. The difference in ß values, or ßy - ßx, is a measure of the birefringence of the medium (fiber). Many fiber sensors are built based on the biréfringent nature of the fiber.

Birefringence of a fiber can either be intrinsic or induced. Intrinsic birefringences are those inherited from manufacturing processes of the fiber caused by, for example, the core ellipticity, cladding eccen­tricity, and so on. Induced birefringences are those induced by exter­nal forces during operation. These include thermal stress, mechanical bending, twisting, and other phenomena. For optical fiber sensing, induced birefringence constitutes a useful phenomenon that one wishes to take advantage of, whereas one would like to minimize or compensate for the intrinsic birefringence as much as possible.

Birefringence can be linear or circular. Both effects can be used to build sensors. But the linear birefringence is most useful in optical fiber sensors.

The State of Polarization 281

The State of Polarization

The state of polarization (SOP) of the electromagnetic wave is char­acterized by the orientation of the electric-field vector representing the propagating wave along a transmission path. The wave is said to be linearly polarized if a single E-field vector, perpendicular to the direction of propagation, can represent the wave. Of course, any vector representing a linearly polarized wave can be resolved into a pair of mutually perpendicular components, such as the x- and y-components of the electric field, traveling in phase along the direction of propagation (z-direction). This is shown in Fig. 10.1a. If the two components along the x- and y-axes are equal in amplitude, but are optically 90° out of phase, then the resultant wave is a circularly po­larized light. This state is shown in Fig. 10.1b. Circularly polarized states are distinguished by the sense of rotation of the vector. The

(a)

(b)

(imaginary , and

negat ive

( c )

t ■ * Figure 10 .1 The state of polarization of lightwaves: (a) linear; (b) circular; (c) elliptical.

282 10. Physical Phenomena for Optical Fiber Sensors

state shown in Fig. 10.1b represents a right circular polarization, as the resultant total polarized vector rotates clockwise when viewed toward the source. If the relative phases of Ex and Ey of this right circularly polarized light is shifted by 180°, left circularly polarized light will result. Linearly polarized light is specified by its amplitude. Circular polarized light is specified by its amplitude and the sense of rotation (left or right). The orientation of a reference x- and y-axes is immaterial.

If x- and y-components of unequal field amplitudes are added, the result is an elliptically polarized light as shown in Fig. 10.1c. This wave is now characterized by its amplitude and ellipticity and by the orientation of the major axis of the ellipse with respect to a reference axis. It is sometimes convenient to consider elliptically polarized light as the sum of a circular component and a linear component.

When polarized light passes through a medium possessing birefrin­gence, the output light will have its state of polarization changed. The detection of a change of the state of polarization constitutes a useful measure of the cause that brought about these changes.

The Electrooptic Effect

In the section titled "External Modulation'' (Chapter 8) we have intro­duced the electrooptic effect as a means of externally modulating the source light for transferring information to the fiber. Since the operational principle of optical fiber sensors utilizes the same mecha­nism to affect the information, the electrooptic effect becomes one specific choice to implement the modulation.

Studies on the application of an electric field to a crystal such as lithium niobate (LiNb03 ) showed that the refractive index of the ma­terial changes differently for different polarization and propagation directions of the field through the crystal [1]. The change in refractive index expressed in terms of Δ(1/η2) (Eq. 8-15) is reproduced here as

A ^ j = α,Ε + 0„Ε* (10-1)

Depending on the crystal structure and orientation, either the lon­gitudinal or the transverse electrooptic effect may be observed. The former is known as PockeVs effect. Here, linear birefringence is intro­duced as a result of applying a field along the wave-propagation axis. This effect is linear with the applied field as indicated in the first term on the right-hand side of Eq. (10-1). This effect can be used to sense a voltage [2].

There is a second effect that is proportional to the square of the field intensity as indicated in the second term of Eq. (10-1). It is called the Kerr effect. Although the Kerr effect is not considered as a good modulator because of its nonlinear field dependence, it is extremely

The Electrooptic Effect 283

fast, and has been used as a switch known as the Kerr cell for optical switching up to 10 GHz in measuring systems [3].

A short discussion on both types of effects will be given in this section.

Pockel's Effect

PockePs effect has been used as an external modulator for optical fiber systems as discussed in the section on external modulation in Chap­ter 8. Since a sensor requires a similar modulation process to affect the birefringence of the crystal, PockePs effect can be applied to it as well. The use of PockePs effect for a voltage sensor will be described in Chapter 11. For now, let us investigate the property of a crystal for this purpose. Obviously, we wish to choose a crystal that has the most strong PockePs coefficient. But we must also consider the availability and the cost of the crystal. From Table 8.1, we noticed that the elec­trooptic coefficients are listed as the scalar quantity a, without the double subscript aijf indicated in Eq. (10-1). This is because by proper choice of the crystal orientation and the direction of lightwave propa­gation in the crystal, the sensor coefficient can usually be reduced to a single coefficient as shown in the table. Lithium niobate (LiNb03) and lithium tantalate (LiTa03 ) crystals have the highest Pockel coef­ficient. However, these materials are difficult to grow into usable sizes and they are very expensive. For this reason, the next best candidate is potassium dihydrogen phosphate (KH2P04 or KDP). Also useful is the crystal KD*P, which is formed by substituting deuterium (in the above crystal) for hydrogen to become KD2P04. It was found that with this substitution the electrooptic property of the KDP crystal can be improved dramatically. The coefficient a has been increased from 10.6 for KDP to 26.4 pm/V for KD*P. Most important of all, the half-wave voltage that is required for maximum transmission is reduced from 10.2 to 5.82 kV for the KD*P crystal. For longer-wavelength applications, cadmium telluride (CdTe) and gallium arsenide (GaAs) are recommended for l -28-μπ ι and l-4-μ,πι-wavelength ranges, respectively.

Kerr Effect

The second term on the right-hand side of Eq. (10-1) that represents electrooptic effects is proportional to the square of the electric field. This effect is called the Kerr effect in honor of its discoverer, J. Kerr, in 1875. The Kerr effect is an electrically induced birefringence that occurs in all materials. The resultant refractive indices may be de­noted by nu and n±, the parallel and perpendicular components of n arising from the applied electric field. Again by a proper choice of the

10. Physical Phenomena for Optical Fiber Sensors

crystal orientation and lightwave propagation direction, the propor­tionality constant can be reduced to a single coefficient Κλ such that the change in the refractive index of the material can be expressed as

An = n - n0 = ΚλΕ2 (10-2)

where K is the Kerr constant and λ is the free-space wavelength. Many liquids, as well as crystals, exhibit the Kerr effect. The most often used liquid is nitrobenzene, which has a K value of 24 pm/V2 at 20°C. Water has a K value of 5.2 pm/V2, and glass has K = 1.7-3.0 pm/V2.

The Kerr effect is very fast for nonpolar liquids. It has been used to build light switches to turn light on and off when an electric field parallel to the optical axis is applied.

Liquid Kerr cells suffer from the disadvantage of requiring a large power for operation. But by mixing ferroelectric crystals operating at a temperature near the Curie points, such as KTN (potassium tan-talite niobate), the Kerr effect can be greatly enhanced, even at re­duced voltage. The Kerr effect has been used effectively as a fiber gyroscope [4, 5],

The Photoelastic Effect

Application of stress to a crystal perpendicular to the direction of propagation of a lightwave passing through it will induce an increase in the dielectric constant for the lightwave polarized along the stress direction. In anisotropie materials this effect will become directional and results in birefringence of the crystal [3].

If the mechanical stress is exerted by an acoustic wave, the effect is to change the refractive index caused by the photoelastic effect and is known as the acoustooptic effect This effect was mentioned in Chap­ter 8, subsection titled "The Acoustooptic Effect,'' for use as an exter­nal modulator. The refractive index change Δη is given by [ -11/2 wj (10-3) Here, p is the photoelastic constant, p is the density, Vs is the velocity of sound through the material, and IaCoustic is the intensity of the acous­tic pressure. Values of the appropriate constants for a number of ma­terials are given in Table 10.1. The photoelastic effect can therefore be used as the basis for a number of transducers for monitoring pres­sure, strain, and other parameters.

The sensing technique may be carried out by measuring either the pure phase changes or the induced birefringence caused by the in­troduction of an isotropie pressure field. The photoelastic effect may also induce circular birefringence when the medium is subjected to torsional stress. Some of these applications will be described in Chapter 11.

The Magnetooptic Effect 285

Table 10.1 Photoelastic Constants for Some Materials

Material

H20 (water) Si02 (quartz) LiNb03

PbM04

Te02 (shear wave)

Density P (g/cm3)

1 2.2 4.7 6.95 6.0

Acoustic Velocity vs (km/s)

1.5 6.0 7.4 3.74 0.62

Refrac­tive Index n

1.33 1.46 2.25 2.30 2.35

Photo-elastic Constant P

0.31 0.21 0.15 0.28 0.09

Table 10.2 Verdet Constant of Several Materials

Material

Quartz (Si02) Zinc sulfide (ZnS) Grown glass Flint glass Sodium chloride (NaCl)

V radians/m-T at λ =

4.0 82 6.4 23 9.6

= 0.689 μπι

The Magnetooptic Effect

The presence of a magnetic field in some materials may also affect its optical properties. One simple example is Faraday rotation, men­tioned in Chapter 8, subsection titled "Magnetooptic Effect," as an external modulator for an optical fiber system. The plane of polariza­tion will be rotated by an angle proportional to the applied magnetic field parallel to the direction of propagation. It is interesting to note that the sense of rotation of the plane of polarization is independent of the direction of propagation, so that the rotation can be doubled by reflecting the lightwave back through a Faraday effect device. The pro­portionality factor is called the Verdet constant. Some representative values of the Verdet constant are shown in Table 10.2. The Faraday effect is small and wavelength-dependent. For flint glass, it amounts to Θ « 1.6°/m-T at λ = 0.589 μτη.

One of the most successful optical fiber sensors is the Faraday ro­tation current or voltage monitor [2], Optical fibers are very attractive for current sensing, especially on high-voltage lines, because of their intrinsic isolation properties. In a fiber where no birefringence other than the magnetooptically induced one exists, a linear state of polar­ization launched at the input of the fiber will be rotated by an angle proportional to the product of the magnetic field intensity and the fiber length. An optical-time-domain reflectometry device can be built to measure the SOP of the fiber. For example, we cite here a Faraday rotation current monitor [2].

286 10. Physical Phenomena for Optical Fiber Sensors

p o l a r i s e r

■0—B—Qi launch o p t i c s

busbar single-mode 'spun' optical fibre

s igna l p r o c e s s i n g

l i

sVir

Wollas ton prism T

I l + I 2

ou tpu t

e l e c t r i c cu r r en t

Figure 10.2 A Faraday rotation current monitor. [After B. Culshaw, Optical fibre sensing and signal pro­cessing, Peter Peregrinus, p. 105, London, 1984.]

A schematic diagram of this device is shown in Fig. 10.2. Light from a helium neon laser is launched into a single-mode spun optical fiber through a polarizer to a polarization sensor. The sensor consists of a coil of spun SMF wound on a busbar carrying the electric current to be monitored. Polarization of the lightwave through the coil is rotated by the magnetic field produced by this current. The rotated polariza­tion is transmitted back to the signal processor to be analyzed. A spun SMF is used to ensure that the polarization of the transmitted light­wave is rotated only by the magnetic field produced by the current. Other schemes involving the use of two-way propagation have also been reported [6]. A drawback to this method is that any residual lin­ear birefringence on the fiber leads to large sensitivity variations as environmental conditions change. Also, the method is limited to us­ing alternating currents. A second approach is to use such a device as a polarimeter. It is more sensitive and does not have the above-mentioned drawback because the method is self-compensating.

It is impossible to name all physical effects that can be used to make sensors. Just a few have been cited in this section. Many new ideas will certainly develop as the search goes on.

Classification of Optical Fiber Sensors

Optical fiber sensors can be classified according to the mechanism by which the modulation of the lightwave in the fiber is implemented. If the lightwave is intensity-modulated, it is classified as Type I (where I stands for intensity). Depending on whether the modulation is im­plemented within or outside the fiber, it is subdivided as Type 1-1 or

Classification of Optical Fiber Sensors 287

Type 1-2, respectively. If the lightwave is phase-modulated, it is clas­sified as Type A (where A stands for phase angle). If the basic Mach-Zehnder interferometric method is used, it is classified as Type A-l; if the Sagnac effect is used, it is a Type A-2. Basically, a Mach-Zehnder interferometer uses two fiber branches, and a Sagnac effect device uses a single fiber. Other types include the Type F for frequency modulated, Type W for wavelength-distribution modula­tion, and Type P for polarization modulation types of sensor.

The Intensity-Modulated Type: Type /

The intensity-modulated-type fiber sensor [7] is usually the simplest one to build. Environmental changes to be measured are caused to interact with the lightwave within or outside the fiber to affect the light intensity. The detected change is then calibrated in terms of the measurement such as the temperature or the pressure.

The operating principle of Type 1-1 sensor is sketched in Fig. 10.3a. Light entering the sensing region remains within the optical fiber, and the intensity is modulated by, in the case shown, an acoustic wave. The pressure wave affects the transmission properties of the fiber, thus varying the lightwave intensity. Light is then collected by a pho-todetector, which produces an electrical signal proportional to the intensity [8].

In Fig. 10.3b, fibers are used to guide the lightwave to and from an external sensor only. The external sensor may be any transducer that converts the environmental change to lightwave intensity, for ex­ample, by reflection or refraction of the lightwave from a surface con­nected to the fibers. Here light from an LED enters a multimode opti­cal fiber that carries the lightwave to the sensing device. In this device, the intensity of the lightwave is modulated by the stimulus, in the case shown, the pressure on a diaphragm. The returned light is processed as in Type i-1 after being picked up by another fiber. This is called Type 1-2 sensor.

The Phase-Modulation Type: Type A

Phase-angle-modulated optical fiber sensors are highly sensitive to environmental changes. Very high resolution measurements are therefore feasible.

The phase-modulation scheme involves the measurement of the light path length of the fiber in terms of the phase angle. The follow­ing properties of the fiber can be utilized to effect the modulation:

1. The total physical length of a fiber may be modulated by the appli­cation of a longitudinal strain, that is, thermal expansion or the

288 10. Physical Phenomena for Optical Fiber Sensors

A c o u s t i c wave g e n e r a t o r I n t e r n a l i n t e n s i t y m o d u l a t i o n

Sens ing e lement

diode Photo-detector"

External intensity modulation (b)

Figure 1 0 . 3 Type I. Intensity-modulated optical fiber sensors: (a) inter­nal modulation type; (b) external modulation type. [After T. G. Giallo-renzi, et al [7] IEEE /. Quantum Electron. QE-18, 626-666 (1982) © IEEE, 1982.]

application of a hydrostatic pressure may cause expansion via Poisson's ratio.

2. The refractive index may vary with the temperature, pressure, and longitudinal strain via the photoelastic effect.

3. The guide dimensions may vary with the radial strain on a pres­sure field, the longitudinal strain through Poisson's ratio, or the thermal expansion.

Classification of Optical Fiber Sensors 289

Variations in environmental parameters other than pressure, strain, and temperature must be converted to cause phase modulation.

A basic Mach-Zehnder interferometric scheme is sketched in Fig. 10.4. Two pieces of optical fibers of approximately equal length, one serving as a reference arm and the other arm exposed to the environ­mental change, are used in a bridge-like arrangement as shown. Co­herent light from a laser diode enters a single-mode optical fiber. A coupler divides the optical power equally between the two arms. En­vironmental changes would affect the length and the refractive index of the sensing arm, which causes the light to be phase-modulated. The phase shift is converted into an intensity modulation when the two beams are recombined by another coupler. The outputs of the com­biner are 180° out of phase and are individually detected and then combined by a differential preamplifier. The processed output of the preamplifier provides an electric signal proportional to the detected stimulus. This type of sensor is classified as Type A-1.

In another Type A-2 optical-phase sensor, only one fiber is used. A typical example is the use of the Sagnac effect to sense rotations. This is shown schematically in Fig. 10.5. Light is split into two beams that travel in opposite directions in an SMF wound around a cylinder (or ring). When the fiber ring rotates, the light beam going in the same direction as the rotation has to travel more than one complete revo­lution to reach its starting point, which has moved as the light trav­eled around the ring. Similarly, the beam traveling counter to the

Ser fi

Diode Lase r

ΛΛΛΑΛΜ m Power s p l i t t e r

R e f e r e n c e f i b e r

P h o t o -d e t e c t o r s

Figure 10.4 Type A-1. Phase-modulation optical fiber sensors. The Mach-Zehnder type. After T. G. Gial-lorenzi et al. IEEE Spectrum, 23, 49 © IEEE 1986.

290 10. Physical Phenomena for Optical Fiber Sensors

detector plane

optical fibre

Figure 10.5 Type A-2. Phase-modulation optical fiber sensors. The Sagnac effect type. After B. Culshaw, Optical fibre sensing and signal processing. Peter Peregrinus, London, 1984.

ring's rotation reaches its starting point after going less than one com­plete rotation. As the speed of light is constant, the difference in path length appears as a phase shift, which can be detected by interfering the two beams with each other.

If the angular velocity of a rotating loop is Ω, then the light that is simultaneously injected into the fiber in opposite directions will exit with a phase difference of

Δφ 47rLRfì

X0c ~ Ω (10-4)

where L is the total fiber length and R is the loop radius. Variation in temperature, pressure, and other parameters may cause a change in the phase angle and thus can be detected and calibrated in terms of the changes. This is the basic working principle of a gyroscope [9,10].

The Frequency-Modulated Type: Type F

In this type of sensor, the Doppler effect of moving objects is ex­ploited. If radiation of a frequency / is incident on a body moving at a velocity v viewed by an observer, then the radiation reflected from the moving body appears to have a frequency ft, where

Classification of Optical Fiber Sensors 291

signal photodiode processing

HeNe Laser large core col

je core iw | . lection fibre M ^Sy |

blood flow information

iv j / / / />>rTTZzziJ^uzyy-rr^^^ blood flow

light scattered by both tissue and moving blood

Figure 10.6 Type F. Frequency-modulation optical fiber sensors. After B. Cul-shaw, ibid., p. 123.

u = 1 - vie f 1 + -:] (10-5)

Doppler shifts provide a very sensitive detection of moving targets and have been used as radars, either electrical or acoustical.

The same principle can be used to build optical fiber motion detec­tors or speed measurement [11]. Laser Doppler flowmeter [12], laser Doppler velocimeters [13] are just a few examples. The principle of one type of bloodflow sensor is sketched in Fig. 10.6. Two fibers, one used as a light input and the other a large-numerical-aperture fiber for collecting light, are mounted side-by-side on a plastic mount with a flat surface to rest on the surface of the object (e.g., the skin of a vein). Laser light from the input head sends light that penetrates the skin to reach the bloodflow that scatters the light. The returned scattered light is collected and processed to reveal the flow information.

The Wavelength-Distribution Type: Type 1/1/

Wavelength-distribution sensors are also called color probes. This is because many physical phenomena can influence the variation of re­flected or transmitted light intensity with wavelength or color of the light. By monitoring the color spectrum of the output lightwave, one

10. Physical Phenomena for Optical Fiber Sensors

can determine the source property quantitatively. One example is the use of a chemical indicator for monitoring pH value [14]. An optical fiber pyromatic probe is another application of this principle [15]. The basic feature of this system is ratiometric measurements of the output power at at least two wavelengths. The ratio should provide information about the measurand. The critical components of the sen­sor are the source and the spectrometer. The fiber simply serves to feed light to the monitoring region and return the modulated light for analysis.

The Polarization-Modulation Type: Type P

A variety of physical phenomena influence the state of polarization of light, as described earlier. We may wish to classify these in terms of the type of polarization modulation one imposes and the physical parameters that may cause this modulation. The birefringence prop­erties of the optical fiber may be affected by a number of physical phenomena of any form, including electrical, magnetic, and mechani­cal means. On the other hand, external polarization modulation may be introduced by using special crystals such as the KDP and other electroelastic materials [16]. Faraday's rotation is another example. In Chapter 11, we shall describe the detailed implementation of these sensors.

Single-Mode versus Multimode Fibers

Both SMF and MMF can be used as fiber sensors. Many of the less demanding applications will be served by MMF, the technology of which is already fairly well advanced. For some applications where extreme sensitivity is of paramount importance, however, it is likely that the more delicate SMF technology will prevail. Single-mode fi­bers are more apt to be used in pure fiber sensors where the fiber itself is the sensor that measures the ambient conditions. In polarization modulation schemes, SMF is an important component. By contrast, MMFs are mostly used to transmit and receive modulated light for a remote-sensing system.

Conclusion

In this chapter we have described some physical concepts and effects that can be exploited for optical fiber sensor applications. The list is by no means complete. Any physical effect can be developed to affect a sensor in some way, depending on the ingenuity of the engineers. We have also arbitrarily classified the sensors into several types ac-

Conclusion 293

cording to their physical operating principles. Specific examples of sensors are given in Chapter 11.

References

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2. A. J. Rogers, Optical measurement of current and voltage on power systems. IEEE J. Electr. Power Appi. 4(2), 120 (1979).

3. A. Yariv, introduction to Optical Electronics. Holt, Rinehart & Winston, New York, 1976.

4. A. J. Rogers, Distributed sensor: A review. Proc. SPIE, 798 Fiber Optic Sensors II. p. 26 (1987). (Society of Photo-Optical Instrumentation Engineers.)

5. R. A. Berch, H. C. LeFevre, and H. J. Shaw, Compensation of the Kerr cell effect in fiber optic gyroscope. Opt. Lett. 7, 282 (1982).

6. J. N. Ross, Measurement of magnetic field by polarization optical time-domain reflectometry. Electron. Lett. 17, 596-597 (1981).

7. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Sigel, J. H. Cole, S. C. Rash-leigh, and R. C. Priest, Optical fiber sensor technology. IEEE]. Quantum Electron. 18(4), 626-666 (1982).

8. N. Lagalos, P. Macedo, T. Litovitz, R. Mohr, and R. Meister, Fiber optic displace­ment sensors in Phys. Fiber Optics, p. 539 (1981).

9. R. A. Berch, H. C. LeFevre, and H. J. Shaw, All fiber gyroscope with inertial navi­gation sensitivity. Opt. Lett. 7(9), 454 (1982).

10. B. Culshaw and I. P. Giles, Fiber optic gyroscope. /. Phys. E 16, 5 (1983). 11. R. B. Dyott, The fiber optic Doppler anemometer. IEEJ. Microwaves, Opt. Acoust.

2(1), 13 (1978). 12. G. E. Nilsson, T. Tenlaud, and P. Akeöberg, Evaluation of a laser Doppler flow-

meter for measurement of tissue blood flow. IEEE Trans. Biomed. Eng. BME-27(10), 597-604 (1980).

13. H. Nishura, J. Koyama, N. Koki, F. Kajiya, M. Hironago, and M. Kauo, Optical fiber laser Doppler velocimeter for high resolution measurement of pulsatile blood flow. IEEE Trans. Biomed. Eng. BME-21(10), 1785 (1982).

14. J. I. Peterson, S. R. Goldstein, and R. V. Fitzgerald, Fiber optic pH probe for phys­iological use. Anal. Chem. 52, 864 (1980).

15. J. P. Dakin, A novel fiber optical temperature probe. Opt. Quantum Electron. 9, 54 (1977).

16. A. J. Rogers, Polarization optical effects and their use in measurement sensors. In "Proceedings of the Optical Sensor and Optical Techniques in Instrumentation." ' Institute of Measurement and Control, London, pp. 208-214 (1981).