Distributed Fiber Optic Sensing: Temperature Coefficient for Polyimide Coated Low Bend Loss Fiber, in the 10°C – 80°C Range
Short Summary
This Engineering Note describes the methods employed in obtaining a temperature coefficient for polyimide coated low bend loss fiber, in the 10°C - 80°C range.
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Engineering Note
EN-FY1405
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Distributed Fiber Optic Sensing: Temperature Coefficient for
Polyimide Coated Low Bend Loss Fiber, in the 10¡C – 80¡C Range
Contents
Introduction
!
This Engineering Note describes the methods employed in obtaining a temperature coefficient for
polyimide coated low bend loss fiber, in the 10¡C – 80¡C range. Results indicate that a linear fit with
coefficient -0.702 ¡C /GHz results in a ±1.28¡C deviation within this temperature range, while a quadratic
fit with first and second order coefficients of -0.771 ¡C /GHz and -0.000564 ¡C /GHz2
(calculated for a
tare at 0¡C) results in a ±0.579¡C deviation within this temperature range.
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Theory
!
Luna utilizes swept-wavelength interferometry to interrogate fiber optic sensors. Physical changes in the
sensors create a measurable change to the light that is scattered in the fiber (Rayleigh scatter). By
comparing locally-reflected spectra between two measurements of the same fiber optic sensor, the local
spectral shift may be deduced and calibrated to an external stimulus (e.g. strain, temperature, etc.)
!
The physical length and index of refraction of the fiber are intrinsically sensitive to environmental
parameters: temperature and strain, and to a lesser extent, pressure, humidity (if the fiber coating is
hydroscopic), electromagnetic fields, etc. In most practical cases the effects of temperature and strain will
dominate the spectral response of the Rayleigh backscatter. Changes in the local period of the Rayleigh
scatter cause temporal and frequency shifts in the locally-reflected spectrum. These shifts can be scaled to
form a distributed sensor.
!
A change in temperature or strain from the baseline condition results in a shift in the spectrum of light
scattered in the fiber. The strain response arises due to both the physical elongation of the sensor, and the
Introduction 1
…………………………………………………………………………………………………………………..
Theory 1
………………………………………………………………………………………………………………………….
Test Setup 2
…………………………………………………………………………………………………………………….
Aluminum Enclosure 2
…………………………………………………………………………………………………..
RTDs 3
………………………………………………………………………………………………………………………..
Fiber Layout 3
………………………………………………………………………………………………………………
Temperature Profile 4 …………………………………………………………………………………………………….
Results 5
…………………………………………………………………………………………………………………………
RTD Calibration 5 ………………………………………………………………………………………………………….
Temperature Coefficient 6
………………………………………………………………………………………………
Exercise Cycle 8
……………………………………………………………………………………………………………
Coefficient Verification 9
…………………………………………………………………………………………………
Summary 11
…………………………………………………………………………………………………………………….
References 11
………………………………………………………………………………………………………………….
Product Support Contact Information 12
………………………………………………………………………………
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EN-FY1405change in fiber index due to photoelastic effects. The thermal response arises due to the inherent thermal
expansion of the fiber material and the temperature dependence of the refractive index,
n
. The thermal
response is dominated by the d
n
/dT effect, which accounts for ~95% of the observed shift. [1]
!
The shift in the spectrum of light scattered in the fiber in response to strain or temperature is analogous to
a shift in the resonance wavelength !” or the frequency shift, !#, of a Bragg grating:
$
where
” and % are the mean optical wavelength and frequency, and K
T
and K
&
are the temperature and
strain calibration constants, respectively. Common values for most germanosilicate core fibers are KT
=
6.45 x 10-6 ¡C-1 and K
&
= 0.780. The values for K
T
and K
&
are somewhat dependent on the dopant species and concentration in the core of the fiber, but also to a lesser extent on the composition of the cladding
and coating. Variations of 10% in K
T
and K
&
between standard telecom fibers are common. [2,3]
!
In the absence of strain, the temperature change can be written as:
$
where
$
is the center wavelength of the scan and c is the speed of light.
!
Assuming a scan center wavelength of 1550 nm, the constant K
T
can be substituted in to yield the conversion factor:
$
such that:
$
!
In other words, the distributed temperature and strain curves are merely rescaled copies of the frequency
shift distribution. However, the linear approximation commonly made in the literature does not fully
account for the observed optical frequency response to temperature. In addition to variation in the linear coefficient with core dopant species and concentration and fiber coating material and thickness, higher
order fitting terms may be needed to fully describe response, especially over wide temperature ranges.
!
The temperature coefficient of a particular fiber type may be calibrated in a straightforward manner by
recording the frequency shift for a known applied temperature shift. For this Engineering Note, the
temperature coefficient for polyimide coated low bend loss (LBL) fiber is calibrated, in the 10¡C – 80¡C
range.
!
Test Setup
Aluminum Enclosure
An enclosure was machined out of solid Aluminum (Figure 1). The mass of the enclosure ensured that the
temperature distribution within the enclosure cavity was uniform throughout the test. Temperature
uniformity within the cavity was verified in a pre-test with multiple passes of acrylate-coated SMF28e+ fiber.
!
”
”
#
#
!
K
T
K
T
+
$
=
$
%
=
$
!
”
#
$
=
#
T
c
K
T
!
G
H
z
C
c
K
k
T
T
¡
!
=
!
=
8
1
.
”
!
”
¡
#
=
”
G
H
z
C
T
8
1
.
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EN-FY1405!
!
$
Figure 1 Aluminum enclosure
RTDs
!
Six calibrated Platinum RTDs (resistance temperature detectors) were used for these tests, as the
temperature measurement standard against which the fiber measurements were compared. The RTDs were
4-wire, class 1 /10B, wire wound. The manufacturer specifies accuracy for these RTDs from 0¡C to
100¡C. The RTD tolerances were measured using an in-house metrology well from 50¡C to 80¡C. An
Agilent 34972A electrical readout system was used to log RTD measurements.
!
Fiber Layout
!
A single fiber sensor was strung in multiple passes within this enclosure (Figure 2). The sensor consisted
of acrylate-coated SMF28e+ spliced to stripped LBL, which was in turn spliced to polyimide coated LBL fiber.
!
The first two acrylate-coated SMF28e+ fiber passes were used as a control sample. The next six stripped
LBL passes were used for comparison with the following seven polyimide coated LBL fibers.
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EN-FY1405$
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Figure 2 Fiber layout within Aluminum enclosure
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Silicon pads were used to hold the fiber ingress and turnarounds. The fiber was instrumented loosely drooping between the silicon pad strips, without touching the bottom of the cavity. This droop was
necessary to compensate for thermal expansion of the Al enclosure at maximum temperature, and
effectively isolated the fiber from strain.
!
An Aluminum lid was bolted on the enclosure before installation in a temperature chamber (Tenney
model TJR).
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Temperature Profile
!
The temperature chamber was programmed to cover the temperature range of 10¡C – 80¡C in 10¡C steps
(Figure 3). Frequency shift and temperature measurements were recorded when the temperature chamber
reached equilibrium at each temperature setting. At every temperature step, equilibrium was defined as
being reached when the RTD temperature changed by less than ±0.03¡C over 20 minutes. Each
temperature change step took 5 hours, resulting in a full cycle being completed once every 72 hours. This
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EN-FY1405setup was put through 5 full cycles. Measurements on both the RTD and the ODiSI B were taken at 1
minute intervals.
!
!
!
!
Figure 3 Temperature profile of a single cycle
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Results
RTD Calibration
!
The RTDs used in this test were measured against a metrology well (Fluke, model 9144) before and after
the test. The RTD measurements taken during the test were then rescaled with calibration coefficients
calculated from the combination of calibration data sets from before and after the test. This achieved the
best correlation to the metrology well (Figure 4). The RTDs had a stated tolerance given by the equation:
0.1*(0.3+0.005*Temperature) ¡C. The tolerance for the metrology well was interpolated from the
manufacturerÃs stated tolerance, based on the depth of the RTDs in the well, and is given by the equation:
0.0844595*(0.129+0.01*Temperature) ¡C. !
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EN-FY1405$
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Figure 4 RTD calibration results
Temperature Coefficient
!
A representative plot of frequency shift as a function of length along the sensor is shown in Figure 5. The frequency shift along the passes of each fiber type is seen to be uniform, confirming the temperature
uniformity within the enclosure.
!
!
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Figure 5 Frequency shift along the sensor length at 80¡C.
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EN-FY1405The resulting temperature response curve is shown in Figure 6. All RTD and polyimide coated LBL fiber
measurements were averaged once the temperature within the enclosure had reached equilibrium.
Equilibrium is defined by RTD temperature changing by less than ±0.03¡C over 20 minutes. The plots on
the top row are the measured response along with a linear fit (left) and a quadratic fit (right). The plots on
the bottom row are the residuals of the linear fit (left) and quadratic fit (right).
!
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Figure 6 Top: Temperature as a function of frequency shift, with a linear fit (left) and quadratic fit (right) applied. Bottom:
Temperature difference between measured and fit results, as a function of frequency shift, with a linear fit (left) and quadratic fit
(right) applied.
!
These results indicate that for temperature tests carried out in the 10¡C – 80¡C range with polyimide
coated LBL fiber, a linear fit with coefficient -0.702 ¡C /GHz will result in a ±1.28¡C deviation, while a
quadratic fit with first and second order coefficients of -0.771 ¡C /GHz and -0.000564¡C /GHz
2
(calculated
for a tare at 0¡C) will result in a ±0.579¡C deviation (Table 1).
!
!
Table 1 Coefficients and residuals for polyimide coated LBL fiber.
Linear
Quadratic tared at 0¡C
Quadratic tared at 25¡C
Quadratic Coefficient
0 ¡C /GHz
2
A
1
= -0.000564 ¡C /GHz
2
B
1
= -0.000564 ¡C /GHz2
Linear Coefficient
-0.702 ¡C /GHz
A
2
= -0.771 ¡C /GHz
B
2
= -0.734 ¡C /GHz
Tare Temperature
Any
A3
= 0 ¡C
B
3
= 25 ¡C
Largest Residual
-1.283 ¡C
-0.579 ¡C
-0.579 ¡C
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EN-FY1405!
For measurements taken with a tare at a temperature other than 0¡C, the following equation describes the
temperature response curve:
$ where:
$
$ $ when
$
!
Exercise Cycle
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By tracking the frequency shift through the 5 full cycles, it was observed that the polyimide coated LBL requires an initial Ãexercise cycleÃ. A plot of temperature difference between RTD and fiber (Figure 7)
shows that the large difference at the start of the test reduces to 23% after 2 cycles and 13% after 3 cycles.
This exercise cycle is required to relax the polyimide coating on the LBL. Customers carrying out
temperature measurements are therefore advised to run their temperature sensors through an exercise
cycle prior to the actual test. The measurement can then be zeroed at a known constant temperature along
the fiber.
!
3
2
2
1
B
B
B
T
+
!
+
!
=
”
”
1
1
A
B
=
)
(
4
3
3
1
2
2
2
A
B
A
A
B
!
+
!
=
T
B
=
3
=
!
”