Patent Publication Number: US-2023136164-A1

Title: Fiber Optic Pressure Sensor

Description:
This invention was made under DARPA SBIR contract D17PC00406 awarded in 2017. The government has certain rights in this invention. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to a pressure sensor. In particular, the invention relates to a temperature-compensated pressure sensor using fiber Bragg gratings (FBGs) applied to a single surface of a diaphragm which is displaced by an applied pressure. 
     BACKGROUND OF THE INVENTION 
       FIG.  1    shows a prior art differential pressure transducer  100 . A first pressure port  110  couples into a first chamber  102 , and a second pressure port  112  couples to a second chamber  104  formed in housing  106 . The differential pressure is thereby transferred to diaphragm  108  in the form of a displacement which is measured by displacement sensor  114 . 
       FIG.  2    shows a prior art single-ended pressure transducer  200 , which has a pressure inlet  210  coupled to a first chamber  202  which includes generally rigid enclosure  206  walls which surround and support diaphragm  208 . A spring  212  provides a resistive pressure, or alternatively, chamber  204  may be filled with a non-hysteresis, temperature neutral fluid, or it may be opened to a neutral pressure environment compared to the pressure to be measured by inlet  210 . Displacement sensor  214  measures the diaphragm  208  movement. 
     In higher pressure applications, the diaphragm  108  of  FIG.  1    and diaphragm  208  of  FIG.  2    may have a suitable thickness which provides a suitable modulus for the differential pressure in use. 
     A problem arises in pressure sensors and transducers which utilize fiber optic Bragg gratings, also known as fiber Bragg gratings (FBG), for displacement measurement where the FBG has response coefficients such that the FBG is responsive not only to pressure but also to temperature. Certain environments, such as high temperature, and high pressure measurements, such as supersonic jet exhaust gas, or oil and gas exploration, where temperature variations from 25 degrees C. to 200 degrees C. or more are challenging for prior art pressure sensors. Additionally, it may be required to isolate the sensor on one side of a diaphragm from the gas or liquid being measured on the other side of the diaphragm. In prior art pressure sensor systems, a per-transducer calibration characteristic has been stored, and a separate temperature sensor is used in combination with the strain reading to compensate for this temperature effect on the pressure measurement. 
     For these reasons, it is desired to provide a pressure sensor for high temperature and high pressure environments which is suitable for single ended or differential pressure measurements. 
     OBJECTS OF THE INVENTION 
     A first object of the invention is a temperature compensated pressure sensor having a diaphragm with a pressure applied to one surface and an opposite surface coupled to an optical fiber having at least one FBG in contact with the surface in a region of deflection and a second FBG in thermal equilibrium with the first FBG, but placed in a region which couples minimal diaphragm deflection, the two FBGs coupled to a source of optical energy, the two FBGs transmitting or reflecting narrowband optical energy, and a wavelength interrogator for determination of pressure and temperature based on the reflected or transmitted wavelengths of the FBG. 
     A second object of the invention is a pressure sensor having a diaphragm coupled to a source of pressure, the diaphragm having an optical fiber with a first FBG mechanically coupled to a deflecting part of the diaphragm, the FBG oriented to couple to mechanical strain of the diaphragm, the diaphragm having a second region with a second FBG which is coupled to the temperature of the first FBG, but not to mechanical strain in the diaphragm, the first and second FBG reflecting or transmitting applied optical energy such that an increase in applied pressure causes the first FBG to reflect or transmit a change in wavelength corresponding to a change in temperature or strain and the second FBG to reflect or transmit a change in wavelength corresponding to a change in temperature only and not to a change in pressure. 
     A third object of the invention is a process for measurement of pressure applied to a diaphragm having FBGs on the same surface of a diaphragm but different regions of the diaphragm, the FBGs operating in reflection mode or transmission mode, the FBGs coupled to an optical source in a series configuration with one optical fiber having two FBG sensors, or independently to two separate optical fibers, each optical fiber having a separate FBG sensor, and a wavelength interrogator for conversion of reflected or transmitted wavelength shifts into pressure measurements. 
     SUMMARY OF THE INVENTION 
     A transducer diaphragm has a first surface with a first optical fiber having a first FBG sensor attached in a measurement region subject to deflection upon application of pressure to the opposite surface of the diaphragm, the first surface also having a datum region in thermal equilibrium with the measurement region but not subject to deflection upon application of pressure to the diaphragm, the datum region coupled to a second FBG sensor for temperature measurement and temperature compensation of the first FBG sensor. The diaphragm first surface measurement region FBG sensor is operative at a wavelength λ1 and responsive to temperature and strain, and is formed on an optical fiber, and a second FBG is operative at a second wavelength λ2 but which is responsive to primarily temperature and positioned in the datum region of the diaphragm. In one example of the invention, the first optical fiber FBG has a first temperature coefficient k1=Δλ1/ΔT which is closely matched to a second optical FBG temperature coefficient k2=Δλ2/ΔT. Additionally, one of the FBG sensors is responsive in a range of wavelengths which is slightly above or below the responsive wavelengths of the other FBG sensor. Each of the FBG sensor gratings generates a narrowband range of response wavelengths, and in the best mode of the invention, these range of response wavelengths are in separate wavelength ranges such that each response can be associated with a particular FBG sensor grating, however other embodiments of the invention may utilize FBG sensors with responses which include overlapping wavelength ranges. When a pressure is applied to the diaphragm, one FBG undergoes an incremental strain which changes the FBG response wavelength, and the other FBG sensor grating is not responsive to the deflection or strain, as it is only coupled to a temperature which is the same as the temperature of the first FBG sensor. A wavelength interrogator converts the first FBG response and the second FBG response into a pressure measurement after compensation for the temperature response which effects both first and second FBG sensor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows a cross section view of a prior art pressure transducer. 
         FIG.  2    shows a cross section view of a prior art single ended pressure transducer. 
         FIG.  3    shows a section view of a pressure transducer according to the present invention. 
         FIG.  4    shows a section view of  FIG.  3   . 
         FIG.  5    shows a section view of a cylindrical pressure sensor. 
         FIGS.  5 A,  5 B,  5 C,  5 D, and  5 E  show various section views of  FIG.  5   . 
         FIG.  6    is a block diagram of the pressure sensors of the present invention coupled to an optical wavelength interrogator. 
         FIG.  7    is a plot of an excitation source with detector responses associated with the AWG filter and detector of  FIG.  6   . 
         FIGS.  8 A and  8 B  shows a block diagram of a two-fiber wavelength interrogator. 
         FIG.  9    shows the waveforms for the wavelength interrogator of  FIG.  8   . 
         FIG.  10    shows a plot of wavelength shift vs strain of an example FBG sensor. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is a pressure sensor where a pressure to be measured is provided on one side of a diaphragm and the pressure is estimated by measuring the strain on the opposite surface of the diaphragm using an FBG oriented to capture a maximum strain of diaphragm deflection. The diaphragm may be circular, oval, rectangular, or any shape which deforms when a pressure is applied on one surface of the diaphragm relative to pressure applied to the other surface of the diaphragm. The invention may be used or adapted for any pressure measuring purpose, including oil or gas exploration, aerospace, or any known application requiring measurement of pressure. The invention has the additional advantage that a series of FBG sensors may be formed along a single fiber, and the optical responses may be individually and concurrently read using a wavelength interrogator, or the responses may be time division multiplexed (TDM) and read sequentially. 
       FIG.  3    shows a cross section view of a first example embodiment of a pressure transducer  300  according to the present invention. The pressure sensor  300  is preferably threaded into an enclosure and secured with threads  302 , and a pressure to be measured is applied to port  318  which is coupled into chamber  304  which is separated from a second chamber  305  optionally containing a reference pressure by a transducer diaphragm  307  which separates the two chambers. An increase of pressure in chamber  304  causes a small deflection in diaphragm  307 . Strain relief  316  protects optical fiber  312 / 314 , which enters chamber  305 , is loosely looped, has regions with FBGs which are secured to diaphragm  307 , and the same fiber  312 / 314  exits the chamber through strain relief  316 . 
       FIG.  4    shows an example section A-A of  FIG.  3    (not to scale), including diaphragm  307  which may be formed from housing  306 , with chamber  304  below shown with a dashed line. Optical fiber  312 / 314  is shown entering and leaving the field of view. Near the center of the diaphragm where diaphragm  307  displacement and strain from pressure is maximum is a first FBG sensor  402  which is placed radially (in the direction of maximum strain and dimensional change in response to pressure on the opposite side of the diaphragm), whereas second FBG sensor  404  is placed circumferentially (following radius  406 ) such that a change in deformation or strain of the diaphragm  307  does not couple a strain into second FBG sensor  404 . 
       FIG.  5    shows a cylindrical (or rectangular) embodiment of a pressure sensor, where a bar of material  502  has a first blind aperture  506  (an aperture which does not pass completely through the material  502 ) formed for introduction of a pressure adjacent to a second blind aperture  504  for introduction of the optical fiber with FBG sensors. The introduced pressure in first aperture  506  results in a deformation of diaphragm  508  which is formed by the separation between first and second apertures  504  and  506 . The apertures may be drilled holes or machined apertures, and the material  504  may be any shape which accommodates these apertures, including circular bar stock, rectangular bar stock, or the apertures may be formed directly into a structure for which a pressure measurement is desired.  FIGS.  5 A through  5 D  show various section views which include the optical fibers  522  and FBG sensors and  524 . In one example of the invention, the pressure sensor of  FIG.  5    is formed using additive machining (3D printing) of a metal such as stainless steel. When the additive axis is the long axis of the sensor (oriented in the long axis of apertures  504  and  506 ), it is possible to form arbitrarily complex shapes such as the irregular apertures  504  and  522  shown in  FIG.  5 B  which form septum diaphragm  508 . As before, a first FBG sensor  520  is positioned in a region of maximum strain and deflection, and a second FBG sensor  524  is positioned in a region of minimal response to strain and deflection, such as in an orientation which is minimally affected by diaphragm displacement. The first and second FBG sensor are preferably formed on the same fiber, although different fibers may be used. Optical fiber  522  may be routed in any manner which is convenient, including into and out of the open aperture  504 , or through additional apertures (not shown). In an example of the invention, the pressure sensor of  FIG.  5    is on the order of 2 cm in length with hemispherical upper and lower apertures  506  and  544  forming a septum diaphragm on the order of 125 u, and the FBGs are on the order of 4-5 mm in length. The dimensions and shapes shown in the pressure sensor of  FIG.  5    may be preferably formed using additive machining (AM) processes in stainless steel to form a monolithic structure. In another example of the invention for decreasing the porosity of the body of the pressure sensor, the pressure sensor may be formed from an Aluminum alloy such as AlSi 10 Mg, or alternatively, the pressure sensor may be formed of a material known in additive machining and then plated with nickel to a thickness on the order of 0.25 mm, or in another example of the invention, the pressure sensor may be anodized to form a surface passivation such as AlOH to decrease the porosity of the pressure sensor. An order of magnitude dimension is understood to be 10× greater or 0.1× smaller than the example dimension, however the dimensions of the pressure sensor of the present invention are not limited by the present example. 
       FIG.  5 E  shows an alternative example for the arrangement of sensors shown in  FIG.  5 D , where the temperature sensor  524 A is collinear with the pressure strain sensor  520 A. In this example embodiment, the temperature sensor  524 A is mechanically uncoupled from strain by placement into an annular sleeve which couples temperature to the FBG of temperature sensor  524 A but not strain, since the unconstrained FBG sensor free to move in the sleeve is not mechanically coupled to strain developed in diaphragm  522 , whereas strain sensor  520 A is mechanically and thermally coupled to the diaphragm  508  and associated strains it produces from deflection. In a present example of the invention, the fiber terminates at end  521 , however in other transmission mode FBG sensors, the fiber may continue and exit the sensor for connection to a wavelength interrogator. 
     The strain sensing FBGs may be attached to the surface of the diaphragm using any method which minimizes or eliminates hysteresis, and may include metallization of the exterior surface of the FBG sensors for subsequent metallic bonding to the diaphragm using high temperature structural adhesives, or by placing the fiber into a groove in the diaphragm  508  for mechanical attachment. Any means of attachment of the FBG sensor of the fiber to the diaphragm which provides for coupling of the strain or deflection of the diaphragm into a wavelength shift of the FBG sensor while minimizing creep would provide for satisfactory operation of the strain sensor according to the objects of the invention. Additionally, any placement of the temperature sensor which decouples the FBG from strain may be used. While it is preferable for one sensor to measure temperature without the influence of strain, in another example of the invention, the first and second sensor may be exposed to fractionally different strain amounts and substantially the same temperature, as the system of linear equations which resolve pressure are also capable of resolving fractional strains applied to each of the two FBG sensors into a pressure. 
       FIG.  6    shows an example embodiment of a pressure measurement system comprising wavelength interrogator  600  coupled to a plurality of pressure sensors  620 ,  626 , and  632  through add drop multiplexors  618 ,  624 , and  630 , respectively. In operation, a broadband source  602 , which may operate continuously, couples broadband optical power to circulator  604 , which couples broadband optical power to optical fiber  616 , and, in sequence, to any number of Optical Add Drop Multiplexers (OADM)  618 ,  624 , and  630 , each of which is operative to direct optical energy from a first port such as the first port of OADM  618  coupled to fiber  616  to a sensor port fiber such as  619  coupled to a pressure sensor having FBGs such as sensor  620 , where OADM  618  has a wavelength response within an operating wavelength range of the FBGs of  620 , such that optical energy reflected from FBG sensor  620  is in a wavelength range λ1 is directed back to the OADM  618  and then to first port coupled to fiber  616 , where it counter-propagates back to circulator  604 , and to AWG  608  for wavelength detection. The operation of each OADM  618 ,  624 ,  630  is in separate wavelength ranges matched to the corresponding FBGs of the sensor gratings  620 ,  626 , and  632 . Optical energy which is not in the operating range of a particular OADM such as  618  entering the first port (coupled to fiber  616 ) is directed to the second port coupled to fiber  622  with minimal attenuation. Accordingly, each OADM  618 ,  624 , and  630  is operative to direct optical energy applied in a respective wavelength range to the sensor port, where it is reflected back to the OADM first port by the FBGs of the sensor, and optical energy which is outside the respective wavelength range of the associated OADM continues to a subsequent OADM which has a first port coupled to the second port of a previous OADM and operates in a unique wavelength range associated with the FBG sensors coupled to each respective OADM sensor port. In this manner, each of the pressure and temperature sensors  620 ,  626 , and  630  associated with the gratings of  FIG.  3 ,  4   , or  5  reflect superimposed optical energy as λ1 and λ2 through circulator  604  and to Array WaveGuide (AWG) filter  654 , which separates the wavelengths from each reflection grating into separate channels by wavelength as shown in  FIG.  7   . Preferably, the AWG filter response is Gaussian for each channel, whereas typical AWG filters are designed for a flat amplitude response over each channel operating wavelength range. The Gaussian (or other sloped amplitude response) characteristic of the AWG filter provides preferable ability to discriminate wavelength over a greater fractional wavelength of the AWG channel response range compared to the prior art flat channel response. In one example of the invention, the AWG filter outputs are coupled to detectors  610 ,  611 ,  612 , and  613 , and each FBG sensor operating range is selected to operate between two such channels. The AWG optical outputs are coupled in pairs to optical energy detectors  610  to  613 , which are each operative according to the wavelength discrimination principles described in  FIG.  7    to resolve the AWG filter response to a wavelength. The AWG filter  654  may provide differential channel outputs as described in U.S. Pat. No. 9,110,259, and 8,983,250, which are incorporated in their entirety by reference. The controller/pressure calculator  614  receives the detected wavelengths for each sensor pair (temperature and strain) reflected (or transmitted) by the FBG sensors and resolves these into a pressure and temperature estimate based on the linear characteristics of the FBG to temperature and pressure, using, in one example, the FBG isolated from strain as a temperature sensor and the FBG coupled to both strain and temperature to resolve pressure and temperature. Different diaphragm materials will have different strain to pressure coefficients, which may be determined experimentally or in a calibration cycle. Additional measurement channels for other FBG sensors may be added by placing additional FBG sensors which are operative within unique wavelengths which also couple optical energy out of AWG filter  608  and are coupled to additional wavelength detectors (not shown) operative at each unique wavelength to detect additional measurement phenomenon such as an optional temperature-only sensor. 
       FIG.  6    also shows simplified wavelength responses to each of the FBG sensor pairs with respect to OADM operation. Each of the amplitude drops in forward propagating wavelength response plots  634 ,  638 ,  642 , and  646  correspond to optical energy captured by corresponding OADM  618 ,  624 , and  630  as found in optical fibers  616 ,  622 ,  628 , and  631 , respectively. The counter-propagating optical energy returned by the FBG sensors is shown in wavelength plots  636 ,  640 , and  644 , and represent the counter-propagating optical energy in optical fibers  616 ,  622 , and  628 , respectively, as reflected by each of the FBG sensors  620 ,  626 , and  632 . 
       FIG.  7    shows an example response plot for AWG filter and detector pairs such as  610 / 611  and  612 / 613  of  FIG.  6   , as well as the broadband source spectral plot  714  (of source  602  of  FIG.  6   ), which changes the amplitude of the reflected FBG sensor energy according to wavelength, since the reflected optical energy will typically be a large fraction (typically &gt;90%) of the input power which varies with wavelength as shown in plot  714 . Reflected narrowband optical signals  706  and  710  from an example FBG strain or temperature sensor in first wavelength range λ1  728  and second wavelength range λ2  732  produces a detector response L1_DetA associated with detector channel for  722  at point  704  associated with the first AWG output  722 , and also L1_DetB detector output  702  from the detector associated with the second AWG channel  724  responding to reflected optical energy  706 . The second associated FBG sensor response  710  in second wavelength range λ2  732  generates a detector output L2_DetA  708  and second AWG output filter characteristic  727  detector output L2_DetB  722 . Determination of the wavelengths λ1 and λ2 may then be determined from the characteristic plot of  FIG.  7   , either by a lookup table which maintains the profiles of plots  722 ,  724 ,  726 , and  727 , or by using a stored formula which converts the detector responses to resolved wavelengths. 
     The conversion from wavelength to temperature may be performed using a linear relationship between the measured wavelengths of the two sensor FBGs (λ 1  and λ2) and pressure P, temperature T and the nominal FBG wavelengths at zero differential pressure and at 0° C. (λ 01  and λ 02 ) as follows: 
     
       
         
           
             
               λ 
               1 
             
             = 
             
               
                 
                   a 
                   11 
                 
                 ⁢ 
                 P 
               
               + 
               
                 
                   a 
                   12 
                 
                 ⁢ 
                 T 
               
               + 
               
                 λ 
                 01 
               
             
           
         
       
       
         
           
             
               λ 
               2 
             
             = 
             
               
                 
                   a 
                   21 
                 
                 ⁢ 
                 P 
               
               + 
               
                 
                   a 
                   22 
                 
                 ⁢ 
                 T 
               
               + 
               
                 λ 
                 02 
               
             
           
         
       
       
         
           
             
               [ 
               
                 
                   
                     
                       
                         λ 
                         1 
                       
                       - 
                       
                         λ 
                         01 
                       
                     
                   
                 
                 
                   
                     
                       
                         λ 
                         2 
                       
                       - 
                       
                         λ 
                         02 
                       
                     
                   
                 
               
               ] 
             
             = 
             
               
                 [ 
                 
                   
                     
                       
                         a 
                         11 
                       
                     
                     
                       
                         a 
                         12 
                       
                     
                   
                   
                     
                       
                         a 
                         21 
                       
                     
                     
                       
                         a 
                         22 
                       
                     
                   
                 
                 ] 
               
               [ 
               
                 
                   
                     P 
                   
                 
                 
                   
                     T 
                   
                 
               
               ] 
             
           
         
       
     
     Therefore, the pressure P and temperature T can be found from the following equations. 
     
       
         
           
             
               [ 
               
                 
                   
                     P 
                   
                 
                 
                   
                     T 
                   
                 
               
               ] 
             
             = 
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             a 
                             11 
                           
                         
                         
                           
                             a 
                             12 
                           
                         
                       
                       
                         
                           
                             a 
                             21 
                           
                         
                         
                           
                             a 
                             22 
                           
                         
                       
                     
                     ] 
                   
                   
                     - 
                     1 
                   
                 
                 [ 
                 
                   
                     
                       
                         
                           λ 
                           1 
                         
                         - 
                         
                           λ 
                           01 
                         
                       
                     
                   
                   
                     
                       
                         
                           λ 
                           2 
                         
                         - 
                         
                           λ 
                           02 
                         
                       
                     
                   
                 
                 ] 
               
               = 
               
                 
                   [ 
                   
                     
                       
                         
                           C 
                           1 
                         
                       
                       
                         
                           C 
                           2 
                         
                       
                     
                     
                       
                         
                           C 
                           3 
                         
                       
                       
                         
                           C 
                           4 
                         
                       
                     
                   
                   ] 
                 
                 [ 
                 
                   
                     
                       
                         
                           λ 
                           1 
                         
                         - 
                         
                           λ 
                           01 
                         
                       
                     
                   
                   
                     
                       
                         
                           λ 
                           2 
                         
                         - 
                         
                           λ 
                           02 
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
       
         
           
             where 
             , 
           
         
       
       
         
           
             
               
                 [ 
                 
                   
                     
                       
                         a 
                         11 
                       
                     
                     
                       
                         a 
                         12 
                       
                     
                   
                   
                     
                       
                         a 
                         21 
                       
                     
                     
                       
                         a 
                         22 
                       
                     
                   
                 
                 ] 
               
               
                 - 
                 1 
               
             
             = 
             
               [ 
               
                 
                   
                     
                       C 
                       1 
                     
                   
                   
                     
                       C 
                       2 
                     
                   
                 
                 
                   
                     
                       C 
                       3 
                     
                   
                   
                     
                       C 
                       4 
                     
                   
                 
               
               ] 
             
           
         
       
     
     Calibration constants C 1 , C 2 , λ 01 , and λ 02   
     
       
         
           
             
               λ 
               01 
             
             ⁢ 
                
             and 
             ⁢ 
                 
             
               λ 
               02 
             
           
         
       
     
     can be found using a series of wavelength measurements at known pressure points by applying linear regression combined with the set of equations shown below. 
         P   m1   =C   1 λ 1   m1   −C   1 λ 01   +C   2 λ 2   m1   −C   2 λ 02   (Equation 1)
 
         P   m2   =C   1 λ 1   m2   −C   1 λ 01   +C   2 λ 2   m2   −C   2 λ 02   (Equation 2)
 
     Similarly, calibration constants C 3 , C 4 , λ 01 , and λ 02  can be found using a series of wavelength measurements at known temperature points by applying linear regression combined with the set of equations shown below. 
         T   n1   =C   3 λ 1   n1   −C   3 λ 01   +C   4 λ 2   n1   −C   4 λ 02   (Equation 3)
 
         T   n2   =C   3 λ 1   n2   −C   3 λ 01   +C   4 λ 2   n2   −C   4 λ 02   (Equation 4)
 
     Each pressure P m1 , P m2 , and (and corresponding temperature T n1 , T n2 ) can be found from the measured wavelengths using the equations above using measured reflected FBG sensor wavelengths λ 1   m1 , λ 2   m1 , λ 1   m2 , λ 2   m2 . 
       FIG.  9    shows a timing diagram for an alternative wavelength interrogator system shown in  FIG.  8 A . During a first measurement interval of arbitrary time duration, a first broadband source SRC_ 1   902  ( 804  of  FIG.  8 A ) is enabled with second broadband source SRC_ 2   904  ( 804  of  FIG.  8 A ) disabled, and during the first measurement interval, SRC_ 1   804  couples optical energy through circulator  806  to the first FBG strain sensor (operative initially at λ1), and narrowband reflected energy (initially at λ1) from the first sensor is coupled through circulator  806  to combiner  814  (with no optical energy returned from circulator  808  as SRC_ 2   802  is not enabled during the interval that SRC_ 1  is enabled), which couples optical energy into wavelength detector  815  which in one embodiment includes a splitter  816  and to a means for discriminating wavelength such as sine filter A  818  and sine filter B  820 , which are coupled to first detector DET_A  822  and second detector DET_B  824 , respectively. The output from the two detectors  822  and  824  are fed to a pressure calculator  826  which computes the pressure from the amplitude responses (the amplitudes presented to the detectors derived from the wavelength-dependent transfer function of the sine filter), of the two detectors DET_A  822  and DET_B  824  as was described in the previously described equations. During a second measurement interval of arbitrary time duration following the first measurement interval, the first source SRC_ 1   804  is disabled and the second broadband source SRC_ 2  is enabled. During the second measurement interval, the second circulator  808  couples broadband optical energy to the second FBG strain sensor (operative initially at λ2) through bidirectional port  812 , and narrowband optical energy (initially at λ2) reflected from the second sensor is coupled through circulator  808 , through combiner  814 , and to wavelength detector  815 , through splitter  816 , and to first sine filter  818  and second sine filter  820 , which generate optical outputs related to wavelength as will be described for  FIG.  7   , and the optical outputs of sine filters  818  and  820  are converted to an electrical signal by first detector  822  and second detector  824 , after which the electrical outputs of first and second detectors  822  and  824  are converted to a pressure measurement using pressure calculator  826 . For applications with remote measurements having a long optical fiber coupled to the FBG sensors, the first time interval and second time interval are typically established from the time-of-flight interval for the reflected wavelength from the strain sensor FBG to reach the interrogator, and for the detectors to respond thereafter. For a broadband source illuminating the FBGs, it is possible for a wavelength interrogator separated from the measurement gratings by a 10 km fiber length, with an index of refraction of 1.48 for the fiber core (resulting in a 97 us round-trip delay), and a detector with a 2 us response, to therefore operate at a repetition rate of up to 10,000 unambiguous samples per second. In this manner, the repetition rate for any length of fiber and detector response time can be calculated. 
     The interrogator  800  of  FIG.  8 A  may be operated in at least one other configuration. For the case where a pair of fibers with FBG sensors are used for redundancy, with each fiber sensing the same mechanical property (one sensor sensing a strain+temperature and the other sensing temperature only), a redundant configuration which provides protection from a single fiber failure is used with reflection gratings, each pair of sensors formed on a single fiber, the separate fibers placed with sensing of strain+temperature and temperature only on diaphragm  307  or  508 .  FIG.  8 B  shows an alternative example with a double ended sensor of  FIG.  3  or  5    (with the closed fiber end  521  instead continuing through with a return optical fiber for use with transmission mode FBG sensors) is a non-redundant configuration with transmission mode FBGs on the diaphragm surface and located in the previously referenced sensing regions and using the interrogator of  FIG.  8 A  with the FBG connection of  FIG.  8 B . Any number of FBGs may be used beyond the exemplar two shown. 
     The present examples of the invention describe Wavelength Division Multiplexing (WDM), where each sensor is operative in a unique wavelength range. In another example of the invention, the optical source may be pulsed on for brief instants of time corresponding to the time-of-flight from a broadband source and back to the wavelength discriminator, operating instead in a Time Division Multiplexing (TDM) mode, with the ON time of the source governed by the spatial separation of the FBGs. It may be preferred to use TDM mode where the separation between FBG sensors is long enough for accurate wavelength resolution, and WDM when the separation between FBG sensors is comparatively shorter. 
     Typical FBGs are formed using gratings which are formed with variations in index of refraction which are directed coaxially to the central axis of the optical fiber. In another example of the invention, tilted gratings are used in the FBG sensors and the optical source is a multi-mode source with a short duration pulse. Tilted FBG gratings tend to exhibit a mode-specific behavior, such that higher modes of propagating optical energy are reflected towards the cladding of the optical fiber, which results in greater losses of certain higher modes, but also increased optical path length for lower modes. Such a tilted FBG sensor with multi-mode pulsed source configuration, with the FBGs operative in either transmission mode or reflection mode, results in additional modal information which presents at the detector as a time domain response with multiple peaks separated in time, as wavefronts for the various modes arrive separated in time according to the longer path length for each mode. As each of the propagation modes in the FBG respond differently to temperature and pressure variations, it is then possible to provide extraction of temperature and strain from a single FBG by examination of both the wavelength shift and time domain spread in detector response to the reflected (or transmitted for transmission mode FBGs) optical energy. In one example of the invention, increased strain causes a greater shift in time domain reflected wavefronts than does increased temperature, which causes a greater time domain separation in the returned optical energy, resulting in a single tilted grating providing both strain and temperature. 
       FIG.  10    shows a wavelength shift characteristics (Y axis) of an FBG having a strain applied (X axis). The wavelength shift is shown with reference to an unspecified starting wavelength associated with the unstressed FBG after mounting into a surface such as the diaphragm  307  of  FIG.  3    or diaphragm  508  of  FIG.  5   . The relationship between wavelength shift and FBG strain can be described as a linear equation, shown for  FIG.  11    as Y=0.7328X (ignoring temperature effects for simplicity of illustration). 
     In a preferred embodiment of the invention, the reflection wavelengths λ1 and λ2 are distinct and non-overlapping over the combinations of temperature and pressure, as shown in the x-axis of  FIG.  6    corresponding to a single cycle of sine filter response for uniqueness of y-axis response with λ1 and λ2 in exclusive and non-overlapping wavelength ranges. 
     There are several motivations for the best mode of non-overlapping ranges of wavelengths produced by the pair of FBGs of a particular pressure transducer. One motivation is to provide a clear association between a particular response wavelength and a given sensor FBG, such that λ1 and λ2 are not indeterminate in the equations. Another advantage of using separate wavelength response ranges is to prevent the “shadowing” of a downstream reflection-mode sensor or additive superposition of a downstream transmission-mode sensor, which would cause two sensors responses to appear as a single sensor response. While it is possible to operate the two sensors in overlapping ranges, a disadvantage is the inability of the wavelength discriminator to distinguish between a single sensor response caused by two separate sensors operating in the same wavelength and a failure in the fiber which interconnects the two FBG sensors, resulting in a single sensor reflection response. By tracking each sensor response for association to a particular sensor, and detection of same-wavelength sensor response, it is possible for the two sensors to operate in overlapping response ranges. 
     The examples provided herein are for illustration only, and are not intended to limit the invention to only the particular embodiments used for explanation, as set forth in the claims which follow.