Abstract:
A fiber Bragg grating based sensor is disclosed. The sensor comprises an optical waveguide having a core and a cladding. The core comprises a pressure sensor such as a fiber Bragg grating. In one embodiment, a support is affixed around the cladding which has two first portions each having a first diameter. The pressure sensor is located at a second portion of the support positioned between the two first portions which has a second smaller diameter, thus giving the sensor a “dog bone” shape. In another embodiment, the dog bone shape is imparted by positioning the pressure sensor at a portion of a waveguide having a reduced cladding diameter.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     This is a continuation of U.S. patent application Ser. No. 09/455,867, filed Dec. 6, 1999 now U.S. Pat. No. 6,422,084, which is a continuation-in-part of U.S. patent application Ser. No. 09/399,404, filed Sep. 20, 1999 now abandoned, which is a continuation-in-part of U.S. patent application Ser. No. 09/205,944, filed Dec. 4, 1998 now abandoned. Priority is claimed to these earlier applications. 
     U.S. patent applications Ser. No. 09/455,865, entitled “Tube-Encased Fiber Grating,” Ser. No. 09/455,866, entitled “Strain-Isolated Bragg Grating Temperature Sensor,” Ser. No. 09/456,112 (now U.S. Pat. No. 6,229,827), entitled “Compression-Tuned Bragg Grating and Laser,” Ser. No. 09/456,113, entitled “Pressure Isolated Bragg Grating Temperature Sensor,” Ser. No. 09/399,504, entitled “Fiber Optic Bragg Grating Pressure Sensor,” Ser. No. 09/455,868, entitled “Large Diameter Optical Waveguide, Grating, and Laser,” and Ser. No. 09/205,845, entitled “Method and Apparatus For Forming A Tube-Encased Bragg Grating,” all contain subject matter related to that disclosed herein. 
    
    
     TECHNICAL FIELD 
     This invention relates to fiber optic pressure sensors, and more particularly to a Bragg grating pressure sensor. 
     BACKGROUND ART 
     Sensors for the measurement of various physical parameters such as pressure and temperature often rely on the transmission of strain from an elastic structure (e.g., a diaphragm, bellows, etc.) to a sensing element. In a pressure sensor, the sensing element may be bonded to the elastic structure with a suitable adhesive. 
     It is also known that the attachment of the sensing element to the elastic structure can be a large source of error if the attachment is not highly stable. In the case of sensors which measure static or very slowly changing parameters, the long term stability of the attachment to the structure is extremely important. A major source of such long term sensor instability is a phenomenon known as “creep”, i.e., change in strain on the sensing element with no change in applied load on the elastic structure, which results in a DC shift or drift error in the sensor signal. 
     Certain types of fiber optic sensors for measuring static and/or quasi-static parameters require a highly stable, very low creep attachment of the optical fiber to the elastic structure. Various techniques exist for attaching the fiber to the structure to minimize creep, such as adhesives, bonds, epoxy, cements and/or solders. However, such attachment techniques may exhibit creep and/or hysteresis over time and/or high temperatures. 
     One example of a fiber optic based sensor is that described in U.S. patent application Ser. No. 08/925,598 (now U.S. Pat. No. 6,016,702), entitled “High Sensitivity Fiber Optic Pressure Sensor for Use in Harsh Environments,” to Robert J. Maron, which is incorporated herein by reference in its entirety. In that case, an optical fiber is attached to a compressible bellows at one location along the fiber, and to a rigid structure at a second location along the fiber. A Bragg grating is embedded within the fiber between these two attachment locations with the grating being in tension. As the bellows is compressed due to an external pressure change, the tension on the fiber grating is reduced, which changes the wavelength of light reflected by the grating. If the attachment of the fiber to the structure is not stable, the fiber may move (or creep) relative to the structure it is attached to, and the aforementioned measurement inaccuracies occur. 
     In another example, an optical fiber Bragg grating pressure sensor where the fiber is. secured in tension to a glass bubble by a UV cement is discussed in Xu, M. G., Beiger, H., Dakein, J. P., “Fibre Grating Pressure Sensor With Enhanced Sensitivity Using A Glass-Bubble Housing,” Electronics Letters, 1996, Vol. 32, pp. 128-129. 
     However, as discussed hereinbefore, such attachment techniques may exhibit creep and/or hysteresis over time and/or high temperatures, or may be difficult or costly to manufacture. 
     SUMMARY OF THE INVENTION 
     Objects of the present invention include provision of a fiber optic pressure sensor with minimal creep. 
     According to the present invention, a pressure sensor comprises an optical sensing element, having at least one pressure reflective element disposed therein along a longitudinal axis of the sensing element, the pressure reflective element having a pressure reflection wavelength; the sensing element being axially strained due to a change in external pressure, the axial strain causing a change in the pressure reflection wavelength, and the change in the pressure reflection wavelength being indicative of the change in pressure; and at least a portion of the sensing element having a transverse cross-section which is contiguous and made of substantially the same material and having an outer transverse dimension of at least 0.3 mm. 
     According further to the present invention, the sensing element comprises: an optical fiber, having the reflective element embedded therein; and a tube, having the optical fiber and the reflective element encased therein along a longitudinal axis of the tube, the tube being fused to at least a portion of the fiber. According further to the present invention, the sensing element comprises a large diameter optical waveguide having an outer cladding and an inner core disposed therein and an outer waveguide dimension of at least 0.3 mm. 
     According still further to the present invention, the reflective element is a Bragg grating. According still further to the present invention, the sensing element has a dogbone shape. According still further to the present invention, the sensing element comprises a dogbone shape and comprises an outer tube fused to at least a portion of large sections of the dogbone shape on opposite axial sides of the reflective element. 
     The present invention provides a fiber grating disposed in an optical sensing element which includes an optical fiber fused to at least a portion of a glass capillary tube (“tube encased fiber/grating”) and/or a large diameter waveguide grating having an optical core and a wide cladding, which is elastically deformable based on applied pressure. The invention substantially eliminates creep and other optical fiber attachment problems. The sensing element may be made of a glass material, such as silica or other glasses. Also, the invention provides sensing with very low hysteresis. The present invention allows forces to be applied axially against the sensor element end-faces thereby allowing for high sensor sensitivity. The present invention also provides improved sensor reliability when used in compression. Also, one or more gratings, fiber lasers, or a plurality of fibers may be disposed in the element. 
     The grating(s) or laser(s) may be “encased” in the tube by having the tube fused to the fiber on the grating area and/or on opposite axial sides of the grating area adjacent to or a predetermined distance from the grating. The grating(s) or laser(s) may be fused within the tube or partially within or to the outer surface of the tube. Also, one or more waveguides and/or the tube encased fiber/gratings may be axially fused to form the sensing element. 
     Further, the invention may be used as an individual (single point) sensor or as a plurality of distributed multiplexed (multi-point) sensors. Also, the invention may be a feed-through design or a non-feed-through design. The sensor element may have alternative geometries, e.g., a dogbone shape, that provides enhanced force to wavelength shift sensitivity and is easily scalable for the desired sensitivity. 
     The invention may be used in harsh environments (high temperature and/or pressure), such as in oil and/or gas wells, engines, combustion chambers, etc. For example, the invention may be an all glass sensor capable of operating at high pressures (&gt;15 kpsi) and high temperatures (&gt;150° C.). The invention will also work equally well in other applications independent of the type of environment. 
     The foregoing and other objects, features, and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a side view of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 2 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 3 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 4 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 5 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 6 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 7 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 8 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 9 is a side view of a tube-encased fiber grating sensor mounted to a wall of a housing, in accordance with the present invention. 
     FIG. 10 is a side view of a tube-encased fiber grating sensor suspended within a housing, in accordance with the present invention. 
     FIG. 11 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having two gratings in a fiber encased in a tube, in accordance with the present invention. 
     FIG. 12 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a dual capillary tube, in accordance with the present invention. 
     FIG. 13 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a capillary tube collapsed and fused to the fiber on opposite sides of a grating, in accordance with the present invention. 
     FIG. 14 is a side view of an alternative embodiment of a tube-encased fiber grating sensor of FIG. 13, in accordance with the present invention. 
     FIG. 15 is a side view of an alternative embodiment of a tube-encased fiber grating having a long axially protruding section, in accordance with the present invention. 
     FIG. 16 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a diaphragm, in accordance with the present invention. 
     FIG. 17 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a long axially protruding section with a portion that is not collapsed onto the fiber, in accordance with the present invention. 
     FIG. 18 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a circular housing cross-section, in accordance with the present invention. 
     FIG. 19 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a piston that has a hollow section ported to pressure, in accordance with the present invention. 
     FIG. 20 is a side view of the alternative embodiment of FIG. 19, in accordance with the present invention. 
     FIG. 21 is a block diagram of a plurality of tube-encased fiber grating sensors connected in series, in accordance with the present invention. 
     FIG. 22 is a side view of a tube-encased fiber grating sensor having two separate optical fibers encased in a common tube, in accordance with the present invention. 
     FIG. 23 is an end view of the embodiment of FIG. 21, in accordance with the present invention. 
     FIG. 24 is an end view of a tube-encased fiber grating sensor having two separate optical fibers encased in a common tube, in accordance with the present invention. 
     FIG. 25 is a side view of a tube-encased fiber grating where the tube is collapsed on the fiber only over the length of the grating, in accordance with the present invention. 
     FIG. 26 is a side view of an alternative embodiment of a tube-encased fiber grating sensor, in accordance with the present invention. 
     FIG. 27 is a tube-encased fiber grating sensor with a portion mounted inside a pressurized region of a housing and a portion of a tube located outside the pressurized region, in accordance the present invention. 
     FIG. 28 is an alternative embodiment of a tube-encased fiber grating sensor having a pressure-isolated temperature grating, in accordance with the present invention. 
     FIG. 29 is an alternative embodiment of a tube-encased fiber grating sensor having a temperature grating exposed to pressure, in accordance with the present invention. 
     FIG. 30 is a side view of an alternative embodiment of a tube-encased fiber grating sensor having a tunable distributed feedback (DFB) fiber laser encased in a tube, in accordance with the present invention. 
     FIG. 31 is a side view of a large diameter optical waveguide having a grating disposed therein, in accordance with the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to FIG. 1, a fiber Bragg grating pressure sensor comprises a known optical waveguide  10 , e.g., a standard telecommunication single mode optical fiber, having a Bragg grating  12  impressed (or embedded or imprinted) in the fiber  10 . The fiber  10  has an outer diameter of about 125 microns and comprises silica glass (SiO 2 ) having the appropriate dopants, as is known, to allow light  14  to propagate along the fiber  10 . The Bragg grating  12 , as is known, is a periodic or aperiodic variation in the effective refractive index and/or effective optical absorption coefficient of an optical waveguide, similar to that described in U.S. Pat. Nos. 4,725,110 and 4,807,950, entitled “Method for Impressing Gratings Within Fiber Optics,” to Glenn et al; and U.S. Pat. No. 5,388,173, entitled “Method and Apparatus for Forming Aperiodic Gratings in Optical Fibers,” to Glenn, which are hereby incorporated by reference to the extent necessary to understand the present invention. However, any wavelength-tunable grating or reflective element embedded, etched, imprinted, or otherwise formed in the fiber  10  may be used if desired. As used herein, the term “grating” means any of such reflective elements. Further, the reflective element (or grating)  12  may be used in reflection and/or transmission of light. 
     Other materials and dimensions for the optical fiber or waveguide  10  may be used if desired. For example, the fiber  10  may be made of any glass, silica, phosphate glass, or other glasses, or made of glass and plastic, or plastic, or other materials used for making optical fibers. For high temperature applications, optical fiber made of a glass material is desirable. Also, the fiber  10  may have an outer diameter of 80 microns or other diameters. Further, instead of an optical fiber, any optical waveguide may be used, such as, a multi-mode, birefringent, polarization maintaining, polarizing, multi-core, or multi-cladding optical waveguide, or a flat or planar waveguide (where the waveguide is rectangular shaped), or other waveguides. As used herein the term “fiber” includes the above described waveguides. 
     The light  14  is incident on the grating  12 , which reflects a portion thereof as indicated by a line  16  having a predetermined wavelength band of light centered at a reflection wavelength λ 1 , and passes the remaining wavelengths of the incident light  14  (within a predetermined wavelength range), as indicated by a line  18 . The fiber  10  with the grating  12  therein is encased in and fused to at least a portion of an elastically deformnable pressure sensing element  20 , such as a cylindrical glass capillary tube, referred to hereinafter as a tube. The tube  20  may have an outer diameter d 1  of about 2 mm and a length L 1  of about 12 mm. The grating  12  has a length Lg of about 5 mm. Alternatively, the length L 1  of the tube  20  may be substantially the same length as the length Lg of the grating  12 , such as by the use of a longer grating, or a shorter tube. Other dimensions and lengths for the tube  20  and the grating  12  may be used. Also, the fiber  10  and grating  12  need not be fused in the center of the tube  20  but may be fused anywhere in the tube  20 . Also, the tube  20  need not be fused to the fiber  10  over the entire length L 1  of the tube  20 . 
     The tube  20  is made of a glass material, such as natural or synthetic quartz, fused silica, silica (SiO 2 ), Pyrex® by Corning (boro silicate), or Vycor® by Corning (about 95% silica and 5% other constituents such as Boron Oxide), or other glasses. The tube  20  should be made of a material such that the tube  20  (or the inner diameter surface of a bore hole in the tube  20 ) can be fused to (i.e., create a molecular bond with, or melt together with) the outer surface (or cladding) of the optical fiber  10  such that the interface surface between the inner diameter of the tube  20  and the outer diameter of the fiber  10  become substantially eliminated (i.e., the inner diameter of the tube  20  cannot be distinguished from and becomes part of the cladding of the fiber  10 ). 
     For best thermal expansion matching of the tube  20  to the fiber  10  over a large temperature range, the coefficient of thermal expansion (CTE) of the material of the tube  20  should substantially match the CTE of the material of the fiber  10 . In general, the lower the melting temperature of the glass material, the higher the CTE, e.g., a fused silica tube and optical fiber. Thus, a silica fiber having a high melting temperature and low CTE and a tube made of another glass material, such as Pyrex® or Vycor® having a lower melting temperature and higher CTE, results in a thermal expansion mismatch between the tube  20  and the fiber  10  over temperature. However, it is not required for the present invention that the CTE of the fiber  10  match the CTE of the tube  20  (discussed more hereinafter). 
     Instead of the tube  20  being made of a glass material, other elastically deformable materials may be used, provided the tube  20  can be fused to the fiber  10 . For example, for an optical fiber made of plastic, a tube made of a plastic material may be used. 
     The axial ends of the tube  20  where the fiber  10  exits the tube  20  may have an inner region  22  which is inwardly tapered (or flared) away from the fiber  10  to provide strain relief for the fiber  10  or for other reasons. In that case, an area  19  between the tube  20  and the fiber  10  may be filled with a strain relief filler material e.g., polyimide, silicone, or other materials. Also, the tube  20  may have tapered (or beveled or angled) outer corners or edges  24  to provide a seat for the tube  20  to mate with another part (discussed hereinafter) and/or to adjust the force angles on the tube  20 , or for other reasons. The angle of the beveled corners  24  is set to achieve the desired function. The tube  20  may have side cross-sectional shapes other than circular, such as square, rectangular, elliptical, clam-shell, or other shapes, and may have side-view (or transverse) cross-sectional shapes other than rectangular, such as circular, square, elliptical, clam-shell, or other shapes. 
     Also, outer rings or sleeves  29  may be located around the outer diameter of the inner tapered region  22  of the tube  20  to help prevent cracking of the fiber  10  at the junction of the tube  20  and the fiber  10 . This cracking is due to the Poisson effect (discussed hereinafter) or other force effects and occurs when axial force is applied to the tube  20 . The sleeves  29  are made of a stiff, hard material, such as a metal. 
     Alternatively, instead of having the inner tapered region  22 , the axial ends of the tube where the fiber  10  exits the tube  20  may have an outer tapered (or fluted, conical, or nipple) section, shown as dashed lines  27 , which has an outer geometry that decreases down to the fiber  10  (discussed more hereinafter with respect to FIG.  12 ). In that case, the rings  29  may not be needed. It has been determined that using the fluted sections  27  provides enhanced pull strength at and near the interface between the fiber  10  and the tube  20 , e.g., 6 lbf or more, when the fiber  10  is pulled along its longitudinal axis. 
     Where the fiber  10  exits the tube  20 , the fiber  10  may have an external protective buffer layer  21  to protect the outer surface of the fiber  10  from damage. The buffer  21  may be made of polyimide, silicone, Teflon® (polytetrafluoroethylene), carbon, gold, and/or nickel, and has a thickness of about 25 microns. Other thicknesses and buffer materials for the buffer layer  21  may be used. If the inner tapered axial region  22  is used and is large enough, the buffer layer  21  may be inserted into the region  22  to provide a transition from the bare fiber to a buffered fiber. Alternatively, if the region has the external taper  27 , the buffer  21  would begin where the fiber exits the tube  20 . If the buffer  21  starts after the fiber exit point, the fiber  10  may be recoated with an additional buffer layer (not shown) which covers any bare fiber outside of the fused region and overlaps with the buffer  21  and may also overlap some of the region  27  or the end of the tube  20 . 
     The glass-encased fiber grating may be used by itself or as a component in a larger configuration to measure pressure. For example, the glass-encased grating tube of the embodiment shown in FIG. 1 may be used by itself directly as a pressure sensor (also discussed hereinafter with FIGS. 9,  10 ). In that case, the diameter, length, and material of the tube  20  determine whether the grating  12  reflection wavelength λ 1  will shift up or down and determine the amount of the wavelength shift. Also, material properties of the tube  20  such as Poisson&#39;s ratio (the relationship between the change in length to the change in diameter of the rod, due to an external force) and the Young&#39;s Modulus (i.e., the axial compressibility of the rod as a function of rod length) help to determine the wavelength shift. 
     In particular, if the tube  20  is placed in an environment with a pressure P, there will be axial pressure forces  26  and radial pressure forces  28 . The pressure P may be fluid pressure (where a fluid is a liquid or a gas or a combination thereof). Depending on Poisson&#39;s ratio and Young&#39;s modulus (or axial compressibility) and other material properties of the tube  20 , the tube  20  may compress or elongate axially as the pressure increases. For the tube  20  made of glass or metal materials (and other materials with low Poisson&#39;s ratios), as pressure increases, L 1  will decrease, i.e., axially compress (independent of length L 1  and diameter d 1  of the tube  20 ), for a uniform axial pressure field around the tube  20 , which causes the grating  12  reflection wavelength λ 1  to decrease. Conversely, if axial pressure  26  is a predetermined amount lower than the radial pressure  28 , the tube  20  may axially stretch or elongate, causing L 1  to increase, which causes the grating  12  reflection wavelength λ 1  to increase. The amount of axial length change for a give pressure P (or force per unit area) is also determined by the axial compressibility of the tube  20 . In particular, the more axially compressible the material of the tube  20 , the more the length L 1  of the tube  20  will change for a given initial length (ΔL 1 /L 1 ). Also, as temperature changes, the length of the tube  20  changes based on a known coefficient of thermal expansion (CTE or α L ). 
     Typical approximate values of Poisson&#39;s ratio, Young&#39;s Modulus and the Coefficient of Thermal Expansion (CTE) for certain glass materials for the tube  20  are provided in Table 1 below. 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Material 
                 Poisson&#39;s ratio 
                 Young&#39;s Modulus 
                 CTE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Natural Quartz 
                 0.16 
                 10.5 × 10 6  psi 
                 5.5 × 10 −7 /° C. 
               
               
                 Synthetic Quartz 
                 0.16 
                 10.5 × 10 6  psi 
                 5.5 × 10 −7 /° C. 
               
               
                 (Silica; Silicone 
               
               
                 Dioxide; SiO 2 ) 
               
               
                 Fused Silica 
                 0.16 
                 10.5 × 10 6  psi 
                 5.5 × 10 −7 /° C. 
               
               
                 Pyrex ® 
                 0.2 
                  9.1 × 10 6  psi 
                 32.5 × 10 −7 /° C.  
               
               
                 Vycor ® 
                 0.19 
                  9.8 × 10 6  psi 
                 7.5 × 10 −7 /° C. 
               
               
                   
               
             
          
         
       
     
     The grating  12  may be impressed in the fiber  10  before or after the capillary tube  20  is encased around the fiber  10  and grating  12 . If the grating  12  is impressed in the fiber  10  after the tube  20  is encased around the grating  12 , the grating  12  may be written through the tube  20  into the fiber  10  as is described in copending U.S. Pat. No. 6,298,184, entitled “Method and Apparatus For Forming A Tube-Encased Bragg Grating,” filed Dec. 4, 1998. 
     To encase the fiber  10  within the tube  20 , the tube  20  may be heated, collapsed, and fused to the grating  12  by a laser, filament, flame, etc., as is described in copending U.S. patent application Ser. No. 09/455,865, entitled “Tube-Encased Fiber Grating,” filed contemporaneously herewith, which is incorporated herein by reference. Other techniques may be used for fusing the tube  20  to the fiber  10 , such as is discussed in U.S. Pat. No. 5,745,626, entitled “Method For And Encapsulation Of An Optical Fiber,” to Duck et al., and/or U.S. Pat. No. 4,915,467, entitled “Method of Making Fiber Coupler Having Integral Precision Connection Wells,” to Berkey, which are incorporated herein by reference to the extent necessary to understand the present invention, or other techniques. Alternatively, other techniques may be used to fuse the fiber  10  to the tube  20 , such as using a high temperature glass solder, e.g., a silica solder (powder or solid), such that the fiber  10 , the tube  20  and the solder become fused to each other, or using laser welding/fusing or other fusing techniques. Also, the fiber may be fused within the tube or partially within or on the outer surface of the tube (discussed hereinafter with respect to FIG.  24 ). 
     For any of the embodiments described herein, the grating  12  may be encased in the tube  20  having an initial pre-strain on the grating (compression or tension) or no pre-strain. For example, if Pyrex® or another glass that has a larger coefficient of thermal expansion than that of the fiber  10  is used for the tube  20 , when the tube  20  is heated and fused to the fiber and then cooled, the grating  12  is put in compression by the tube  20 . Alternatively, the fiber grating  12  may be encased in the tube  20  in tension by putting the grating in tension during the tube heating and fusing process. In that case when the tube  20  is compressed, the tension on the grating  12  is reduced. Also, the fiber grating  12  may be encased in the tube  20  resulting in neither tension nor compression on the grating  12  when no external forces are applied to the tube  20 . 
     The fluted sections  27  where the fiber  10  attaches to the tube  20  may be formed in various ways, such as is described in the aforementioned copending U.S. patent application Ser. No. 09/455,865. For example, the tube  20  may be heated and the tube  20  and/or the fiber  10  pulled on an end to form the fluted sections  27 . Alternatively, the fluted ends  27  may be formed using other glass formation techniques, such as etching, polishing, grinding, etc. Other techniques may be used to form the sections  27 . 
     Also, the inner region  22  may be created by numerous techniques, such as is described in the aforementioned copending U.S. patent application Ser. No. 09/455,865. For example, not collapsing the tube  20  to the fiber  10  in the regions  22  or to create a region  22  that is larger than the inner diameter of the tube  20 , the tube  20  may be heated in the desired region to be expanded and internal pressure applied to the tube  20 . 
     Referring to FIG. 2, in an alternative embodiment, it has been determined that increased sensitivity can be realized by varying the geometry of the capillary tube  20 . In particular, the tube  20  may have a “dogbone” shape having a narrow central section  30  and larger outer sections  32  (or pistons). The narrow section  30  has an outer diameter d 2  of about 2 mm, and a length L 2  of about 9.25 mm. The large sections  32  have an outer diameter d 3  of about 4 mm and a length L 3  of about 6.35 mm. Other lengths L 2 , L 3  of the sections  30 ,  32  may be used, as long as buckling is avoided. For example, the length L 3  may be much more than 6.36 mm (e.g., greater than 25.4 mm long) or may be much less than 6.36 mm long. The ratio of the cross-sectional areas (πd 2 )-of the axial end faces of the tube  20  and the narrow portion  30  provides a force/area gain of 4. 
     Also, the sections  32  of the tube  20  may have the inner tapered regions  22  or the outer tapered sections  27  at the ends of the tube  20 , as discussed hereinbefore. Further, the sections  32  may have the tapered (or beveled) outer corners  24  as discussed hereinbefore. An inner transition region  33  of the large sections  32  may be a sharp vertical or angled edge or may be curved as indicated by dashed lines  43 . A curved geometry  43  has less stress risers than a sharp edge or corner and thus reduces the likelihood of breakage. 
     Also, it is not required that the dogbone geometry be symmetric, e.g., the lengths L 3  of the two sections  32  may be different if desired. Alternatively, the dogbone may be a single-sided dogbone, where instead of the having the two larger sections  32 , there may be only the large section  32  on one side of the narrow section  30  and the other side may have a straight edge  31  which may have beveled corners  24  as discussed hereinbefore. In that case, the dogbone has the shape of a “T” on its side. Such a single-sided dogbone shall also be referred to herein as a “dogbone” shape. Instead of a dogbone geometry, other geometries that provide enhanced strain sensitivity or adjust force angles on the tube  20  or provide other desirable characteristics may be used. 
     It has been determined that such a dimension change between the dimension d 3  of the large section  32  and the dimension d 2  of the narrow section  30  provides increased force to grating wavelength shift sensitivity (or gain or scale factor) by strain amplification. Also, the dimensions provided herein for the dogbone are easily scalable to provide the desired amount of sensitivity. Other geometries which enhance sensitivity or adjust force angles on the tube may be used if desired. 
     The increased sensitivity of the dogbone geometry is provided by strain amplification caused by the difference between the dimensions d 3  and d 2 . To optimize the sensitivity of the dogbone geometry the larger sections  32  should be isolated from opposing axial forces  35  on the inner transition region  33  and the narrow section  30  should be isolated from radial forces  37 . This may be accomplished by surrounding the dogbone with a cylinder, membrane, walls, or other interface, as discussed hereinafter. Radial forces on the narrow section  30  subtract from shifts caused by axial forces due to the Poisson effect, thereby causing decreased sensitivity of the sensor. 
     The dogbone geometry may be formed by etching, grinding, or polishing the central section of the capillary tube  20  to obtain the narrow diameter d 2 . Chemical etching (e.g., with hydrofluoric acid or other chemical etches), laser etching, or laser enhanced chemical etching are some techniques which can be used to reduce the outer diameter without applying direct contact force as is required by grinding and polishing. Other techniques may be used to obtain the narrow diameter region  30 . After the dogbone (or other geometry) is formed in the tube  20 , the surface of the tube  20  may be fire polished to remove surface impurities, enhance strength, or for other reasons. 
     Referring to FIG. 3, alternatively, the dogbone geometry may be formed using multiple pieces such as a center piece  40 , similar to the glass-encased grating  20  of FIG. 1, surrounded by two end pieces  42  (analogous to the large sections  32  in FIG.  2 ). The end pieces  42  may be slid onto the fiber  10  and pressed against the center piece  40 . The center piece  40  may be seated or recessed within the two end pieces  42  (as shown in FIG. 3) or lay flat against the end pieces  42 . 
     Referring to FIG. 4, one way to use the dogbone geometry as a sensor  48  is to surround the dogbone by an outer cylinder or outer tube  50 . The cylinder  50  prevents the pressure P from exerting direct radial forces  37  on the middle narrow section  30  and from exerting opposing axial forces  35  on the large sections  32 . The cylinder  50  material and properties may exert other forces (axial and/or radial) on the device which should be evaluated and selected for the desired application. The cylinder  50  may be made of the same material as that of the sections  32 , e.g., a glass, or of another material, e.g., a metal. If the section  32  and the cylinder  50  are both made of a glass material, the cylinder  50  may be fused to the sections  32 , similar to the way the tube  20  is fused to the fiber  10 . Alternatively, the cylinder  50  may be attached to the outer dimensions of the larger sections  32  of the tube  20  by soldering, welding, melting, adhesives, or epoxies, or by other suitable attachment techniques. The cylinder  50  forms a hermetically sealed chamber (or cavity)  34  between the cylinder  50  and the narrow section  30  of the tube  20 . When pressure P is applied, as indicated by the lines  26 , the radial pressure  28  causes the cylinder  50  to deflect radially into the chamber  34 , and the axial pressure  26  acting on the exterior axial end faces of the sections  32  and the cylinder  50  causes the sections  30 ,  32  and the cylinder  50  to axially compress. The amount of axial compression and radial deflection of the parts  30 ,  32 ,  50  will depend on their material properties and dimensions. Also, the dogbone-shaped tube  20  may be formed by one or more pieces as discussed. 
     Alternatively, the geometry of the outer cylinder  50  may be other than a straight cylinder, and may have a geometry that changes the compliance or elasticity of the outer cylinder  50 . For example, the outer cylinder  50  may have a corrugated (or bellows) shape, as indicated by dashed lines  49 , or a pre-established inward or outward curvature as indicated by dashed lines  47  or  51 , respectively, or other geometries. The bellows shape allows the axial compliance to increase while not reducing the maximum radial break strength pressure of the cylinder. 
     Referring to FIG. 26, alternatively, the outer tube  50  may be fused to the tube  20  away from the inner transition region  33  and/or near the axial ends  46  of the tube  20 . In that case, there would be a gap g 2  of about 0.5 mm between the inner diameter of the cylinder  50  and the outer diameter of the large sections  32  (or pistons) of the dogbone. Also, the thickness T 2  of the outer tube  50  is about 0.5 mm. Further, the length L 2  of the short portion  30  of the dogbone is about 7.0 mm, and the length between where the tube  50  is fused to the pistons  32  (2*L 3 +L 2 ) is about 3.56 cm and the diameters d 2 , d 3  of the sections  30 ,  32  are about 1.0 mm and 3.0 mm, respectively. For these dimensions, and if made of a glass material (fused silica and natural quartz), the sensor  48  provides a grating wavelength shift to pressure sensitivity ratio of about 0.5 picometers/psi (or 2.0 psi/pm) and may be used as a 0 to 5,000 psi sensor for long term operation. We have found that the structure of FIG. 26 with the dimensions described above can withstand an external pressure of greater than 15 kpsi before breaking. 
     For a 0 to 15,000 psi operational range sensor, having a sensitivity of 0.3846 pm/psi (or 2.6 psi/pm), the dimensions may be as follows: wall thickness t 2  of about 1 mm, the diameter d 2  of about 1.12 mm, the outer diameter d 9  of about 6 mm, the length L 2  of about 7.4 mm, and the length (2*L 3 +L 2 ) of about 49 mm and an overall length L 1  of about 59 mm. For such a 15 Kpsi sensor, we have found that the break pressure is greater than about 45 Kpsi. Other operational ranges for the given dimensions may be used if desired. 
     Alternatively, the pistons  32  may extend axially beyond the end of the outer tube  50  as indicated by the axially extended regions  44 . In that case, the regions  44  may be axially symmetric or not, depending on the application. For a single ended 15 Kpsi sensor, the length L 20  of the section  44  may be about 20 mm. Also, there may be axially extended regions  36  (also discussed hereinafter with FIG. 8) on one or both axial ends. The length L 21  of the axial extended sections  36  may be any desired length based on the design criteria, e.g., 12 mm. Other lengths may be used. 
     Alternatively, as discussed hereinbefore with the single-sided dogbone, the pistons  32  of the dogbone may have unequal lengths or there may be only one piston  32  having the length of the two pistons (2*L 3 ) on one side of the tube/grating  30  and the end cap  46  on the other side. In the later case, there would be more compression of the single piston  32  due to its increased length. Also, if the sensor is not a feed-through design (i.e., single ended), one end may be cleaved at an angle to reduce optical back-reflections, e.g., 12 deg. from vertical, as indicated by a dashed line  59 . Other angles may be used. 
     Also, such a configuration allows for the sensitivity (or resolution) to be scaled by changing the overall length L 1  (i.e., the lengths L 3  of the pistons  32  and outer tube  50 ). In particular (for a given length of the pistons  32  and the tube  50 ), for a change ΔL in length L 1  due to a pressure change, a large portion ΔL′ of the change ΔL occurs across the length L 2  of the small section  30  where the grating  12  is located (the remainder being across as the large pistons  32 ). Then, if the length of the pistons  32  and the tube  50  are increased, the tube  50  will compress or deflect more (i.e., a larger ΔL) for the same pressure change (because the amount of compression for a given force scales with length). This increased ΔL is seen across the same length L 2 , thereby increasing the sensitivity ΔL/L 2  (discussed more hereinafter with FIG.  7 ). 
     Other values for the gap g 2  and thickness t 2 , the lengths L 1 , L 2 , L 3 , and the diameters d 2 , d 3  may be used if desired depending on the design specification and application. For example, there are various ways to increase the sensitivity (pm/psi), such as decreasing the wall thickness t 2  (while withstanding the required maximum external pressure), increasing the gap g 2 , increasing the overall length L 1  between where the outer tube  50  is fused to the pistons  32  (e.g., increase the tube  50  length and the piston length L 3 ), decreasing the diameter d 2  of the narrow section of the dogbone, or increasing the diameter d 3  of the large sections  32  (or pistons) of the dogbone. In particular, for a sensitivity of about 0.6 picometers/psi, the overall length L 1  may be increased from about 3.56 cm (1.4 inches) to about 5.08 cm (2.0 inches). 
     Also, in that case, the chamber  34  would be an I-shaped (or rotated H-shaped) chamber. Further, there may be a bump  52  near where the outer tube  50  fuses to the inner tube  20 . 
     Referring to FIG. 5, an alternative embodiment of the present invention comprises a housing  60  having a pressure port  62  and an interior chamber  64 . The pressure port  62  ports pressure PI into the chamber  64 . The fiber  10  passes through a front wall (or end cap)  66  of the housing  60  through a hermetic feed-through  67  and exits through a rear wall (or end cap)  68  of the housing  60  through a hermetic feed-through  69 . A bellows  70  is located within the chamber  64  and has one end of the bellows  70  connected to the rear housing wall  68  and the other end connected to a bellows plate  72 . The tube  20  is located within a bellows  70  and is positioned between the rear housing wall  68  and the bellows plate  72  which is free to move axially. A portion  73  of the fiber  10  outside the bellows  70  may have slack to allow the fiber  10  to flex with compression of the bellows  70  without placing the portion  73  of the fiber  10  in tension. The slack may be provided by a bend or helix wrap or other strain relief technique for the fiber  10 . The plate  72  and the wall  68  apply axial forces against the grating/tube  20  within the bellows  70 . Between the tube  20  and the bellows  70  is a bellows chamber  74 . The pressure P 2  in the bellows chamber  74  may be 0 psi for an absolute sensor or atmospheric pressure, e.g., 14.7 psi (1 atm), or other fixed pressures. If a delta-P pressure sensor is desired, a pressure port  76  may be provided to port a second pressure P 2  into the bellows chamber  74 . The axial ends of the tube  20  may be recessed into the plate  72  and wall  68  as shown in FIG. 5 or be flush against the plate  72  and/or the wall  68 . 
     As pressure P 1  increases around the outside of the bellows  70 , it causes the bellows  70  to shorten or compress (and the plate  72  to move to the right), which compresses the tube  20  and the grating  12 , and causes the reflection wavelength λ 1  light from the grating  12  to decrease. The spring constant of the bellows  70  is selected to be small relative to the spring constant of the tube  20 , but large enough to not rupture under applied pressure. This minimizes error induced by creep by delivering the maximum amount of source pressure to the tube  20 . The tube  20  may also be shaped in a dogbone geometry or other shapes as discussed herein if desired. Alternatively, if the pressure P 2  is greater than P 1  by a predetermined amount, the tube  20  (and the bellows  70 ) would expand axially and the reflection wavelength of the grating  12  would increase. 
     Referring to FIG. 6, another embodiment of the present invention comprises two encased gratings in a push/pull arrangement. In particular, the configuration is substantially the same as that shown in FIG. 5, with a second grating  80  encased in a second tube  82  similar to the first tube  20  having a second reflection wavelength λ 2 . The grating-encased tube  82  is positioned between the plate  72  and the front wall  66  of the housing  60 . With this design, at “zero” applied pressure P 1 , strain is developed across the second grating  80  by the spring force of the bellows  70 , while the first grating  12  is left unstrained (or at a lower strain). As pressure P 1  is increased, the bellows  70  compress, releasing the strain on the second grating  80 , and applying more compression to the first grating  12 . Other push-pull strain conditions and configurations on the gratings  12 ,  80  may be used if desired. Alternatively, if the pressure P 2  is greater than P 1  by a predetermined amount, the tube  20  (and the bellows  70 ) would expand axially and the reflection wavelength of the grating  12  would increase. 
     In this configuration, the pressure is determined by measuring the difference between the reflection wavelengths λ 1 , λ 2  of the two gratings  12 ,  80 , since both grating wavelengths λ 1 , λ 2  move in opposite directions as pressure is changed. Thus, the force required to obtain a given wavelength shift (Δλ) is one half that of a single grating transducer, or, alternately, for a give force, the wavelength shift is double that of a single grating transducer. Also, the two grating wavelengths λ 1 , λ 2  shift in the same direction as the temperature changes. Thus, by measuring the shift in the average value of the two reflection wavelengths λ 1 , λ 2 , the temperature can be determined, which allows for temperature compensation to be performed. Also, if creep exists, the maximum creep error can be determined. In particular, the average reflection wavelength between the two gratings should remain the same if no creep exists for a given temperature and pressure. 
     Referring to FIG. 7, another embodiment of the present invention comprises a cylindrical-shaped housing  90  comprising an outer cylindrical wall (or outer tube)  98 , two end caps  95 , and two inner cylinders (or pistons)  92  each connected at one end to one of the end caps  95 . The tube  20  (with the grating  12  encased therein) is disposed against the other ends of and between the two pistons  92 . Other cross-sectional and/or side-view sectional shapes may be used for the housing  90  and elements  98 ,  95 ,  92  if desired. The end caps  95  may be separate pieces or part of and contiguous with the pistons  92  and/or the outer cylinder  98 . The pressure P ( 26 ,  28 ) is applied to the external walls  98 ,  95  of the housing  90 . The pistons  92  have holes  94  having a diameter d 8 , which the fiber  10  passes through. The end caps  95  of the housing  90  may have tapered regions  96  to provide strain relief as discussed hereinbefore. Also, the end caps  95  have feedthroughs  106  where the fiber  10  exits and may be hermetically sealed feedthroughs. Any known optical fiber hermetic feedthrough may be used for the feedthroughs  106 , such as plating the fiber  10  with a metal and soldering the fiber to the feedthrough  106 . Between the tube  20  and the feedthroughs  106 , the fiber  10  may have the external protective buffer layer  21  discussed hereinbefore to protect the outer surface of the fiber  10  from damage. Also, a region  88  between the fiber  10  and the inner dimension of the hole  94  may be filled with a liquid or solid material, e.g., silicone gel, that further protects the fiber  10  and/or is thermally conductive to allow a temperature grating  250  (discussed hereinafter) to quickly sense changes in the temperature of the pressure grating  12 , or for other uses. 
     Between the inside dimension of the walls  98  and the outside dimension of tube  20  and pistons  92  is an inner I-shaped (or rotated H-shaped) chamber  100 . Also, there may be hollow regions  99  in the pistons  92  to allow some slack or service loop  101  in the fiber  10  between the tube  20  and the end  106  of the housing  90  to accommodate for thermal expansion of the pistons  92  or for other reasons. The pistons  92 , the outer cylinder walls  98 , the end caps  95 , and the tube  20  may be made of the same or different materials. Further, the pistons  92  may be of unequal length or there may be only one piston having the length of the two pistons  92  on one side of the tube  20  and the end cap  95  on the other side. In the later case, there would be more compression of the single piston  92  due to its increased length. 
     An example of some possible dimensions for the housing  90  are as follows: The tube  20  has the outer diameter d 2  of about 2 mm (0.07 inches) and a length L 1  of about 12.5 mm (0.5 in.); the pistons  92  each have outer diameters d 5  of about 19.1 mm (0.75 inches); the length L 5  of each of the pistons  92  is about 6.25 cm (2.5 in.); the diameter of the holes  94  in the pistons  92  is about 1 mm (1000 microns); the overall length L 4  of the housing  90  is about 12.7 cm (5 inches); the thickness t 1  of the outside walls  98  is about 1.0 mm (0.04 inches); and the gap g 1  between the inner dimension of the outer walls  98  and the outer dimensions of the pistons  92  is about 1.52 mm (0.06 inches). The walls  98  should be made of a material and thickness capable of withstanding the external pressure P applied to the housing  90 . 
     The dimensions, materials, and material properties (e.g., Poisson&#39;s ratio, Young&#39;s Modulus, Coefficient of Thermal Expansion, and other known properties) of the walls  98  and the pistons  92  are selected such that the desired strain is delivered to the capillary tube  20  at a specified pressure P (or external force per unit area). The resolution and range for sensing pressure P are scalable by controlling these parameters. For example, if the overall length L 4  is increased, the sensitivity ΔL/L will increase. 
     In particular, as the pressure P increases, the axial length L 4  of the housing  90  decreases by an amount ΔL due to compression and/or deflection of the outer walls  98 . A predetermined portion of the total axial length change ΔL′ is seen at the tube  20  due to compression of the tube  20 . Compression of the tube  20  lowers the Bragg reflection wavelength λ 1  of the grating  12  by a predetermined amount which provides a wavelength shift indicative of the pressure P. If the pistons  92  have a spring constant higher than that of the glass tube  20 , the tube  20  will be compressed more than the pistons  92  for a given force. Also, for a given external force, a predetermined amount of the force is dropped across the outside walls  98 , and the remainder is seen by the tube  20 . 
     The housing  90  may be made of a material having high strength, low Poisson ratio and low Young&#39;s modulus, such as titanium (Ti). For example, when the walls  98 , pistons  92  and end caps  95  are all made of titanium having the dimensions discussed hereinbefore, for an external force of 2200 lbf, 2000 lbf is dropped across (or used to compress/deflect) the outside walls  98 , and 200 lbf is dropped across the tube  20 . The cylinder walls  98  act similar to a diaphragm or bellows which compress or deflect due to increased external pressure. Other metals and metal alloys may be used for some or all of the parts  92 ,  98 ,  95  of the housing  90 . These include stainless steel, titanium, nickel-based alloys, such as Inconel®, Incoloy®, Nimonic® (registered trademarks of Inco Alloys International, Inc.) containing various levels of Nickel, Carbon, Chromium, Iron, Molybdenum, and Titanium (e.g., Inconel 625). Other high strength, or corrosion resistant, or high temperature or heat resistant metals or alloys may also be used, or other materials having sufficient strength to compress the tube  20 . Other materials having other properties may be used if desired depending on the application. 
     Typical approximate values for the Poisson ratio, Young&#39;s Modulus and the Coefficient of Thermal Expansion (CTE) for titanium are provided in Table 2 below. 
     
       
         
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Material 
                 Poisson&#39;s ratio 
                 Young&#39;s modulus 
                 CTE 
               
               
                   
               
             
             
               
                 Titanium (Ti) 
                 0.3 
                 15.5 kpsi 
                 10.5 × 10 −6 /° C. 
               
               
                   
               
             
          
         
       
     
     Alternatively, one or more of the parts  92 ,  95 ,  98  of the housing  90  may be made of a glass material. In that case, one or more of the glass materials and properties shown in Table 1 hereinbefore may be used. Other materials may be used for the housing  90  if desired, depending on the application and design requirements. 
     The tube  20  may have the dogbone shape discussed hereinbefore with FIGS. 2,  3 . Also, the sensor housing  90  may be split transversely into two halves that are assembled as indicated at the attachment points  104 . Alternatively, the housing  90  may be split longitudinally. Further, a spacer or disk  97  may be provided to aid in assembly, alignment, and/or setting the pre-strain on the tube  20 . Other assembly techniques may be used if desired. 
     Also, the axial end faces of the tube  20  and/or the seats on the pistons  92  may be plated with a material that reduces stresses or enhances the mating of the tube  20  with the seat surface on the pistons  92 . 
     To make a delta-P sensor, a pressure port  102  may be provided through one or both of the pistons  92  to port a second pressure P 2  into the inner I-shaped chamber  100 . 
     The configuration of FIG. 7 requires no bellows and is therefore likely easier and cheaper to fabricate than a bellows-based design. Also, it has a robust construction capable of enduring harsh environments. 
     Referring to FIG. 8, alternatively, to help reduce strain on the fiber  10  at the interface between the fiber  10  and the tube  20 , the tube  20  may have the sections  36  which extend axially along the fiber  10  and attach to the fiber  10  at a location that is axially outside where the pressure (or force) is applied on the large sections  32  by the pistons  92  (or other end pieces as described herein). The axial lengths of the sections are set depending on the application, as discussed hereinbefore with FIG.  26 . Also, the sections  36  need not be axially symmetrical, and need not be on both axial ends of the tube  20 . The sections  32  may have the inner tapered regions  22  or the outer fluted sections  27  where the fiber interfaces with the tube  20 , as discussed hereinbefore. Alternatively, there may be a stepped section  39  as part of the sections  36 . In that case, the region  22  may be within or near to the stepped section  39  as indicated by dashed lines  38 . The regions  106  may be air or filled with an adhesive or filler. Also, the tube  20  may have a constant cross-section as discussed hereinbefore and as indicated by the dashed lines  107  instead of a dogbone shape. Further, the hole  94  through the pistons  92  may have a larger diameter as indicated by the dashed lines  109  for all or a portion of the length of the hole  94 . 
     Referring to FIG. 12, more than one concentric tube may be fused together to form the tube  20  of the present invention. For example, a small inner capillary tube  180  having a diameter d 4  of about 0.5 mm (0.02 in.), may be located within a larger outer capillary tube  182 , having the diameter d 1  discussed hereinbefore, and the two tubes  180 ,  182  are fused together. One or both ends of the small tube  180  may be shrunk down and fused to the fiber  10  to form the fluted sections  27 . Other values for the diameters d 1 , d 4  of the inner and outer tubes  180 ,  182  may be used if desired. Also, more than two concentric capillary tubes may be used. The material of the tubes may be the same to minimize thermal expansion mismatch over temperature. Also, the shape of the outer tube  182  may have a dogbone shape as indicated by dashed lines  184 , or other shapes as discussed hereinbefore. Alternatively, the dogbone shape may be created by fusing two separate tubes  188 ,  190  onto the inner tube  180  on opposite axial sides of the grating  12 , as indicated by dashed lines  186 . 
     Referring to FIGS. 13 and 14, alternatively, the tube  20  may be fused to the fiber  10  on opposite axial ends of the grating  12  adjacent to or a predetermined distance L 10  from the grating  12 , where L 10  can be any desired length or at the edge of the grating  12  (L 10 =zero). In particular, regions  200  of the tube  20  are fused to the fiber  10  and a central section  202  of the tube around the grating  12  is not fused to the fiber  10 . The region  202  around the grating  12  may contain ambient air or be evacuated (or be at another pressure) or may be partially or totally filled with an adhesive, e.g., epoxy, or other filling material, e.g., a polymer or silicone, or another material. The inner diameter d 6  of the tube  20  is about 0.1 to 10 microns larger than the diameter of the optical fiber  10 , e.g., 125.1 to 136 micron. Other diameters may be used; however, to help avoid fiber buckling when the tube  20  is axially compressed, the diameter d 6  should be as close as possible to the fiber  10  outer diameter to limit the amount of radial movement of the grating  12  and fiber  10  between the fusion points. Also, the distance L 10  need not be symmetric around both sides of the grating  12 . 
     Referring to FIG. 14, alternatively, the same result can be achieved by fusing two separate tubes  212  on opposite sides of the grating  12 , and then fusing an outer tube  214  across the tubes  212 . Alternatively, the tubes  212  may extend beyond the ends of the outer tube  214  as indicated by the dashed lines  216 . Alternatively, the tube  20  may be a single piece with a shape indicative of the tubes  212 ,  214 . 
     Referring to FIGS. 7,  8 ,  15 ,  17 ,  19  the reflection wavelength of the grating  12  changes with temperature (ΔX/ΔT), as is known. Also, the strain on the grating  12  may change over temperature due to a thermal mismatch between the tube  20  and the fiber  10 . Also, the force on the tube  20  may change over temperature due to the expansion or contraction of the housing  90  over temperature. In that case, a separate temperature grating  250  may be used to measure temperature to correct for temperature-induced shifts in the reflection wavelength λ 1  of the pressure grating  12 . The temperature grating  250  has a reflection wavelength λ 3  that is different from the reflection wavelength of the pressure grating  12  and that changes with change in temperature but does not change due to a change in the pressure P. This is achieved by locating the temperature grating  250  in thermal proximity to the pressure grating  12 , outside the pressure-strained region of the tube  20  and otherwise isolated from the pressure being measured. In particular, the temperature grating  250  may be located in the fiber  10  between the tube and the feedthrough  106 . Referring to FIG. 8, alternatively, the temperature grating  250  may be located in the fiber  10  portion that is encased or fused in the axially protruding section  27 ,  36  of the glass tube  20 , outside the region that is compressed by the pistons  92 . Alternatively, the temperature grating  250  may be in a separate optical fiber (not shown) located near or in the sensor housing  90  and may be optically coupled to the fiber  10  or separate from the fiber  10 . Alternatively, the temperature grating  250  may be a strain-isolated temperature sensor in a separate tube (not shown), such as that described in commonly-owned, copending U.S. patent application Ser. No. 09/455,866, entitled “Strain-Isolated Fiber Grating Temperature Sensor” filed contemporaneously herewith. Also, for any of the embodiments shown herein, the temperature grating  250  may be encased in the tube  20  having an initial pre-strain on the grating (compression or tension) or no pre-strain. 
     Referring to FIG. 28, alternatively, the temperature grating  250  in the extended section  251  may be encased in a second outer tube  400  to form a pressure-isolated temperature sensor such as is discussed in copending U.S. patent application Ser. No. 09/445/113, entitled “Pressure-Isolated Fiber Grating Temperature Sensor”, which is incorporated herein by reference. In particular, the second tube  400  is fused to the section  251  and to the outer diameter of an end cap tube  402 . The end cap tube  402  may be made of the same material as the tube  20 . The fiber  10  is fed through and fused to the end cap tube  402  similar to the way the fiber  10  is fused to the tube  20 . A sealed chamber  406  exists between the section  251 , the end cap tube  402 , and the outer tube  400 . Also, the fiber  10  has some slack  404  to allow the chamber  406  to expand. As the external pressure changes, the outer tube  400  compresses or deflects, the end cap tube  402  and/or the section  251  move toward each other, and the fiber  10  flexes in the chamber  406 ; however, the section  251  with the grating  250  is not exposed to the pressure change. Thus, the reflection wavelength of the temperature grating  250  does not change due to the pressure change. Further, the outer tube  50  and the second outer tube  400  may be one tube that is fused to the inner tubes  20 ,  402 . Other embodiments and configurations for the pressure-isolated temperature sensor may be used such as those described in the aforementioned patent application Ser. No. 09/445,113. Also, for a non-feed through sensor, instead of the fiber  10  being fed through the chamber  406  and the end cap  402 , the fiber  10  may end within the section  251  to the left of the temperature grating  250 . Further, instead of the end cap  402 , the tube  400  may be collapsed on itself to form the chamber  406 . 
     Referring to FIG. 29, alternatively, the temperature grating  250  may be located in a non-pressure-isolated area, such as in the wide region  32  of the dogbone geometry. In that case, both the gratings  12 ,  250  are subjected to pressure and temperature variations where the pressure-to-wavelength shift sensitivities for the gratings  12 ,  250  are different. Thus, pressure and temperature can be analytically determined. Alternatively, if the change in wavelength with temperature is the same (or predictable) for both gratings  12 ,  250 , and the change in wavelength with pressure is different for the two gratings  12 ,  250 , then a temperature-compensated pressure measurement can be obtained analytically, e.g., by subtracting the two wavelengths. Alternatively, a temperature grating  450  may be located in the region where the outer tube  50  is fused to the inner tube  20  or a temperature grating  452  may be located in the axial extended section  251 . In those locations, the temperature gratings  450 ,  452  would exhibit a lower sensitivity to pressure changes than the temperature grating  250 , which may increase the temperature compensation accuracy. 
     Alternatively, instead of using a fiber grating to measure the temperature of the pressure grating  12 , any other technique may be used to determine the temperature of the pressure grating  12 , e.g., electronic, thermocouple, optical, etc. 
     Referring again to FIG. 7, the housing  90  may be designed to minimize changes in compression of the tube  10  over temperature. In particular, if the walls  98  and the pistons  92  are made of the same material, e.g., titanium, and the tube  20  is made of a different material, e.g., glass, having a lower CTE, as temperature increases, the pistons  92  will increase in length as much as the outer walls  98 , except over the region  86  between the ends of the pistons  92  (where a CTE mismatch will exist). As a result, the force on tube  20  decreases as temperature increases. Alternatively, a section  230  on one or both pistons  92  may be made of a material that has a CTE that compensates for the additional expansion of the section  86  to maintain a substantially constant force on the tube  20  over temperature. Alternatively, the outer walls  98  may be made of a material that has a CTE so as to maintain a substantially constant force on the tube  20  over temperature or otherwise compensate for a predetermined amount of force change over temperature. 
     Referring to FIG. 15, an alternative geometry for the capillary tube  20  may have one axial end  251  that is longer than the other axial end. In that case, the temperature compensating grating  250  may be located in the fiber  10  in the long axial end  251 . Some exemplary dimensions for the tube  20  of FIG. 15 are as follows: L 6  is about 1.05 inches; L 7  is about 0.459 inches; L 8  is about 0.5 inches; L 9  is about 0.09 inches; and d 7  is about 0.032 inches. The long axial end  251  may be made by fusing the section  251  to the section  32  (before or after the fiber  10  is encased in the tube  20 ) at a point  253  or may be made by other methods discussed hereinbefore for making the dogbone or other shapes for the tube  20 . Alternatively, tube  20  shown in FIG. 15 with the section  251  may be formed by using two tubes, an inner tube with the length L 6  slid through the dogbone sections  30 ,  32  as indicated by the dashed lines  258  and fused to the sections  30 ,  32  similar to that discussed with FIG.  12 . 
     Referring to FIG. 17, the long axial end  251  may be collapsed and fused to the fiber  10  where the temperature grating  250  is located and not collapsed onto the fiber  10  at a region  290  near the end of the section  251 . In that case, the region  290  may be filled with an epoxy or other filter. The inner diameter d 6  of the tube  20  in the section  290  is about 125 to 135 microns and the diameter d 8  of the hole  94  is about 1 mm (1000 microns) as discussed hereinbefore. Other diameters and dimensions may be used if desired. Where the fiber  10  exits the extended region  251 , the fiber  10  may have the external protective buffer layer  21  to protect the outer surface of the fiber  10  from damage, as discussed hereinbefore. 
     Referring to FIG. 19, one or both of the pistons  92  may have a hollow section  310  which is ported to the external pressure P through holes  311  in the end cap  95 . The hollow section  310  has outer walls  312  and inner walls  314 . Such a configuration may be used to help increase sensitivity, or for other reasons. The length and thickness of the walls  312 ,  314  will determine the amount of increased sensitivity that exists. For example, as the pressure P increases, the walls  312 ,  314  will be put in tension and the piston  92  will lengthen. Alternatively, the inner wall  314  may be a pipe that may have a different material than the rest of the piston  92  and that is attached to the pistons  92  at a point  318 . Also, the wall  314  may have a bulge  316  to allow for slack in the fiber  10 . Alternatively, the inner wall  314  eliminated if desired. In that case, the fiber  10  would be exposed to the pressure P. The fiber  10  may have the external protective buffer coating  21  as discussed hereinbefore. Referring to FIG. 20, the end cap  95  may have holes  311  or support beams  320  to stabilize the wall and/or to provide a stable exit point for the fiber  10 . 
     Referring to FIG. 16, in an alternative embodiment, a housing  270  has a diaphragm  274  which is connected to one end of the tube  20 . The other end of the tube  20  is connected to a rigid back wall  278 . Rigid walls  280  connect the back wall  278  and the diaphragm  274 . Inside the housing  270  is a chamber (or cavity)  272 . The chamber  272  may be evacuated, be at atmospheric pressure, or be ported to a second pressure P 2 , for a differential pressure (or delta P) measurement. As the pressure P 1  increases, the diaphragm  274  deflects into the chamber  272 , as indicated by dashed lines  277 , which compresses the tube  20  and the grating  12  causing a wavelength shift. Alternatively, if the pressure P 2  is greater than P 1  the diaphragm  274  will deflect outward as indicated by dashed lines  279 . 
     Referring to FIG. 18, an alternative embodiment of the present invention has a housing  300  having a circular side-view section and an inner chamber  306 . The overall shape of the housing  300  may be a sphere or a cylinder or other shapes having a circular cross-section. The tube  20  with the fiber  10  and grating  12  encased therein is attached to the inner diameter of the housing  300 . The fiber  10  exits the housing  300  at feedthrough points  316 , which may be hermetic feedthroughs, as discussed hereinbefore. As the external pressure P 1  increases, the diameter of the housing  300  decreases and the tube  20  is compressed which results in a shift in the reflection wavelength of the grating  12  as discussed hereinbefore. The amount of wavelength shift for a given pressure change will depend on the material properties of the housing  300  and the tube  20 , e.g., Poisson&#39;s ratio, Young&#39;s modulus, etc., as discussed hereinbefore. If the housing  300  and the tube  20  are a similar material, e.g., glass, the tube  20  may be part of or fused to the housing  300  as shown by dashed lines  302 . In that case, stresses between the housing  300  and the tube  20  may likely be lower. Also, the tube  20  may have a dogbone shape as indicated by dashed lines  304  or other shapes as discussed herein. 
     Referring to FIG. 11, for any of the embodiments described herein, instead of a single grating encased within the tube  20 , two or more gratings  150 ,  152  may be embedded in the fiber  10  that is encased in the tube  20 . The gratings  150 ,  152  may have the same reflection wavelengths and/or profiles or different wavelengths and/or profiles. The multiple gratings  150 ,  152  may be used individually in a known Fabry Perot arrangement. Further, one or more fiber lasers, such as those described in U.S. Pat. No. 5,513,913, entitled “Active Multipoint Fiber Laser Sensor,” U.S. Pat. No. 5,564,832, entitled “Birefringent Active Fiber Laser Sensor,” or U.S. Pat. No. 5,666,372, entitled “Compression Tuned Fiber Laser,” may be embedded within the fiber  10  in the tube  20 , and are incorporated herein by reference to the extent necessary to understand the present invention. In that case, the gratings.  150 ,  152  form an optical cavity and the fiber  10  at least between the gratings  150 ,  152  (and may also include the gratings  150 ,  152 , and/or the fiber  10  outside the gratings, if desired) would be doped with a rare earth dopant, e.g., erbium and/or ytterbium, etc., and the lasing wavelength would shift as pressure changes. 
     Referring to FIG. 30, another type of tunable fiber laser that may be used is a tunable distributed feedback (DFB) fiber laser  154 , such as that described in V. C. Lauridsen et al., “Design of DFB Fibre Lasers,” Electronic Letters, Oct. 15, 1998, Vol.34, No. 21, pp. 2028-2030; P. Varming et al., “Erbium Doped Fiber DGB Laser With Permanent π/2 Phase-Shift Induced by UV Post-Processing,” IOOC&#39;95, Tech. Digest, Vol. 5, PD1-3, 1995; U.S. Pat. No. 5,771,251, “Optical Fibre Distributed Feedback Laser,” to Kringlebotn et al.; or U.S. Pat. No. 5,511,083, “Polarized Fiber Laser Source,” to D&#39;Amato et al. In that case, the grating  12  is written in a rare-earth doped fiber and configured to have a phase shift of λ/2 (where λ is the lasing wavelength) at a predetermined location  180  near the center of the grating  12  which provides a well defined resonance condition that may be continuously tuned in single longitudinal mode operation without mode hopping, as is known. Alternatively, instead of a single grating, the two gratings  150 ,  152  may be placed close enough to form a cavity having a length of (N+½)λ, where N is an integer (including 0) and the gratings  150 ,  152  are in rare-earth doped fiber. 
     Alternatively, the DFB laser  154  may be located on the fiber  10  between the pair of gratings  150 ,  152  (FIG. 11) where the fiber  10  is doped with a rare-earth dopant along at least a portion of the distance between the gratings  150 ,  152 . Such configuration is referred to as an “interactive fiber laser”, as is described by J. J. Pan et al., “Interactive Fiber Lasers with Low Noise and Controlled Output Power,” E-tek Dynamics, Inc., San Jose, Calif., internet web site www.e-tek.com/products/ whitepapers. Other single or multiple fiber laser configurations may be disposed on the fiber  10  if desired. 
     Referring to FIG. 21, a plurality of the pressure sensors  20 ,  110 ,  112  described herein, each having at least one grating  12  encased therein, may be connected in series by the common optical fiber  10  to measure multiple pressure points as distributed sensors. Any known multiplexing techniques may be used to distinguish one sensor-signal from another sensor signal, such as wavelength division multiplexing (WDM), time division multiplexing (TDM), or other multiplexing techniques. In that case, the grating  12  in each sensor may have a different reflection wavelength. 
     Referring to FIGS. 22 and 23, alternatively, two or more fibers  10 ,  350 , each having at least one grating  12 ,  352  therein, respectively, may be encased within the tube  20 . In that case, the bore hole in the tube  20  prior to heating and fusing may be other than circular, e.g., square, triangle, etc. Also, the bore hole for the tube  20  need not be centered along the center line of the tube  20 . 
     Referring to FIG. 24, alternatively, instead of the fibers  10 ,  350  touching each other as shown in FIG. 23, the fibers  10 ,  350  may be spaced apart in the tube  20  by a predetermined distance. The distance may be any desired distance between the fibers  10 ,  350 . Also, for any of the embodiments shown herein, as discussed hereinbefore, part or all of an optical fiber and/or grating may be fused within, partially within or on the outer surface of the tube  20 , as indicated by the fibers  500 ,  502 ,  504 , respectively. 
     Referring to FIG. 25, alternatively, the tube  20  may be collapsed and fused onto the fiber  10  only where the grating  12  is located. In that case, if the tube  20  is longer than the grating  12 , the inner tapered or flared regions  22  discussed hereinbefore may exist and the areas  19  between the tube  20  and the fiber  10  may be filled with a filler material, as discussed hereinbefore. 
     Referring to FIGS. 9,  10 , any of the sensor configurations described herein (shown collectively as a sensor  110 ) may be placed within a housing  112  having a pressure port  114  which ports a pressure P 1  into a chamber  116  which exposes the sensor  110  to the pressure P 1 . The sensor  110  may be attached to at least one wall  118  of the housing  112  as shown in FIG.  9 . 
     Referring to FIG. 10, instead of attaching one side of the sensor  110  to a wall of the housing  112 , the sensor  110  may be suspended within the housing  112  by supports  120 ,  122  connected to one or more of the walls of the housing  112  and to one end of the sensor  110  (or from the middle or any other desired point along the sensor  110 ). The fiber  10  is fed through two hermetic feedthroughs  111 ,  113 . Also, the fiber  10  may have some slack  117  between the sensor  110  and the feedthroughs  111 ,  113 . Also, the sensor  110  may be a delta-P sensor if a second pressure P 2  is ported to the sensor  110  as indicated by the lines  124 . 
     Alternatively, instead of the supports  120 ,  122 , the sensor  110  may be suspended by the fluid in the chamber  116 , e.g., a viscous fluid, grease, silicone oil, or other fluids that provide shock and/or vibration isolation and prevent the sensor  110  from hitting the inner walls of the housing  112 . Instead of or in addition to using a fluid to suspend the sensor  110 , compliant radial and/or axial spacers (or seats)  130 ,  131  respectively, may be provided between the sensor  110  and the inner walls of the housing  112 . The spacers  130 ,  131  may be floating or attached to the inner housing walls. Also, small solid granular pellets or gel capsules (liquid contained in a small compliant membrane bubble)  132  may also be used. The spacers  130 ,  131 , or pellets/capsules  132  may be made of a compliant material such as Teflon®, polyimide, silicone, of other compliant materials. Alternatively, a fish net or sock-like lattice support  134  may be attached to opposite walls of the housing  112  on opposite axial sides of the sensor  110 , which holds the sensor  110  between the inner walls of the housing  112  but which allows some motion of the sensor  110  and allows the pressure to be transferred to the sensor  110 . Also, instead of the radial spacers  130 , the radial space Ds between the sensor  110  and the inner walls of the housing  112  may be small (e.g., about 3 mm), if desired, with a layer or film of the fluid there-between to act as a protective layer. Any other technique for suspending the sensor  110  within the housing  112  that provides shock and vibration isolation and allows pressure P 1  to be transferred to the sensor  110  may be used. 
     Referring to FIG. 27, alternatively, the sensor  110  may be partially inside and partially outside the pressurized chamber  116 . In that case, the pressure exposed portion  48  of the sensor  110  would be exposed to the pressure P 1  and the axial extended portion  251  having the temperature grating  250  may be outside the chamber  116  and isolated from the pressure P 1 . Also, in that case, there may be an optional additional portion  121  added to the housing  112  to protect the axial extended portion  251 , which creates a chamber  125 , and the fiber  10  exits through a feedthrough  123 . Alternatively, the temperature grating  250  may be exposed to the pressure P 1 , as discussed hereinbefore. 
     It should be understood that the glass-encased fiber grating pressure sensor of the present invention may be used in compression or compressive strain (e.g., where axial compression occurs with increasing pressure) or in tension or tensile strain, e.g., where axial elongation (increase in tension) or a decrease in length (decrease in tension) occurs with increasing pressure, depending on the configuration. One example of a tension based system would be where the tube  20  is attached to a tension-based transducer mechanism and pulled axially. For example, for the dogbone geometry (such as in FIG.  8 ), the inside surfaces of the sections  32  may be pulled in opposite axial directions to place the grating  12  in tension. A tension based configuration is also described in the commonly-owned copending U.S. patent application Ser. No. 08/925,598, entitled “High Sensitivity Fiber Optic Pressure Sensor for Use in Harsh Environments,” to Robert J. Maron, discussed hereinbefore in the Background Art section hereto and incorporated herein by reference. In that case, the grating is pre-strained in tension and the tension decreases with increasing pressure. Other tension-based configurations which use the tube-encased grating described herein may be used. Alternatively, for configurations where the axial forces are less than the radial forces by a predetermined amount (based on the material properties), the tube  20  may be operated in tension (such as when the axial ends of the tube  20  are outside the pressure field; see the discussion of FIGS. 5,  6 , and  16 ). 
     Also, if the elastic element (e.g., bellows or diaphragm) discussed herein have very low stiffness relative to the tube  20 , only a small amount of force will be dropped across (or lost to) the elastic element. In that case, the sensor may be used as a force transducer. 
     Further, for any of the embodiments shown herein, instead of the fiber  10  passing through the sensor housing or the tube  20 , the fiber  10  may be single-ended, i.e., only one end of the fiber  10  exits the housing or the tube  20 . In that case, one end of the fiber  10  would be at the exit point of the fiber  10  from the tube  20  or prior to the exit point. Alternatively, the fiber  10  may exit from both sides of the tube  20  but one end of the fiber  10  would terminate before exiting the housing. 
     Also, it should be understood that the gratings of the invention may be used in reflection and/or transmission depending on whether the reflected or transmitted light from the grating is used to measure the measurand. Also, the term “tube” as used herein may also mean a block of material having the properties described herein. 
     The chambers or regions  34 ,  64 ,  74 ,  100 ,  116 ,  202 ,  306 ,  406  described herein may be filled with ambient air, or they may be evacuated (or be at another pressure), or they may be partially or completely filled with a fluid (liquid or gas), e.g., an oil. The type of filling fluid will depend on the desired thermal time constant, viscosity, and other fluid properties based on the desired application. 
     Also, it should be understood that, in operation, an instrumentation box (not shown), connected to the optical fiber  10 , having a broadband source, a scanned laser light source, or other suitable known optical source, and having a suitable spectrum analyzer or other known opto-electronic measuring equipment, all well known in the art, may be used to provide the incident light  14 . It may also be used to decode and measure the resultant wavelength or other optical parameter shift of the returned light (reflected  16  and/or transmitted  18 ) from the sensor(s) described herein, such as is described in U.S. Pat. Nos. 5,401,956, 5,426,297, or 5,513,913, or using other known optical instrumentation techniques. 
     Referring to FIG. 31, alternatively, a portion of or all of the tube-encased fiber grating  20  may be replaced by a large diameter silica waveguide grating  600 , such as that described in copending U.S. patent application Ser. No. 09/455,868, entitled “Large Diameter Optical Waveguide, Grating and Laser”, which is incorporated herein by reference. The waveguide  600  has a core  612  (equivalent to the core of the fiber  10 ) and a cladding  614  (equivalent to the fused combination of the tube  20  and the cladding of the fiber  10 ) and having the grating  12  embedded therein. The overall length L 1  of the waveguide  600  and the waveguide diameter d 1  are set the same as that described hereinbefore for the tube  20  (i.e., such that the tube  20  will not buckle over the desired grating wavelength tuning range) and the outer diameter of the waveguide is at least 0.3 mm. An optical fiber  622  (equivalent to the fiber  10  in FIG. 1) having a cladding  626  and a core  625  which propagates the light signal  14 , is spliced or otherwise optically coupled to one or both axial ends  628  of the waveguide  600  using any known or yet to be developed techniques for splicing fibers or coupling light from an optical fiber into a larger waveguide, that provides acceptable optical losses for the application. 
     The large diameter waveguide with grating  600  may be used in the same ways as the tube encased grating  20  is used herein where the fiber  10  is analogous to (and interchangeable with) the core  612  of the waveguide  600 . For example, the waveguide  600  may be etched, ground or polished to achieve the “dogbone” shape described hereinbefore with the tube  20 . Alternatively, the “dogbone” shape may be obtained by heating and fusing two outer tubes  640 ,  642  onto opposite ends of the waveguide  600 , like discussed hereinbefore with FIG.  2 . All other alternative embodiments described herein for the tube  20  and the tube-encased grating are also applicable to the waveguide  600  where feasible, including having a fiber laser or a DFB fiber laser, multiple fibers (or cores), various geometries, etc. 
     The tube-encased fiber grating  20  and the large diameter waveguide grating  600  may each also be referred to herein as a “optical sensing element”. The tube-encased grating  20  and the large diameter waveguide grating  600  have substantially the same composition and properties in the locations where the tube  20  is fused to the fiber  10 , because the end (or transverse) cross-section of the tube-encased grating  20  and the large diameter waveguide grating  600  are contiguous (or monolithic) and made of substantially the same material across the cross-section, e.g., a glass material, such as doped and undoped silica. Also, in these locations both have an optical core and a large cladding. 
     Also, the waveguide  600  and the tube-encased grating  20  may be used together to form any given embodiment of the sensing element described herein. In particular, one or more axial portion(s) of the sensing element may be a tube-encased grating or fiber and/or one or more other axial portion(s) may be the waveguide  600  which are axially spliced or fused or otherwise mechanically and optically coupled together such that the core of said waveguide is aligned with the core of the fiber fused to the tube. For example, a central region of the sensing element may be the large waveguide and one or both axial ends may be the tube-encased fiber which are fused together as indicated by dashed lines  650 ,  652 , or visa versa (FIGS. 1,  11 ,  30 ,  31 ). 
     It should be understood that the dimensions, geometries, and materials described for any of the embodiments herein, are merely for illustrative purposes, and as such, any other dimensions, geometries, or materials may be used if desired, depending on the application, size, performance, manufacturing or design requirements, or other factors, in view of the teachings herein. 
     Further, it should be understood that, unless otherwise stated herein, any of the features, characteristics, alternatives or modifications described regarding a particular embodiment herein may also be applied, used, or incorporated with any other embodiment described herein. Also, the drawings shown herein are not drawn to scale. 
     Although the invention has been described and illustrated with respect to exemplary embodiments thereof, the foregoing and various other additions and omissions may be made therein and thereto without departing from the spirit and scope of the present invention.