Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26QuestionsSlide 28Strain Sensitivity in Fiber Strain Sensitivity in Fiber Optic SensorsOptic SensorsPHANEENDRA MEDIDABrieflyBriefly…… Optical Fiber Sensor Strain Concepts Interferometers Fabry-Perot interferometer Bragg grating fiber optic sensor Strain Sensitivity CalculationsOptical Fiber Sensor Definition of Optical Fiber SensorOptical TxOptical fibers&ActuatorsOptical RxControl systemData AcquisitionAnd health AssessmentBlock Diagram of Optical Fiber Sensor SystemOptical Fiber Sensor (contd)(contd) Large bandwidth and fast response. Immunity to, and no emission of EMI. Chemical and environmental ruggedness. Small size and weight. Cost effective.Strain Concepts Strain is the relative change in shape or size of the body due to applied force or pressure.)( TeQjjiji ijQ = the stiffness matrix j = the thermal expansion coefficient  = the stress = F/A T = the temperature changeHookes’s lawStrain Concepts (contd)Far-field strains 11111dxduee  2332234dxdudxdue u= displacement22222dxduee  1331135dxdudxdue e= strain=ll33333dxduee 1221126dxdudxdue =shear strain Total strain inside the sensor is,siritieee rie is the residual strain and sieis the applied strainFar field strain are those strains which are present in the absence of sensor.Strain Concepts (contd)Optical fiber sensor, representing strain directionsX3X1X2The far field strain components are given by 654321121323332211eeeeeeeInterferometers A fiber optic, interferometric strain gauge is based on the change in the optical path length caused by straining the fiber. These strains cause a phase delay.)()//()( nnkLnnLLknLnLLnkLL )2(6121ffPnkLn Strain optic effect – modulation of fiber refractive index.  Mode dispersion effect-due to change in the diameter of the fiber.FABRY-PEROT INTERFEROMETERFABRY-PEROT INTERFEROMETER Semi-reflective fiber splices.  films are sputtered on the fiber end faces 2TiO 2TiO 2TiO 2TiOGauge Length (L)Semi reflective Fusion spliceMirrored EndHe-Ne LaserDetector3dB CouplerSemi reflective Fusion spliceMirrored EndR1 R2PiPrPtLcos21cos)1(2)1(21211212121RRRRARRZARRPPircos21212121RRRRTTPPitnL4FABRY-PEROT INTERFEROMETER FABRY-PEROT INTERFEROMETER (contd)(contd) Interference occurs at the half silvered separating the sensing portion of the fiber.Strain Phase (Degrees) Sensing Mechanism A light radiation gets reflected from the semi-reflective splice. Second radiation gets reflected from the mirror and then travels back to the fiber. Two radiations overlap to give interference pattern.FABRY-PEROT INTERFEROMETER FABRY-PEROT INTERFEROMETER (contd)(contd) Due to applied pressure, the phase changes with respect to the intensity, due to the change in the length of the gauge length.FABRY-PEROT INTERFEROMETER FABRY-PEROT INTERFEROMETER (contd)(contd)Relation between optical, geometrical properties and output22effqeffpeffdiffeffqeffpeffavgnnnnnnchange in length due to applied strain LLLdwhen light reflects back there will be two phase shifts, fast and slow varying terms LnnLLntavgth0000000444difftsnL004FABRY-PEROT INTERFEROMETER FABRY-PEROT INTERFEROMETER (contd)(contd)Butter and Hocker ModelzSLS is the phase strain sensitivity 212eIPnknSeP is the effective strain-optic coefficient,  121112PPvPPeFor pure silica core and boron doped cladding the values of strain optic coefficient are 11P=0.113 and 12P=0.252 with n=1.458 and v=0.17BRAGG GRATING FIBER OPTIC SENSORBRAGG GRATING FIBER OPTIC SENSOR periodic modulation of the core index There is a strong back reflection at the Bragg wavelength, B n2B Monitoring the wavelength of narrowband spectrum will help in determining the strain. Laser BeamsInduced GratingOptical FiberIntracore Bragg Gratingen1.46351010 tonLLReflected signalSignal OUTBFiber Core Index Grating Z1 I2 ZBack reflected Bragg signalReflected Signals for 3 values of strainBragg signal transmitted, missing signalBRAGG GRATING FIBER OPTIC SENSOR (contd)BRAGG GRATING FIBER OPTIC SENSOR (contd)Sensing principle When a strain is applied the reflected wavelength shifts and the shift is proportional to the amount of strain applied.When stress is applied to the sensors, BRAGG GRATING FIBER OPTIC SENSOR (contd)BRAGG GRATING FIBER OPTIC SENSOR (contd)teffqteffqeffpteffptnnnnnnddd0000Taylor expansion of the Bragg’s relation  nn,0,0,011Butter-Hocker model  1,01effPBRAGG GRATING FIBER OPTIC SENSOR (contd)BRAGG GRATING FIBER OPTIC SENSOR (contd)Wavelength-strain sensitivity of the Bragg grating sensor, effBPS1  1211122,02PPvPneffP= is the index-weighted strain-optic coefficientCalculationsRelation between Phase-strain sensitivity and refractive index for FP interferometer Strain Sensork, is the free-space propagation constant k 6.871 106n, is the refractive indexP is the effective strain-optic coefficient,P110.113P120.252P P120.17 P11P12 P 0.19/mn 20 i 0 nn_vari1 i 1( ) .05Phase strain( )sensitivityS_Iik n_vari 1 n_vari 2P2S_I001234567891011121314156.459 10 �-66.69 10 �-66.909 10 �-67.118 10 �-67.314 10 �-67.499 10 �-67.67 10 �-67.829 10 �-67.973 10 �-68.104 10 �-68.22 10 �-68.321 10 �-68.406 10 �-68.475 10 �-68.527 10 �-68.562 10