Transcript Slide 1 - Drexel ECE

Strain Sensitivity in Fiber Optic
Sensors
PHANEENDRA MEDIDA
Briefly…
 Optical Fiber Sensor
 Strain Concepts
 Interferometers
 Fabry-Perot interferometer
 Bragg grating fiber optic sensor
 Strain Sensitivity Calculations
Optical Fiber Sensor
 Definition of Optical Fiber Sensor
Block Diagram of Optical Fiber Sensor System
Optical Tx
Optical fibers
&
Actuators
Control system
Optical Rx
Data Acquisition
And health
Assessment
Optical Fiber Sensor (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.
Hookes’s law
 i  Qij (e j   j T )
Qij
= the
stiffness matrix
j
= the
thermal expansion coefficient

= the
stress = F/A
 T = the temperature change
Strain Concepts (contd)
 Far-field strains
du
e1  e11  1
dx1
e4   23 
du2 du3

dx3 dx2
u = displacement
e2  e22 
du2
dx2
e5   13 
du1 du3

dx3 dx1
e = strain=
e3  e33 
du3
dx3
e6   12 
du1 du2

dx2 dx1
 =shear strain
l
l
Total strain inside the sensor is, eit  eir  eis
eir is the residual strain and eis is the applied strain
Far field strain are those strains which are present in the absence of sensor.
Strain Concepts (contd)
Optical fiber sensor, representing strain directions
X2
X1
X3
The far field strain components are given by
 e11   e1 
e  e 
 22   2 
 e   e 
e   33    3 
 23   4 
 13   5 
   
 12   6 
Interferometers
 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.
  L  L  k (nL  Ln)  knL(L / L  n / n)  kL(n  n)
 Strain optic effect – modulation of fiber refractive index.
 Mode dispersion effect-due to change in the diameter of the fiber.
n2
  kLn ( 
2
f
1
6
P   )


f
1
TiO2
FABRY-PEROT INTERFEROMETER
 Semi-reflective fiber splices.
 TiO2 films are sputtered on the fiber end faces
Semi reflective
Fusion splice
Mirrored End
Gauge Length (L)
Semi reflective
Fusion splice
He-Ne Laser
3dB Coupler
Detector
Mirrored End
R1
R2
Pi
Pt
Pr
L
2
Pr R1  R2 (1  A1)  2 RZ1R2 (1  A1) cos

Pi
1  R1R2  2 R1R2 cos
Pt
T1T2

Pi 1  R1R2  2 R1R2 cos

4nL

FABRY-PEROT INTERFEROMETER (contd)
 Interference occurs at the half silvered separating the sensing
portion of the fiber.
Phase (Degrees)
Strain
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 (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 (contd)
Relation between optical, geometrical properties and output
n
eff
avg
n
eff
diff


n eff
 n qeff
p
n eff
p
2
 n qeff
2
change in length due to applied strain
Ld  L  L
when light reflects back there will be two phase shifts, fast and slow varying terms
h 
4
0
n0 L0 
4L0
0
t navg 
4
0
n0 t L
s 
4L0
0
t ndiff
FABRY-PEROT INTERFEROMETER (contd)
Butter and Hocker Model
  SL z
 n 2 Pe
S  kn 1 
2

I
S is the phase strain sensitivity



Pe
is the effective strain-optic coefficient,
Pe  P12  vP11  P12 
For pure silica core and boron doped cladding the values of strain optic coefficient are
P11 =0.113 and
P12 =0.252 with n=1.458 and v=0.17
BRAGG GRATING FIBER OPTIC SENSOR
 periodic modulation of the core index
B
 There is a strong back reflection at the Bragg wavelength,
B  2n
 Monitoring the wavelength of narrowband spectrum will help in
determining the strain.
Intracore Bragg
Grating
Optical Fiber
Induced Grating
Laser Beams
Fiber Core
Reflected signal
Index Grating
B
Signal OUT
L
L
ne
n  105 to103

1.46
Z1
Back reflected
Bragg signal
Reflected
Signals for 3
values of strain
I2
Z
Bragg signal
transmitted,
missing signal
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.
BRAGG GRATING FIBER OPTIC SENSOR (contd)
When stress is applied to the sensors,
d  d 0  t d
t eff
n eff
p  n0   n p
n qeff  n0  t n qeff
   0  t 
Taylor expansion of the Bragg’s relation

0,

1
 0,

1
 

n0,
  
Butter-Hocker model

0,


 1  Peff  1
n






BRAGG GRATING FIBER OPTIC SENSOR (contd)
Wavelength-strain sensitivity of the Bragg grating sensor,
S B  1  Peff
eff
P =
n02,
2
P12  vP11  P12 
is the index-weighted strain-optic coefficient
Calculations
Relation between Phase-strain sensitivity and refractive index
for FP interferometer Strain Sensor
k, is the free-space propagation constant
n, is the refractive index
P is the effective strain-optic coefficient,
 0.113
P
11
P  P
12
P
12
 11  P12
 0.17 P

 0.252
P  0.19
6
k   6.871 10 /m
n 20
0
i   0  n
n _v ar   1  ( i  1)  .0 5
i
( P h ase  st rai n)sen sit iv i ty
S_I   k n _v ar   1   n _v ar 
9 10
8 10


i
i

i
2 P 

2 
6
6
S_I
7 10
6 10
6
6
1
1.5
2
2.5
0
0
6.459·10 -6
0 1.05
1
6.69·10 -6
1 1.1
2
6.909·10 -6
2 1.15
3
7.118·10 -6
3 1.2
4
7.314·10 -6
4 1.25
5
7.499·10 -6
5 1.3
6
7.67·10 -6
6 1.35
S_I  7
7.829·10 -6
n _v ar  7 1.4
8
7.973·10 -6
8 1.45
9
8.104·10 -6
9 1.5
10
8.22·10 -6
10 1.55
11 8.321·10 -6
11 1.6
12 8.406·10 -6
12 1.65
13 8.475·10 -6
13 1.7
14 8.527·10 -6
14 1.75
15 8.562·10 -6
15 1.8
n_var
S_I is given in Degrees strain 1cm 1
Relation between wavelength-strain sensitivity and refractive index of Bragg sensor
S_B 
i
2
n_var 

i
P _eff 
0.19
i
0.105
0.885
0.115
0.874
0.126
0.863
0.137
0.852
0.148
0.839
0.161
0.827
0.173
0.814
0.186
0.8
0.2
0.786
0.214
0.772
0.228
0.757
0.243
0.741
0.259
2.5
0.725
0.275
2.05
0.709
0.291
0.692
0.308
S_B  1  P _eff
i
0.895
S_B
0.8
0.601 0.6
1
1.05
1.5
2
n_var
i
0.895
2
i
P _ eff 
S_B is given in pm  strain1
Conclusion
 Sensing mechanisms show that the strain is directly related to the
phase change for the interferometric type.
Advantage of Bragg sensor is the Bragg’s wavelength is a linear
function of the measurand.
Increasing change in the refractive index, the sensitivity increases for
a Fabry-Perot sensor.
Decreases for a Bragg grating sensor
 Selecting a strain sensor for particular range of sensitivity.
References:
1.“Fiber Optic Sensors”, Eric Udd, John Wiley and Sons, Inc.
2.“An Introduction to Fiber Optic Systems”, john P. Powers, Aksen Associates
Incorporation Publishers.
3.Single-Mode Optical Fiber Measurement: Characterization and Sensing”,
Giovanni Cancellieri, Artech House, Inc.
4.“Selected Papers on Fiber Optic Sensors”, Reinhardt Willsch, Ralf Th.
Kersten, SPIE Milestone Series.
5.“Strain and Temperature Measurement with Fiber Optic Sensor”, Regis
J.Van Steenkiste, George S.Springer.
6.“Fiber Optic Fabry-Perot strain Gauge”, Tomas Valis, Dayle Hogg, and
Raymond M.Measures, IEEE Photonics Technology Letters, Vol. 2, No. 3,
227-228, March 1990.
7.“Fiber Bragg grating temperature sensor with controllable sensitivity”,
Jaehoon Jung, Hui Nam, Byoungho Lee, Jae Oh Byun, and Nam Seong
Kim, APPLIED OPTICS , Vol. 38, No. 13 ,1 May 1999.
8.“Fiber Grating Sensors”, Alan D. Kersey, Michael A. Davis, Heather J.
Patrick, Michel LeBlanc, K. P. Koo, C. G. Askins, M. A. Putnam, and E.
Joseph Friebele, JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 15,
NO. 8, AUGUST 1997.
9.“Fiber optic sensors in concrete structures: a review”, C I Merzbacher, A D
Kersey and E J Friebele, Smart Mater. Struct. 5 (1996) 196–208.
10.“Optical fiber Fabry-Perot sensors for smart structures”, C E Lee, J J
Alcoz, Y Yeh, W N Gibler, R A Atkins and H F Taylor, Smart Mater.
Struct. 1 (1992) 123-127.
Questions





What is Far field Strain?
State Hookes’s Law.
What are smart structures?
What is the principle of interferometry?
What is Bragg relation?
THANK YOU
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