WO1997037256A1 - A fiber optic sensor based upon buckling of a freely suspended length of fiber - Google Patents

Abstract

A new class of fiber optic sensors (30) based on nonlinear buckling of fibers (41, 44, 61) and optical bend loss provide intrinsic, all-fiber displacement sensors (30) which exhibit several unique properties. Primary among them is a sensing range from less than 1 νm to several νm, which is convenient for many structural monitoring applications. This sensing range is also very convenient for many actuator and lever arm sensing applications. In addition, the sensors (30) exhibit a very low temperature dependence of the response, and are easily configurable for a variety of novel applications. They may be implemented with single-mode, few mode, or highly multimode fibers (41, 44, 61), including plastic optical fiber (POF). Both step index and graded index profile fibers produce useful sensors (30) with differing response characteristics.

Description

A FIBER OPTIC SENSOR BASED UPON BUCKLING OF A FREELY SUSPENDED LENGTH OF FIBER

FIELD OF THE INVENTION

The present invention relates generally to the field of fiber optic sensors and more specifically to fiber optic sensors wherein the shape of a length of fiber is changed under carefully controlled boundary conditions, providing a reproducible acro-bending-induced loss which can be implemented in a variety of highly precise and wide range of sensor applications.

BACKGROUND ART

Numerous types of fiber optic sensors have been developed. Of the intensity-based sensor types (Udd 1991) , the microbend sensors have been the most popular and carefully tested. A recent review of microbend sensors (Berthold 1995) points out that theoretical models have had difficulty predicting light loss versus ^" deformer displacements, aε well as the saturation effects that occur at large displacements when the core light has been substantially depleted. Although several papers have reported on field use of a variety of fiber optic microbend sensors, most have not found wide use in practice (other than for alarm mode or tactile sensing) due to problems associated with erratic response, tolerances of the deformers, mechanical fatiguing of the fiber, and a limited quantitative understanding of the mode problems and radiation loss associated with the use of highly multimode fiber. Berthold also points out the large stiffness of microbend sensors which have spring constants generally in the range of 500-2000 lbs. /in. There are reports of industrial use of a high temperature microbend pressure transducer (see Berthold in Udd) . Similarly, several patents have been granted on fiber optic sensors employing microbending. All such patents relate to microbending optical fiber rather than to macrobending or non-linear buckling. The significant advantage of the latter over the former relates to the predictability and reproducibility, which are difficult at best in microbending, but readily achievable in macrobending which employs non¬ linear buckling. This feature is especially significant in sensors used for making precise measurements over a wide dynamic range.

The following are some examples of prior art microbend devices:

U.S. Patent No. 4,163,397 to Har er discloses an optical strain gauge using periodically repeating bends in an optical fiber to determine the strain of a substrate. Unlike the present invention, this prior art disclosure relates to a microbend phenomenon incurred by distorting the fiber along its length in response to movement of a cantilever structure.

U.S. Patent No. 4,071,753 to Fulenwider et al discloses a device for converting acoustic energy to optical energy, such aε for communications. In one disclosed embodiment, a diaphragm bends the mid-section of a continuous loop of optical fiber to cause variations in light transmission through the fiber in response to the mechanical travel of the diaphragm. In contrast to the present invention, thiε device relies on mechanical distortion of the fiber along its length and the use of hinged boundary conditions.

U.S. Patent No. 5,134,281 to Bryenton et al relates to a physiological sensor for monitoring heart beats and other muscle movement. The sensor uses a fiber configured aε a multiple period sinusoid and relies on microbending of the fiber upon expansion and contraction of a resilient backing which iε εecured, for example, around the chest of an infant who's heart beat or breathing iε to be monitored. Unlike the present invention, there iε no diεcloεure of non-linear buckling or macrobending of a boundary condition- controlled fiber wherein movement in one or more εelected directions at the boundary is the sole source of transmission or reflection changes. Although the use of just one loop is disclosed, the impressed movement of the entire fiber, rather than only at the boundaries, would make it difficult, if not imposεible, to precisely relate loεε to the monitored parameters such aε minute amounts of strain or the like. U.S. Patent No. 5,274,226 to Kidwell et al relateε to an optical poεition εenεor wherein rotation of a εhaft cauεes microbending of the fiber which can be used to meaεure the rotation of the shaft via transmisεion loεε. Again, displacement of the entire fiber cauεes microbending losseε, rather than motion only of the boundarieε which produce non-linear buckling in a macrobending approach.

Moεt εuch εensors employ a plurality of periodic or random bends to provide the desired transduction loss mechanism. It is well-established that small random or periodic undulations in the direction of an optical fiber's axis, known as microbends, can cauεe a significant reduction in the fiber's optical transmission. Microbending is generally distinguished from macrobending by the criterion that in microbending the transverse displacementε of the fiber axiε from εtraightness are generally small compared to the fiber lateral dimenεions. Furthermore, macrobending combined with selective boundary conditionε with an otherwiεe unreεtricted length of fiber provideε a much greater range of motion aε compared to a microbending-baεed optical sensor. The basic equation governing the bending of thin rods and beams (those whose lateral dimenεions are small compared to the radius of curvature) is given in numerous books discussing elasticity see:

1. A TREATISE ON THE MATHEMATICAL THEORY OF ELASTICITY by A.E.H. Love, Dover, New York (1944), pp. 381-398 Chapter XVIII and pp. 399-426 Chapter XIX;

2. FIBER OPTIC SENSORS: AN INTRODUCTION FOR SCIENTISTS AND ENGINEERS, E. Udd, ed. , (Wiley, New York, 1991) pp. 142 (several references to microbend sensors on pp. 154 and pp. 333, 337, 339, 421-422 and 427-428);

3. HISTORICAL REVIEW OF MICROBEND FIBER-OPTIC SENSORS" by John W. Berthold III, Journal of Lightwave Technology Vol. 13, No. 7 (July 1995) pp. 1193-1199 and

(Erratum Vol. 13, No. 9 (September 1995) pp. 1935;

4. STRENGTH OF MATERIALS by J.P. Den Hartog, Dover, New York (1961) , pp. 79-81 and 184-191;

5. THE FEYNMAN LECTURES ON PHYSICS by R.P. Feynman , R.B. Leighton and M. Sands, Vol. II, Addison Wesley (1964), pp. 38-9 through 38-12; and

6. THEORY OF ELASTICITY by L.D. Landau and E.M. Lifshitz, Pergamon, New York (1970) , pp. 75-100. SUMMARY OF THE INVENTION

The present invention provideε a highly reproducible εhape by application of forceε and/or torqueε (any of which may be zero) to two locationε of a freely εuεpended length of optical fiber, which allowε controlled and reproducible transition and (macro) bending losses. The optical fiber is completely unconstrained laterally between the two locations of forces or torque application by any agent (although masseε may be attached to it in certain applicationε) . The design also greatly reduces problems associated with the different moduli of the fiber coating and fiber, since the shape of the fiber, and thus its attendant loss, is independent of the moduli and cross- sectional area of the fiber (provided it is prismatic, i.e., uniform along the length) . Thiε has the effect of eliminating temperature sensitivity due to changing moduli or thermal expansion changes in the croεs- section of the fiber or fiber coating. Residual temperature εensitivity comes from increases in length of the fiber due to temperature, which amounts to changeε in free length of no more than 10^~\ Another contribution to temperature sensitivity of bending losε is due to changes in the photoelastic constants and refracture index with temperature, which is also very small for fused silica optical fiberε. The inventive εhapeε have the advantage of minimizing overall elastic strain energy εo as to prevent overstrain of the fiber at any given location, and allow for convenient design evaluation of maximum allowable strain, consiεtent with deεired optical waveguide loεε and diεplacement sensing range.

The invention includes a variety of clamped, clamped- free and clamped-hinged configurations using both multimode, few mode, two mode and single mode fiberε with both incoherent and coherent light sources. The clamped-free configurations can alεo be interrogated in a reflective mode of operation (a CCD mode of operation is possible in accelerometer applications) . A further advantage of the present invention is that the optical fiber is secured only at either end of its bent section. Considerable size and geometric advantages are realized because of the absence of any restraining εtructure εurrounding the bent section. For example, microbend transducerε would be hard to adapt to actuation by a fuel gauge, whereas the invention iε eaεily adapted to many actuator/lever arm εituations. The invention can be implemented in highly multimode, plaεtic optical fiber, single-mode optical fiber, and two mode or few mode optical fiber, each with respective differences. Single mode and two mode versions exhibit interf erometric losε oscillations which can be used to provide absolute sensor calibration when using coherent light sources. The sudden change in curvature of the fiber near the clamping points produceε enhanced backεcattering, which can be utilized in optical time domain ref lectometry , OTDR, odeε of εenεor interrogation to reduce averaging time required by weak Rayleigh backεcattering.

The inventive εenεor ε take advantage of transmission losses due to macroscopic bending of optical fibers. We initially diεtinguish only two types: the so-called fi -sensor and a -εenεor which are distinguished by their respective shapes between the clamping points. The two end-points of the sensor are mobile with respect to each other (initially confined along the axis of the sensor; this reεtriction will later be lifted). Typical dimenεionε are approximately 1 cm for the εenεor length (between the two end-points) , which implies that the maximum height of the senεor iε on the order of 0.4 cm. More details on the explicit shape of the sensor are discussed below.

One of the key features of this sensor is the way in which the boundary conditions (the shape of the fiber at the end-points of the sensor) are enforced: both location and slope of the clamping points are controlled. In the case of clamped-clamped boundary conditions, the slope of the fiber is controlled at the clamping points. We indicate three different means of doing so: one can adhere the fiber onto a subεtrate while it iε in a well-defined orientation (i.e., while an Ω-sensor iε fully extended) , one can feed the fiber through a small tube connected to the substrate, or one can clamp it between two external blocks. Other possibilities also exiεt and will be mentioned below.

This control ensures that, irrespective of which shape the sensor will take by virtue of moving the two ends with respect to each other, one can reproducibly make the tranε iεεivity of the sensors go from 100% to lesε than detectable levelε. Thiε enormous range allows sensitive measuring of distances. We have demonstrated better than lμ strain resolution of the sensors. At the same time, the senεorε are capable of withεtanding εtrains of over 100%.

The exact shape of an Ω-type senεor iε related to the shape of a thin pillar buckling under stress while rigidly connected at both ends. Generally speaking, thiε is a problem of interest to mechanical engineers; note, however, that they are only interested in the very limiting case of how much force the pillar can take before buckling - we are explicitly intereεted in the buckling εhape and diεplacement , curvature, etc.

Modeling the Ω-type sen or, we find that the losses are mostly due to the three different regions of higheεt curvature.

One of the most significant advantages of the inventive sensors is their versatility. The εensors can be used in series and can easily be multiplexed. By correctly pre-ben ing the sensors one can ensure being in a region of maximum senεitivity. The phyεical εize of the εensors can be changed for tuning them to specific senεitivitieε. The shape of the senεor need not be restricted to two dimensions: corkscrew and other three-dimensional fiber arrangements have applicationε. The εenεors are also exceptionally easy to attach and are essentially two-dimensional in most caseε .

Both the Ω-type and α-type εenεorε can be uεed both in OTDR and straight transmiεsion mode. By immobilizing one of the two end-points, distanceε can be measured to approximately 2xl0^~9 meters in certain cases.

By adding a small mass onto the senεor, one can build optical accelerometerε. Making the detection mass magnetic/dielectr ic/paraelectr ic/fer roelectr ic reεults in a magnetic/elect ic field detector. Any masε material of a denεity different for a fluid in queεtion, will make a εenεor capable of detecting fluid levels. Sensorε can be put into other configurations for multidirectional sensors: any (one, two or three- dimensional) amount of movement will be detected.

OBJECTS OF THE INVENTION

It is therefore a principal object of the present invention to provide a unique fiber optical displacement sensor which utilizes macrobending to achieve new levels of sensitivity, resolution and dynamic range in a variety of senεing applicationε.

It is another object of the invention to provide a fiber optic displacement senεor based upon optical bend loss due to non-linear buckling of fibers under controlled boundary conditions.

It is still another object of the invention to provide a fiber optic displacement senεor comprising a length of optical fiber secured at spaced points and having no restraints therebetween whereby highly predictable optical loss occurs through the fiber when the diεtance between the pointε iε changed. It is still another object of the invention to provide a fiber optic diεplacement sensor compriεing a length of optical fiber secured at spaced pointε and having no reεtraints therebetween whereby optical loss variations through the length of fiber correspond to precise distances between the spaced pointε.

It iε still another object of the invention to provide a fiber optic sensor compriεing a length of optical fiber secured at spaced points and having no restraints therebetween whereby optical losε variationε through the length of fiber correεpond to the distance between the spaced points and orientation and relative direction of the length of fiber at the spaced pointε.

BRIEF DESCRIPTION OF THE DRAWINGS

The aforementioned objects and advantages of the present invention, as well as additional objects and advantages thereof, will be more fully understood hereinafter aε a result of a detailed description of a preferred embodiment when taken in conjunction with the following drawingε in which:

FIG. 1 iε a εchematic of the sensor in which various relevant points and distances are identified;

FIG. 2 is a graphical representation of some of the shapes the Ω-type sensor will asεume upon displacement of the attachment points with respect to each other;

FIG. 3 is a three-dimensional view of a device uεed to clamp fibers ;

FIG. 4 is a three-dimensional view of two components of a preferred clamping device;

FIG. 5 is a three-dimenεional view preεenting the location of the fiber within an attachment tube; FIG. 6 is a three-dimensional view of the senεing part of the fiber with attachmentε illuεtrating where the attachmentε are relative to the fiber;

FIG. 7 iε a three-dimenεional view of how expanεion pins are used in the construction proceεε of the εenεor ε;

FIG. 8 iε a three-dimenεional view of an alternative attachment method utilizing a εmall tube and an expansion pin;

FIG. 9, which compriεeε FIGε. 9a and 9b, indicateε the two stepε used in yet another attachment method;

FIG. 10 iε a view of a pre-bent tube εection of the sensor used in another alternative attachment method;

FIG. 11 is a block diagram illustrating the experimental setup used for measuring the reεponεe of εenεorε in one di enεion and which εetup iε uεed for taking data presented in FIG. 12 through FIG. 21; FIG. 12 is a graphical representation of transmission data taken using the εetup shown in FIG. 11;

FIG. 13 provides a summary of the data shown in FIG. 12;

FIG. 14 iε a graphical repreεentation of reflection data taken uεing the εetup εhown in FIG. 11;

FIG. 15 provideε a summary of the data shown in FIG. 14 and presents a linear fit to that data;

FIG. 16 is a graph of transmiεsion data taken uεing two different light εourceε;

FIG. 17 iε a graphical repreεentation of a compariεon of tranε ission data taken under slightly different mounting conditions;

FIG. 18 is a graphical representation of transmisεion data aε a function of the wavelength uεed in illumination of the sensor for various amounts of displacement; FIG. 19, which comprises FIGs. 19a and 19b, provide a summary of the data presented in FIG. 18 shown on two different scales;

FIG. 20 provides a partial summary of the data presented in FIG. 19, for variouε selected wavelengths;

FIG. 21 is a graphical representation of a comparison of transmission and reflection data;

FIG. 22 is a block diagram of the setup for measurement of the data shown in FIG. 23 through FIG. 26;

FIG. 23 is a graphical representation of transmission data taken for Ω sensors of four different fully extended lengths L₀ ;

FIG. 24 is an expansion of data preεented in FIG. 23 and illustrates how to find a threshold length L_t;

FIG. 25 is a graphical representation of the data presented in FIG. 23 uεing the threεhold length L_t of FIG. 24; FIG. 26 is a graphical representation of the relation between the extended senεor length L₀ and the threεhold length L_t;

FIG. 27 iε a graphical representation of the shapes that four various length sensorε aεεume when displaced by their respective threshold lengths;

FIG. 28 iε a graphical repreεentation of the radii of curvature of εame four εenεor ε along the initial part of the fiber;

FIG. 29 iε a graphical repreεentation comparing the response of an Ω-type εensor of length L_G - 20 mm with a model;

FIG. 30, which comprises FIGs. 30a and 30b, indicates the two principal directions in which an Ω sensor can be displaced in the so-called "of f set- parallel" configuration;

FIG. 31 is a graphical repreεentation of tranε iεsion data taken uεing the fiber configuration in FIG. 30b; FIG. 32 iε a view of the εenεing portion of the fiber on an Ω εensor in the so-called "90 degree" configuration;

FIG. 33, which comprises FIGs. 33a and 33b, preεentε two of the εhapeε that the sensor of FIG. 32 asεumeε under εpecific displacements;

FIG. 34, which compriεeε FIGε. 34a and 34b, is a graphical representation of reflection data taken utilizing the fiber configuration presented in FIGs. 33a and 33b;

FIG. 35 provides a graphical summary of various data taken using the fiber configuration preεented in FIGs. 33a and 33 b;

FIG. 36, which compriseε FIGs. 36a and 36b, is a graphical repreεentation of tranεmiεεion data taken utilizing the fiber configuration presented in FIGs. 33a and 33b;

FIG. 37 iε a graphical repreεentation comparing transmiεεion data of an Ω εenεor taken uεing different typeε of fiberε; FIG. 38 iε a graphical representation for the transmission data presented in FIG. 37 of only one of the two fibers;

FIG. 39 is a graphical representation of tranεmiεεion data taken using a single-mode fiber;

FIG. 40, which comprises FIGs. 40a, 40b and 40c, iε a εche atic of variouε εhapes that an Ω sensor asεumes for different displacements;

FIG. 41, which compriseε FIGε. 41a, 41b and 41c, iε a εchematic of various shapes that an senεor aεεumeε for different displacements;

FIG. 42, which comprises FIGs. 42a and 42b, provides a view of an Ω sensor used at an arbitrary, off-axis angle in rotation and translation, respectively;

FIG. 43 iε a εchematic view of an Ω εenεor combined with a reflecting mirror; FIG. 44 is a block diagram of a εystem designed to measure displacementε uεing the mirrored sensor of FIG. 43 ;

FIG. 45 illustrates a non-planar, three-dimenεional version of the invention wherein the fiber bending occurs at leaεt partially outside the plane containing the two attachment points;

FIG. 46 indicates how the shape of a transversely offset Ω sensor progresses for extremely large displacements (between 70% and 130% of the extended length) ;

FIG. 47 is a representation of the "racetrack" shape an α senεor will aεsume for diεplacementε of more than 100% ;

FIG. 48 depictε the change of the εenεor from an Ω shape through an a shape into the racetrack shape; and

FIG. 49 is an example of a clamped-hinged Ω senεor . DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

ANALYSIS OF SHAPE FUNCTION FOR PLANAR FIBER SENSORS

For the purposes of our present discuεsion, the inventive fiber optic senεor conεiεtε of a freely εuspended length of optical fiber whose shape iε solely determined by the application of forces and/or torques applied at two specific locations which we call the attachment or clamping points. The fiber iε unconεtrained laterally between the two locationε of application of forces and/or torques. There are numerous shapes that can be implemented for a variety of fiber sensing configurations, each with unique properties. The firεt and moεt baεic εhape we conεider iε the uniaxial-type of εensor which iε straight in the extended configuration, aε εhown schematically in FIG. 1. We call this the Ω senεor configuration, since the buckled shape resembleε the greek letter omega for large def ormationε. In thiε configuration, the boundary conditions on the clamped regions are that the lateral displacement is zero and the slopes are zero at these points (pointε A and E in FIG. 1) so-called clamped clamped boundary conditions, although this is not necessary in more general cases.

The basic equation governing the bending of thin rodε and beamε (thoεe whoεe lateral dimenεionε are small compared to the radiuε of curvature) iε given in numerouε books discuεεing elaεticity (see Feynman , Landau and Lifshitz, Den Hartog, Love) as

= M (1)

R

where M is the bending moment at a particular location along the fiber, E is the fiber Young's modulus, R is the local radiuε of curvature, and I is the moment of inertia of the croεε-section. For the case of a cylindrical cross-section of radius a made of a single material

/ = ££_ (2)

(the form of the equation must be slightly modified when both the glass fiber and its coating are to be taken into account by replacing the product E_fI by (E_fI_f + E_CI_C) (Den Hartog pp. 109-110) where the subscripts c and f refer to fiber and coating respectively, and the moment of inertial of the coating iε given by I_c = ^■»" (b¹* - a¹* ) / 4 , where b iε the coating outer diameter. In typical telecommunicationε fibers, the coating outer diameter iε uεually almoεt a factor of 2 larger than the fiber diameter (240 μ vs. 125 μm) , and the soft acrylate modulus is considerably smaller than that of the glasε. In the caεe of polyimide coated fiber, the coating outer diameter iε somewhat smaller than for the acrylate fiber, but the modulus of polyimide is considerably larger than that of acrylate coatings. For the caεe of gold coated fiber, the coating iε typically a εmall fraction of the fiber diameter (~10uπι) , and the moduluε for gold εmaller than that of glaεs. In each individual case, if one is interested in determining the bending moments involved, one would have to calculate using explicit values for each of these. However, the shape function y(x) of the uniaxial elaεtica iε independent of the modulus and moment of inertia, and only depends on the straight length L₀ and the fractional compresεional from thiε value . The form that the bending moment takeε dependε on the boundary conditionε. For the caεe of a uniaxial planar shape shown in FIG. 2, and boundary conditions appropriate to the clamped-clamped case, the local bending moment is given by

M = M₀-Py ₍3₎

where M₀ is the torque applied at the ends of the freely suspended length P is the longitudinal force required to deform the rod, and y(x) is the function describing the lateral diεplacement of the fiber from the axiε as a function of the distance x measured from one clamping point. The terminology is εhown in the following figure. Note that both M₀ and P are unknown and must be determined by solving the bending beam equation and applying the clamped-clamped boundary conditions. An example of this procedure will follow.

For the case of planar deformations, the local radiuε of curvature R is related to the lateral displacement of the fiber y(x) by

(4)

Thus we find the equation describing the shape of the Ω-type planar sensor subject to the clamped end boundary conditions

In most discussions in engineering literature, the deformation of the rod or beam (or in this case, fiber) is small, and an approximation is usually made that neglects the first derivative of the displacement with reεpect to poεition, the εmall εlope approximation. Thiε reεultε in a linear, εecond order differential equation. In contrast, the senεors of the current invention employ nonlinear buckling and operate at displacementε far beyond the limits of validity of the small slope approximation εo that the full nonlinear equation 5 iε required to describe their operation. The solution to equation 5 which describes the shape of the planar configuration of the fiber is given in the form of the following parametric equations,

j *I₎[2E(φ\μ)-F(φ\μ)]/F(2π\μ) (6)

where y and x are the coordinates of a point on the curve describing the shape of the fiber, F(ψ>μ ) and E (Φ>μ ) are the elliptic integrals of the firεt and εecond kindε reεpectively , φ iε a parametric variable between 0 and 2τr which deεcribes where on the curve the point of interest is, L₀ is the εtraight length of the fiber and μ iε a variable determined by the solution to the following transcendental equation,

where Δx is the amount the fiber attachment points are displaced towards each other. As can be seen from equation 8, μ depends on the amount the fiber attachment pointε are displaced towards each other relative to the straight fiber length L₀. The shapes of the curveε are thuε univerεal for a given fractional amount of compression. Some shapes are presented in FIG. 2. Each succeεsive curve corresponds to an increase in compresεion of 10% relative to the straight fiber length between 90% and 50%. Note that the coordinates are scaled by the straight fiber length L₀, emphasizing the universal nature of the fiber shapeε, independent of the εtraight fiber length.

Having diεcussed the basic fiber shape, numerous other useful fiber shapes are posεible, uεing the εame principleε discussed above. Some of these are discuεsed in what follows.

MANUFACTURING

One makes the inventive senεorε by controlling the movement of an optical fiber at the two end-points (the attachments) , while the section of fiber between these two points iε left unrestricted. The two attachmentε are then moved with reεpect to each other. Moεt important iε to enεure a controlled location and slope of the fiber at the attachment points. The lengths L_Q to be employed will be discuεsed in the εection on εcaling.

1. SIMPLEST CONSTRUCTION TECHNIQUE: CLAMPING THE FIBER

The simplest Ω-type sensorε are made by clamping an optical fiber (61) (see FIG. 3) at two locationε. It iε important to realize that thiε method iε not ideal, εince it is necessary to hold the fiber sufficiently tight to ensure that it will not slip, while at the same time trying to avoid crushing the fiber. Thiε construction technique often introduces additional loss, rendering the sensor less senεitive than optimal, or introduσeε mechanical instabilities. One can reduce this problem somewhat by adding small grooves 62 to one or both of the two clamps (59, 60) (see block 60 in FIG. 3) . An example of a preferred clamp iε depicted in FIG. 4. The clamp 56 iε injection molded to have an inner diameter that iε εlightly smaller than the outer diameter of the fiber used. The fiber iε εlipped into the clamp through εlit 57. A εuitable locking mechaniεm 58 then closes the clamp, which is of εufficient length (typically 1 to 3 cm) to enεure that εlippage is avoided. The clamps can be mounted at any desired location on the fiber.

2. PRE-BENDING THE SENSOR:

A pre-bent configuration of the senεor could be manufactured by employing robotic deviceε programmed to provide preciεely identical conf gurations automatically in large quantities.

3. EXTERNAL ATTACHMENT TUBES ON THE FIBERS:

It iε easiest to first ensure that the fiber will bend in the desired way and to then deal with the attachment problem since it is important to ensure the boundary conditions. Baεically, thiε meanε that we firεt coaxially attach εmall pieceε of tubing 55 to the fiber (FIG. 5) (inner diameterε of slightly more than the diameter of the fiber; we are using 23 gauge hypo tubes for 50-125 acrylate coated fiber) , and to later clamp onto these tubeε to diεplace the sensor. FIG. 6 illustrateε how the fiber 51 enters tubes 52 and 54 and iε bent into εhape 53 between them. Thiε technique enεureε control in satisf action of the boundary conditions. The technique also allows for the easy transportation of fiber with sensors already built onto it, since the εmall tubes 55 do not greatly interfere with winding the fiber onto a spool.

Once the two attachment points 55 are connected to the fiber, making an operational εensor requires only moving these two attachment points in a controlled way. Thiε can be achieved by a mounting mechanism to secure the fiber and tubeε to the εtructure in queεtion.

We have found that it iε εometimeε eaεier to replace the closed tubeε 55 with expanεion pinε 50 of smaller inner diameterε (εee FIG. 7) . The εmall slot allows us to slip the fiber into the expansion pins at any location along the whole fiber, inεtead of having to pull great lengths of fiber through a εmall tube. The fiberε are εecured uεing cement 49.

One can alεo employ two different hypo- tubeε mounted inεide each other (see FIG. 8). Two inner tubeε 47 (23 gauge) are slid over the fiber 46, and the fiber iε attached to them at the deεired locations. The small inner diameter of these tubeε 47 ensures that the fiber iε centered and oriented coaxially. Since theεe tubes are thin walled and compresε under exceεs streεε, two expanεion pins 48 are then cemented over the inner tubes to provide additional strength. The final asεembly is depicted in FIG. 8.

Another technique shown (see FIG. 9) is to first mount two small hollow tubes 40 , 42 to the εtructure or mounting device at specific locations. The fiber 41 is fed through both tubeε 40, 42, and attached permanently to one of them (40) . Afterwardε, exceεε fiber iε fed into the other tube 42. The fiber 44 between tubeε 40 and 42 will again take on the character iεtic εhape. During the process the transmiεεion/ref lection loεs of the fiber is monitored until the desired loss is achieved. Then the fiber iε attached to the εecond tube. FIG. 9 illuεtrateε thiε procedure. 4. USING TUBING:

A different approach is to first inεtall tubing 43 (εee FIG. 10) in the deεired εhape and to later insert fiber into this tubing. FIG. 10 indicates the procedure to be used. Advantages are that the tubing is easier to bend and that one can avoid inεtalling the fiber until moεt of the εyεtem iε aεεembled. Another possibility is to use tubing that is pre-εhaped (and thuε of εpecified length and curvature). Thiε will:

(a) Eliminate problemε of having to deal with fiber that is under tension due to displacement; and

(b) Ensure reproducibility. Examples of tubing that can be used include PEEK (poly ether-ether-ketone) or polymide. Non-resilient clamps 63 and 64 define the attachment pointε.

EXPERIMENTAL RESULTS:

We now describe the experimental setup, how to perform transmission and reflection experiments, and some typical results to provide an idea of the capabilities of the inventive sensors. More detailed resultε for both tranεmiεεion and reflection experimεntε follow.

EXPERIMENTAL SETUP

The sensorε are mounted on two εides of a gap of controllable size and the signal is monitored as a function of the gap size.

As εhown in FIG. 11, we mounted the εenεor 30 at 90 degrees to the gap axiε. The distance between the two attachment points 33 , 34 of the senεor waε controlled uεing a Oriel Model 18011 motorized εtage 32 that has a reεolution of 0.1 μm. One of the two attachmentε waε driven, while the other, 31, was held εtationary. TRANSMISSION EXPERIMENTS

In doing transmission experiments with the inventive sensors one needs to ensure mode stripping of multi¬ mode fiberε both before and after the εensor. The light source should also be εpecified becauεe the response of the sensor is wavelength dependent.

Two different light εourceε were uεed for the experi sntε described, an Aab Hafo 1A191 LED adapted for connection to a fiber, operating at a nominal wavelength of 844 nm and an incandescent light bulb (CUDA Model 1-150) .

The fibers were alwayε in an overfilled launch condition. Mode stripping was achieved either by using a very long (1 km) lead-in or by adding a mode-stripper (10 turns on a 1.2 cm diameter mandrel) .

TYPICAL RESULTS

FIG. 12 presents the trans iεεion coefficient of a L₀ = 15 mm Ω εensor made using 50-125 multi-mode fiber (MMF) buffered by poly-acrylate (PA) and alternately displaced by plus and minus 50 μm/s with data collected at 2 Hz. The sensor waε illuminated with a CUDA incandescent light source and the signal waε directed onto a Si PIN photodiode. FIG. 13 preεentε the εame data versus the displacement from full extension; the linearity and reproducibility of the sensor iε evident. Note the large senεing range (>25% εtrain) . The sensor can be displaced further without damage. The laws deεcribing the εcaling factorε of the εenεor will be preεented below.

REFLECTION EXPERIMENTS

Reflection data were taken using a Tektronix TFP2 Fibermaster OTDR operating at 850 nm. Generally, data were taken with 3 , 8 or 20 ns pulεe lengthε and averaged 4096 timeε before εaving them on diεk. TYPICAL RESULTS

FIG. 14 presentε the OTDR data (20 ns. pulεe length; 4096 averageε) of an Ω εenεor of length L₀ = 15 mm made uεing 50-125 multi-mode fiber (MMF) buffered by a thin (~10 micronε) coating of gold. The εenεor waε diεplaced in εtepε of 250 μm from 0 to 2000 μ . The left hand scale displays the induced loεε across the sensors. The bottom axis illustrateε the diεtance of the εensor from the OTDR machine. FIG. 15 summarizes the data from FIG. 14 by displaying the size of the sensor transmisεion loεε versus the displacement. The linearity and large sensing range of the sensor are demonstrated.

DIFFERENT LIGHT SOURCES

Changing the light source from the 840 nm LED to an incandescent lamp changes the response of the senεor appreciably, as is indicated by FIG. 16 which compares the response of an L₀ = 15 mm 50-125 MMF Ω senεor under these different illumination conditions. In both caεeε, the εenεor only reεponded after a certain amount of displacement had been applied; however, that amount of diεplacement dependε upon the wavelength of the light εource used. Note that the LED light source haε a larger εenεing range than the white light and that the εlope of the reεponεe curve iε about 10% steeper for the white light. The source dependency of the response is expected.

DIFFERENT MOUNTING CONDITIONS

The effects of varying mounting conditions were tested on Ω εenεors by measuring a reεponεe, then unmounting and re-mounting the εensor , and taking the data a second time. Resultε are preεented in FIG. 17.

The differences in the mounting conditions show up in the slightly different responses. However, it is important to note that the relative senεitivity (the εlope of the sensor) is not affected by theεe conditions. Ω senεorε can thuε be calibrated in εitu to give abεolute reεponεeε, or directly uεed to indicate relative reεponses. WAVELENGTH DEPENDENCE OF THE SENSOR RESPONSE

The wavelength dependence of the Ω sensor reεponεe waε εtudied aε a function of diεplacement. Meaεurementε were taken with an ANDO AQ-6315B Optical Spectrum Analyzer and the CUDA incandeεcent light εource. The sensor was fabricated from Corning SMF28 fiber and had a straight length L₀ = 10 mm. The senεor waε diεplaced in incrementε of 100 μm from 0 to 1500 μm. FIG. 18 preεentε the tranεmitted power meaεurements in steps of 200 μm.

FIGs. 19a and 19b show the wavelength dependence of the sensor-induced losε on two different scales (logarithmic and linear) . This waε done by normalizing each εpectru for a given diεplacement with respect to the spectrum for zero displacement. The vertical lines in FIG. 19a correspond to the cutoff wavelengths for succeεsively higher order propagating modes. The fiber only propagates a single mode for wavelengths longer than approximately 1280 nm, two modes between 1280 nm and 810 nm, and εo on. Aε can be εeen clearly in FIG. 19, the εenεor reεponεe varieε conεiderably aε a function of wavelength. FIG. 20 summarizeε the εenεor reεponεe for the four wavelengthε of 650 nm, 840 nm, 950 nm and 1300 nm, which are quite different. For example, between 400 μm and 700 μm displacement, the slope of the response at 1300 nm is -1.7xl0^~3 /μm and the slope at 840 nm is -7.9xl0^-lt /μm. This wavelength dependent response can be used to great advantage in practical situationε. An example would be that by selecting the wavelength at which the senεor iε interrogated, one can achieve a high response for various diεplacementε and extend the εenεing range of the εenεor .

COMPARING TRANSMISSION AND REFLECTION MEASUREMENTS

We compared transmission and reflection measurements on an L_Q = 10 mm 50-125 polyacrylate buffered MMF Ω sensor. The transmiεεion data were taken uεing 840 nm LED aε a light εource and the reflection data using a Tektronix TPF2 FiberMaster operating at 850 nm with a pulse length of 8 ns and averaged over 4096 scanε. The εenεor was compresεed in εucceεεive increments of 250 μm. FIG. 21 compareε the reεults due to transmiεεion and reflection meaεurementε. In order to compare the two measurements, we converted the reflection data (triangles) in dB into transmiεεion data (εquareε) uεing

T = \0~^{R 10 (9)}

where R are the reflection data. Aε can be seen, the cor espondence between the different measurement methods iε excellent.

SCALING LAWS

There are certain scaling laws that have been experimentally found for Ω senεorε which enable a theoretical underεtanding of the reεponεe of theεe εensors. We investigated the specific case of 50-125 polyacrylate buffered multi-mode fiber under illumination by an 840 nm LED. EXPERIMENTAL SETUP

With reference to FIG. 22, a εetup in which four εenεor ε (of lengths L_Q = 5 mm, 10 mm, 15 mm and 20 mm) was built all within 1 on a polyacrylate buffered 50- 125 MMF fiber. Light was injected from 840 nm LED 20 and pasεed through a mode εtripper 22 conεisting of a 1 km long segment of 50-125 MMF to remove cladding modes, then injected into the segment of fiber containing the four sensors 24, passed through a second mode stripper 26 consisting of 10 turns on a 1.5 cm diameter mandrel and finally directed onto a silicon photodetector 28. Splices 21 and 27 connect the εensors to the other parts of the setup. The four different sensors were thus exposed to identical optical conditions. Each sensor uses attachment point 23 and 25.

RESULTS

The resultε of the meaεurementε are preεented in FIG. 23 which showε the tranεmiεεion coefficient of the four different sensors versuε the diεplacement to which they are exposed. The four curves are, from left to right, ordered in increasing L₀. We see that the L_Q = 5 mm εensor iε much more sensitive than the

L₀ = 20 mm sensor, but that it alεo haε a much smaller εenεing range.

DEFINITION OF THE THRESHOLD DISPLACEMENT

We proceed to show that these four curves scale, i.e., that there is a general law describing the loεε of an Ω εenεor. In order to do so, we define a threshold displacement L_t aε the displacement at which the two asymptotes of a loss curve (the flat initial region and the linear loεε) interεect. FIG. 24 de onεtrateε how to determine the location of the threεhold diεplacement L_t for the caεe of the L₀ = 20 mm senεor .

For all the εtudied εenεor lengthε we found that the εignal at the cor reεponding threshold displacementε was between 97.2% and 97.3% of the maximum tranεmiεεion of the εenεor . TRANSMISSION VS. SCALED DISPLACEMENT

We now define a εcaled diεplacement L_g aε the diεplacement L of the sensor divided by the corresponding threshold diεplacement L_fc, i.e., L_s = L/L_t. Upon plotting the transmisεion coefficients of all four senεorε vs. thiε εcaled diεplacement, we εee that the four curveε overlap very well (FIG. 25) .

We find that there iε a univerεal law that deεcribeε the response of an Ω sensor if the displacement is measured aε a εcaled diεplacement.

Empirically, we find that the threεhold diεplacement L_t for 50-125 polyacrylate buffered MMF at 840 nm illumination of a εensor depends on the unstretched length L_Q of the sensor in a power-law fashion:

2.44

L_j.[μm]= 1.63 L [mm] (10)

FIG. 26 demonstrateε that this relationship (solid line) and the empirical data (dots) coincide well. CORRELATION BETWEEN SCALED LENGTH AND OVERALL SHAPE AND LOCAL CURVATURE

In order to understand why εensors of identical scaled length L_s (but different overall length L₀) have the εame transmission loss, we plotted the εhape of the four different εensors studied when compresεed to a εcaled length of L_s = 1. FIG. 27 represents the reεultε of this calculation.

We see that the senεor s overlap (have εimilar radii of curvature) in the part of the εenεor adjacent to the attachment point. By symmetry of the Ω shape function, the radii of curvature are identical for a given senεor at points A, C and E of FIG. 1 and all locations that are at identical distanceε from theεe pointε. FIG. 28 presents the local radii of curvature along the senεo ε out to ε = 1.2 mm from point A.

SIMPLIFIED MODEL FOR THE TRANSMISSION RESPONSE OF AN Ω SENSOR

The normalized general reεponεe of an εenεor made from 50-125 MMF-PA can thuε be deεcribed in detail uεing a general model which haε 3 diεtinct regions:

1) An initial linear region for displacement less than threshold L_t of very small sensitivity (from L_g = 0 to 0.75);

2) A linear region of high sensitivity (between L_s = 1.5 and 3) ; and

3) A crosε-over region between theεe two linear regionε.

We approximate the intermediate region aε having a linear response. Least square fits to the scaled εensor reεponse curves, yield the following relationship between the transmiεεion coefficient T and the εcaled diεplacement L_g:

FIG. 29 represents this idealized reεponse (solid line) as well as the actual reεponse of the L₀ = 20 mm εenεor (dashed line) showing the agreement with the simple model. For compression of more than L_s = 4, the senεor reεponse flattens out (εee FIG. 21) .

CONCLUSIONS FROM THE SCALING LAWS

Baεed upon the foregoing:

1) Ω sensor ε (at least those made out of 50-125 polyacrylate coated MMF and illuminated by an 840 nm LED) have a universal response curve that depends only on the amount by which they have been compres εed and their overall uncompressed length L₀ ;

2) It iε poεεible to cuεto -deεign sensorε for εpecific applicationε. Baεed on the relation between sensitivity and range for Ω εenεorε. Thuε, for any deεired εenεitivity, we can predict the range of the senεor. We can alεo find the optimal initial diεplacement that will allow a linear responεe over that range;

3) Although not preεented here, the response of an sensor is highly sensitive to the amount of cladding light present. The sensorε will be more senεitive (i.e., have a larger change in tranεmission for the same amount of displacement) if cladding modes are present. Thiε iε why we need to enεure that all cladding modeε are taken into account. In certain circumstances cladding mode excitation prior to a sensor may be used to enhance the senεitivity even further.

OMNI-DIRECTIONAL OFFSET SENSOR

One can alεo build Ω εenεor s with attachment pointε that are off εet from parallel. FIG. 30, which compriseε FIG. 30a and 30b, repreεentε an implementation of thiε deεign. One can then meaεure diεplacementε in either the y-direction (FIG. 30a) or the x-direction (FIG. 30b) , aε well aε any combination of theεe displacements. FIG. 31 iε a graphical representation of data taken in the configuration of FIG. 30a. The measured senεor waε made from 50-125 PA MMF and illuminated by white light. The εenεor with an L₀ of 10 mm waε diεplaced by Δx = 2.5 mm; data were taken for motion in the y-direction.

OMNI-DIRECTIONAL - 90 DEGREES

One can alεo mount the inventive sensorε εo that their diεplacement doeε not occur along the principal axis joining the two attachment points. A εpecialized mounting condition (at 90 degrees) is depicted in FIG. 32. For this mounting condition, any relative diεplacement of the two attachmentε can be deεcribed as a diεplacement of one of the two in the x-direction, while the other iε moving in the y-direction.

The advantage of εuch a mount iε that a crack that occurε in an arbitrary direction between the two attachment pointε will change the relative diεplacement of one with reεpect to the other. Thiε will result in a change in the shape of the εenεor, which, in turn, will change the transmission properties. While it will be impoεεible to determine the exact relative motion (two variableε) from the output of the εenεor (one variable) , the εenεor can determine the fact that some movement has taken place and the amount of that movement.

Examples of posεible relative motion are preεented in FIGε. 33a and 33b. The arrow indicateε the motion for which measured data are preεented in FIG. 34a. FIG. 33b εhowε the εhape of the εensor after one of the two attachment pointε has been displaced substantially. Again, the arrow refers to the motion for which data were taken and as presented in FIG. 34b.

The data presented in FIGs. 34a and 34b were taken using 50-125 polyacrylate MMF fiber. The initial separation of the attachment points waε x₀= 4mm and y₀ = 4mm. All motion εtudied reεulted in an increase in this εeparation. In FIG. 34a the x-attachment iε moved by up to 4 mm further in the direction indicated in FIG. 33a. Data were taken every 500 μm of diεplacement and are preεented in FIG. 34a. The sensor was then returned to its original poεition, the y-attachment moved by 2 mm, and data taken while the x-attachment was moved by up to 2 mm. Data were taken every 500 μm of displacement and are preεented in FIG. 34b.

FIG. 35 combineε all the data taken. Either the x-attachment or the y-attachment waε offεet by 0 , 1 or 2 mm from x₀ or y₀, reεpectively . Data were then taken for displace entε in the y-direction and x-direction, reεpectively.

Aε can be εeen in FIG. 35 , the sensor response is independent of which attachment was offset and which one was moved, as expected from symmetry considerations. The sensor iε thuε capable of detecting arbitrary crack directionε.

Further confirmation of the omni-directional reεponεe characteristics of the 90 degrees Ω-type senεor εhown in FIG. 32, iε shown in FIGs. 36a and 36b, where the same sensor aε deεcribed above waε measured in tranεmiεεion uεing the CUDA white light εource. FIG. 36 εhowε that x and y-diεplacementε have nearly identical optical reεponses with minimal hystereεiε. No special precautions were taken to ensure that the sensor was fabricated symmetrically. The small residual difference in reεponεe between increasing and decreasing diεplacementε iε believed to be due to backlash in the micropositioning stages used.

TWO MODE SENSORS

Corning SMF 28 fiber, which is single mode at 1300 nm wavelength, supports two propagating modes at 840 nm, the LP_Q1 and LP_n modes. FIG. 37 showε the optical reεponse of two L_Q = 10mm Ω-type εenεorε made with Corning 50-125 multimode fiber and with Corning SMF-28 fiber. Both sensors were illuminated with an 840 nm LED. As can be seen in FIG. 37, the threshold diεplacement iε much greater for the highly multimode 50-125 fiber, and the SMF 28 two-mode fiber haε a εignif icantly greater εenεitivity for diεplacementε between 200 and 800 ym. For larger displacements, the two different fiber types exhibit nearly identical εlopeε. The SMF 28 data alone iε presented in FIG. 38, with two linear leaεt εquare fit lineε εuper impoεed. The data clearly demonstrate a two regime response associated with the different losses of each mode.

SINGLE MODE SENSORS

FIG. 39 presentε the optical reεponεe of a εingle mode L₀ = 9 mm Ω-type εenεor . The εenεor waε illuminated with a four mode He-Ne laser operating at 633 nm. The data presented are for three different εcanε cor reεponding to expansion, compresεion and a final expanεion. The data exhibit far more intenεity noise than the LED data due to the He-Ne amplitude noiεe. In εpite of thiε noiεe, the data clearly exhibit reproducible loεε oεcillationε, thought to be due to interference of the guided mode with whiεpering gallery modeε of the cladding and fiber coating. Thiε interf erometric effect can be utilized in device applications for enhancing εenεitivity and providing an abεolute diεplacement calibration by uεing a frequency modulation technique known in the field of optical interf erometric εensors. SUMMARY

It will now be understood that what has been disclosed herein compriseε a new concept in εenεorε and particularly in fiber optic εensors. A number of different embodiments have been disclosed. FIG. 40, comprising FIGs. 40a through 40c, illustrates what is referred to herein as the Ω-type fiber optic displacement sensor . As εhown in FIG. 40 , a length of optical fiber, restrained only at two spaced pointε to move in a unitary direction, becomes increasingly buckled as the distance between those spaced points is reduced. The optical tranεmiεεion loss through the fiber increases in a highly predictable manner that permits extremely sensitive displacement measurement over a wide dynamic range. FIG. 41, comprising FIGs. 41a through 41c, illuεtrateε what iε referred to herein as an α-type εenεor wherein the buckling-induced optical transmission loss is a result of a loop- configured length of fiber having boundary conditionε εimilar to the Ω-type εenεor. A more generic form of the Ω-type εenεor iε εhown in FIGs. 42a and 42b wherein one of the two directions of movement of the spaced pointε may be at an angle Φ with reεpect to the other direction, where Φ is any angle from 0 to 90 degrees. Loεε through a εenεor of the preεent invention may be meaεured in many wayε. By way of further example, FIGε. 43 and 44 illuεtrate uεe of a mirror 18 at one end 17 of an Ω-type εenεor wherein a light εource 10 and a detector 15 are connected at end 16 through a terminated end 14/coupler 11 to an Ω-type sensor 12 wherein a mirror 13 reflectε light which thuε experienceε a double bend loεε induced by the buckling effect. Finally, it will be understood that although each of the heretofore diεclosed embodiments relieε on a planar configured fiber between the εpaced attachment pointε, the present invention is not neceεεarily limited to εuch a configuration. FIG. 45 illuεtrateε a non-planar or three-dimenεional verεion of the invention wherein the fiber bending occurs at least partially outside the plane containing the two spaced attachment points between which a distance is determined by the light transmiεεion loεε through the fiber. The variouε directionε of motion are indicated by arrowε. FIG. 45 εhowε a poεεible three-dimenεional εhape the εensor can assume. Any relative motion between the two attachment points can be resolved into being composed of motion along the three principal axes, as indicated in the figure, and consequently εenεed. Note that the moving attachment point can be located anywhere inεide a εphere of εlightly leεε than radiuε L_Q (the extended εenεor length) around the εtationary attachment point.

FIG. 46 preεentε the progreεεion of the εhape of an Ω sensor whose two attachment pointε were offset transversely with respect to each other by a distance Δz . The three shapes a, b and c correspond to displacements by 70%, 100% and 130% of the extended sensor length L₀, respectively. The distance Δz is only necesεary to allow the two attachment points to pass next to each other and can be small in practice. Such an Ω sensor can be displaced by up to 180% of its length and still remain operational.

FIG. 47 iε a repreεentation of the εhape a planar εenεor will aεεume when displaced by more than 100% of itε extended length. We call thiε shape the "racetrack" shape. The parts of the fiber leading into and away from the senεor again have to avoid each other, but the εhape haε no other reεtriction.

FIG. 48 presents another posεible progreεεion of the sensor shape when the εenεor iε diεplaced by large amounts. Unlesε εpecial precautionε (εpecif ically , twisting the fiber) are taken, the Ω senεor will (for diεplacements larger than about 75% of itε length) twiεt in the third dimension (as indicated in case a) , eventually crosεing into a εhape related to that of the α sensor . For a displacement of 100% (caεe b in the figure), the εenεor will aεεume a circular εhape, and for greater diεplacementε move into a racetrack-like εhape aε introduced in FIG. 47. The εenεor can εenεe and εurvive an exceptionally large diεplacement.

FIG. 49 εhowε an Ω type εenεor having clamped-hinged boundary conditionε. Thiε iε uεeful for εituationε where there are extremely large dimenεional variations where the hinged end allowε for larger diεplacementε than clamped endε. Those having skill in the art to which the present invention pertains, will now perceive variouε modif icationε and additionε which may be made to the invention while εtill achieving the objectε and advantageε thereof. Accordingly, it will be underεtood that all εuch modif icationε and additionε are deemed to be within the scope hereof which is to be limited only by the appended claims and their equivalents.

We claim:

Claims

1. A fiber optic sensor comprising: a selected length of optical fiber positioned between two εpaced points, at leaεt one of εaid pointε being free to move relative to the other of εaid εpaced pointε along a selected direction in responεe to a sensed parameter, the length of fiber being unrestrained between the spaced points to permit predictable non-linear buckling of the fiber as the distance between said spaced pointε iε reduced; and meanε for meaεuring relative light transmission loss through said length of fiber to determine the preciεe diεtance between εaid εpaced pointε aε a function of said light transmiεεion loss.

2. The senεor recited in claim 1 wherein said length of fiber is parallel to said selected direction at said spaced points.

3. The senεor recited in claim 2 wherein said length of fiber is held parallel to said selected direction at said spaced points without any subεtantial compreεεion of said fiber.

4. The εenεor recited in claim 3 wherein said fiber iε held parallel at εaid εpaced points by external tubes.

5. The sensor recited in claim 3 wherein said fiber is held parallel at said spaced points by elongated slotted pins.

6. The sensor recited in claim 3 wherein εaid fiber is held parallel at said spaced points by non- compressing clamps.

7. The senεor recited in claim 1 wherein εaid fiber iε configured aε a loop between εaid εpaced points.

8. The εenεor recited in claim 1 wherein εaid εpaced pointε are located on two diεtinct parallel lineε .

9. The εenεor recited in claim 1 wherein said spaced points are located on two distinct lineε forming an angle of from 0 to 180 degrees therebetween.

10. The sensor recited in claim 1 wherein said spaced points are located on two distinct lines, each such line being in a different plane intersecting at leaεt a portion of said length of fiber.

11. The sensor recited in claim 1 wherein said length of fiber is taken from the group of fibers consisting of single mode fiber, two mode fiber, εeveral mode fiber and multi-mode fiber.

12. The senεor recited in claim 1 wherein εaid length of fiber iε εelected to have a wavelength- dependent loεε characteriεtic which provideε a εelected reεolution for the expected range of diεtance variation between said spaced points.

13. The sensor recited in claim 1 wherein said means for meaεuring comprises a source of light at a first end of εaid fiber and a detector at a εecond end of εaid fiber.

14. The εensor recited in claim 1 wherein said means for measuring compriseε an optical time domain reflectometer.

15. The sensor recited in claim 1 wherein said means for measuring compriseε a εource of light and a detector at a firεt end of said fiber and a mirror at a second end of said fiber.

16. A εensor comprising: a length of optical fiber at least one selected portion of which iε secured between two spaced points, at least one of said points being movable relative to the other of said spaced points along a selected direction in response to a physical phenomenon, said selected portion of fiber being unrestrained between said εpaced pointε to permit macrobending of said selected portion of fiber aε the diεtance between said spaced points is changed by said physical phenomenon; and means for measuring the light transmisεion attenuation through εaid εelected portion of εaid fiber due to εaid macrobending.

17. The sensor recited in claim 16 wherein said length of fiber is parallel to said selected direction at εaid εpaced pointε.

18. The εenεor recited in claim 17 wherein εaid length of fiber iε held parallel to εaid εelected direction at εaid spaced points without any subεtantial compreεsion of said fiber.

19. The sensor recited in claim 18 wherein said fiber is held parallel at εaid spaced points by external tubes.

20. The senεor recited in claim 18 wherein εaid fiber is held parallel at said spaced points by elongated slotted pins.

21. The sensor recited in claim 18 wherein said fiber is held parallel at said spaced points by non- compressing clamps.

22. The senεor recited in claim 16 wherein εaid fiber iε configured aε a loop between εaid εpaced points.

23. The εenεor recited in claim 16 wherein εaid εpaced pointε are located on two diεtinct parallel lineε.

24. The εenεor recited in claim 16 wherein εaid εpaced pointε are located on two diεtinct lineε forming an angle of from 0 to 180 degreeε therebetween.

25. The sensor recited in claim 16 wherein said εpaced pointε are located on two diεtinct lineε, each εuch line being in a different plane interεecting at least a portion of said length of fiber.

26. The εenεor recited in claim 16 wherein εaid length of fiber iε taken from the group of fiberε conεisting of single mode fiber, two mode fiber, several mode fiber and multi-mode fiber.

27. The εenεor recited in claim 16 wherein εaid length of fiber iε εelected to have a wavelength- dependent losε characteriεtic which provides a selected resolution for the expected range of distance variation between said spaced points.

28. The sensor recited in claim 16 wherein εaid meanε for meaεuring compriseε a source of light at a firεt end of εaid fiber and a detector at a εecond end of εaid fiber.

29. The sensor recited in claim 16 wherein said means for measuring compriεeε an optical time domain reflectometer.

30. The εensor recited in claim 16 wherein said means for meaεuring compriεeε a εource of light and a detector at a firεt end of εaid fiber and a mirror at a εecond end of said fiber.

31. The εensor recited in claim 16 wherein said selected portion of fiber is clamped at one of εaid εpaced pointε and hinged at the other of εaid εpaced pointε.