# Distributed Fiber Optic Sensing: Temperature Coefficient for Polyimide Coated Low Bend Loss Fiber, in the -40Â°C to 200Â°C Range

Methods employed to obtain a temperature coefficient for polyimide coated low bend loss fiber, in the -40Â°C – 200Â°C range

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1.540.769.8400 Technical Note EN-FY1403

Revision 1 July 23, 2014

Distributed Fiber Optic Sensing: Temperature Coefficient for

Polyimide Coated Low Bend Loss Fiber, in the -40Â°C to 200Â°C

Range

Contents

Introduction …………………………………………………………………………………………………………………………………………………………. 1

Theory …………………………………………………………………………………………………………………………………………………………………… 1

Test Setup …………………………………………………………………………………………………………………………………………………………….. 3

Aluminum Enclosure …………………………………………………………………………………………………………………………………….. 3

RTDs ………………………………………………………………………………………………………………………………………………………………….. 3

Fiber Layout ……………………………………………………………………………………………………………………………………………………. 3

Temperature Profile ………………………………………………………………………………………………………………………………………. 5

Results …………………………………………………………………………………………………………………………………………………………………… 5

RTD Calibration ………………………………………………………………………………………………………………………………………………. 5

Temperature Coefficient ………………………………………………………………………………………………………………………………. 6

Segmented Linear Fit …………………………………………………………………………………………………………………………………… 11

Exercise Cycle ……………………………………………………………………………………………………………………………………………….. 13

Coefficient Verification ……………………………………………………………………………………………………………………………….. 13

Summary …………………………………………………………………………………………………………………………………………………………….. 15

References ………………………………………………………………………………………………………………………………………………………….. 15

Appendix …………………………………………………………………………………………………………………………………………………………….. 16

Product Support Contact Information ………………………………………………………………………………………………………….. 17

Introduction

This Technical Note describes the methods employed to obtain a temperature coefficient for

polyimide coated low bend loss fiber, in the -40Â°C – 200Â°C range. Results indicate that a linear fit

with coefficient -6.38E-1 Â°C /GHz results in a maximum deviation of 10.63Â°C within this

temperature range, while a quartic fit with coefficients of -7.80E-1Â°C /GHz, -7.96E-4 Â°C /GHz2

,

-1.57E-6Â°C /GHz3

, and -1.57E-9Â°C /GHz4

, (calculated for a tare at 0Â°C) results in a much reduced

maximum deviation of 0.28Â°C within this temperature range. A piece-wise linear fit of the data also

results in reduced deviation. Humidity effects are a significant factor in temperature measurements

and should be controlled for best measurement accuracy.

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.)

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EN-FY1403 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 change 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 dn /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

IK

IST and KB are the temperature

and strain calibration constants, respectively. Common values for most germanosilicate core fibers

are KT = 6.45 x 10-6 Â°C-1 and KB = 0.780. The values for KT and KB 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 KT and KB 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 KT 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.

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EN-FY1403 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 Technical

Note, the temperature coefficient for polyimide coated low bend loss (LBL) fiber is calibrated, in the

-40Â°C – 200Â°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 by looking at the temperature uniformity

along all fiber sensor segments (Figure 5).

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 /3B, wire wound. The manufacturer specifies accuracy for these RTDs

from -100Â°C to 350Â°C. The RTD tolerances were measured using an in-house metrology well from

50Â°C to 200Â°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 stripped LBL spliced to polyimide coated LBL fiber. The six stripped LBL passes were

used for comparison with the following seven polyimide coated LBL fibers.

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EN-FY1403

Figure 2: Fiber layout within Aluminum enclosure

Silicone pads were used to hold the fiber ingress and turnarounds. The fiber was instrumented

loosely drooping between the silicone 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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EN-FY1403

Temperature Profile

The temperature chamber was programmed to ramp over the temperature range of -40Â°C – 200Â°C

at a rate of 20Â°C per hour (Figure 3), with a 5 hour plateau at the limits of this range. Frequency

shift and temperature measurements were continuously recorded. This setup was put through 2

full cycles. Measurements on both the RTDs and the ODiSI B were taken at 1 minute intervals.

Figure 3: Temperature profile of the test

Results

RTD Calibration

The RTDs used in this test were measured against a metrology well (Fluke, model 9144) before the

0.1*(0.3+0.005*Temperature) Â°

without any further calibration (Figure: 4).

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EN-FY1403

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.

Figure 5: Frequency shift along the sensor length at 200Â°C

The resulting temperature response curve for polyimide coated LBL is shown in Figure 6. The plots

on the top row are the measured response along with a linear fit (left) and a quartic fit (right). A

quartic fit was selected as an alternative to the linear fit as it resulted in much smaller deviations.

The plots on the middle and bottom row are the residuals of the linear fit (left) and quartic fit

(right) against frequency shift and time respectively. RTD Verification

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EN-FY1403

Figure 6: Polyimide coated LBL temperature response. Dash lines are at 0Â°C and 100Â°C. Top: Temperature as a function of

frequency shift, with a linear fit (left) and quartic fit (right) applied. Middle: Temperature difference between measured and

fit results, as a function of frequency shift, with a linear fit (left) and quartic fit (right) applied. Bottom: Temperature

difference between measured and fit results, as a function of time, with a linear fit (left) and quartic fit (right) applied.

Up ramp

0 1 R0 1 R

0 0 R0 0 R

A

B

C D

E F

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EN-FY1403 It is clear from Figure 6C that the sensor behavior is different on the up ramp (green) compared to

the down ramp (blue), with the down ramp showing a smoother and more repeatable responseIt is

postulated that this is due to humidity effects on the polyimide coating as it is known that polyimide

may absorb moisture from air and swell in response, causing a humidity-dependent strain on the

optical fiber. We believe that on the down ramp, moisture has been baked out of the environment

and therefore the polyimide coated LBL exhibits a repeatable behavior. The sensor is then held at –

40Â°C. The time spent at low temperatures then allows polyimide to start absorbing moisture,

causing it to exhibit drastic nonlinearities on the up ramp. At temperatures above 100Â°C, the

moisture is once again baked out of the polyimide. The effect of nonlinearities of the polyimide

coating can be seen when comparing results with measurements obtained from the stripped fiber

segments. For the stripped fiber, the temperature response is smooth and uniform throughout the

test (Figure 7).

Considering this, fits were carried out using only the measurements from the down ramps, while

deviations were plotted for the entirety of the test. These results are summarized in Table 1. For the

down ramp of temperature tests carried out in the -40Â°C – 200Â°C range with polyimide coated LBL

fiber, a linear fit results in a maximum deviation of 10.63Â°C at a test temperature of

-34.99Â°C, while a quartic fit results in a much reduced maximum deviation of 0.28Â°C at a test

temperature of -180.52Â°C. For the up ramp, a linear fit will result in a maximum deviation of

15.23Â°C at a test temperature of -40.40Â°C, while a quartic fit will result in a reduced maximum

deviation of 11.85Â°C at a test temperature of 9.05 Â°C.

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EN-FY1403

Figure 7: Stripped LBL temperature response. Dash lines are at 0Â°C and 100Â°C. Top: Temperature as a function of frequency

shift, with a linear fit (left) and quartic fit (right) applied. Middle: Temperature difference between measured and fit results,

as a function of frequency shift, with a linear fit (left) and quartic fit (right) applied. Bottom: Temperature difference between

measured and fit results, as a function of time, with a linear fit (left) and quartic fit (right) applied.

Up ramp

0 1 R0 1 R

0 0 R0 0 R

A

B

C D

E F

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EN-FY1403

Polynomial Fit Order Linear Quartic tared at 0Â°C Quartic tared at 25Â°C

Linear Coefficient (Â°C /GHz) -6.38E-1 A4 = -7.80E-1 B4 = -7.32E-1

2nd

order Coefficient (Â°C /GHz2

) 0 A3 = -7.96E-4 B3 = -6.50E-4

3rd

order Coefficient (Â°C /GHz3

) 0 A2 = -1.57E-6 B2 = -1.37E-6

4th

order Coefficient (Â°C /GHz4

) 0 A1 = -1.57E-9 B1 = -1.57E-9

Tare Temperature (Â°C) Any A5 = 0 B5 = 25

Largest Residual (Â°C) -10.63 (-15.23) -0.282 (-11.85) -0.282 (-11.85)

Table 1: Coefficients and residuals for polyimide coated LBL fiber. Largest residuals in parentheses are for the up ramp.

For comparison purposes, Table 2 summarizes fit results for stripped LBL fiber. Due to the uniform

behavior of stripped LBL, fits were carried out for the whole data set (up and down ramps

combined). A linear fit results in a maximum deviation of 6.73Â°C, while a quartic fit results in a

reduced maximum deviation of 0.78Â°C.

Polynomial Fit Order Linear Quartic tared at 0Â°C Quartic tared at 25Â°C

Linear Coefficient (Â°C /GHz) -7.24E-1 A4 = -8.63E-1 B4 = -8.08E-1

2nd

order Coefficient (Â°C /GHz2

) 0 A3 = -1.03E-3 B3 = -8.36E-4

3rd

order Coefficient (Â°C /GHz3

) 0 A2 = -2.34E-6 B2 = -2.02E-6

4th

order Coefficient (Â°C /GHz4

) 0 A1 = -2.67E-9 B1 = -2.67E-9

Tare Temperature (Â°C) Any A5 = 0 B5 = 25

Largest Residual (Â°C) 6.73 (-7.52) -0.779 (0.660) -0.779 (0.660)

Table 2: Coefficients and residuals for stripped LBL fiber. Largest residuals in parentheses are for the up ramp.

For measurements taken with a tare at a temperature other than 0Â°C, the following equation

describes the quartic form of the temperature response curve:

where:

when

and where can be found by solving the standard Quartic Equation:

This is expanded upon in the Appendix. Additionally, the Appendix contains example coefficients

calculated for a range of tare temperatures.

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EN-FY1403 Piece-Wise Linear Fit

The measurement was also fit with a piece-wise linear fit covering three temperature ranges: -40Â°C

– 25Â°C, 25Â°C – 100Â°C, and 100Â°C – 200Â°C. This resulted in reduced deviation for each temperature

range (Figure 8). Fit coefficients and deviations are given in Table 3. Users carrying out tests within

a smaller range will be able to obtain results with smaller deviations using only a linear fit

coefficient.

Temperature Range (Â°C) -40 to 25 25 to 100 100 to 200

Linear Coefficient (Â°C /GHz) -7.91E-1 -6.73E-1 -5.83E-1

Largest Residual (Â°C) -0.868 (-12.38) -1.017 (-6.23) -1.375 (-1.75)

Table 3: Coefficients and residuals for polyimide coated LBL fiber. Largest residuals in parentheses are for the up ramp.

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EN-FY1403

Figure 8: Polyimide coated LBL temperature response, with segmented linear fits applied. Dash lines are at 0Â°C and 100Â°C.

Top: Temperature as a function of frequency shift. Middle: Temperature difference between measured and fit results, as a

function of frequency shift. Bottom: Temperature difference between measured and fit results, as a function of time.

Up ramp

0 1 R0 1 R

0 0 R0 0 RA

B

C

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EN-FY1403 Exercise Cycle

In a previous test carried out within the 10Â°C – 80Â°C range, it was observed that the polyimide

fiber (Figure 9) 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.

Figure 9: Temperature difference between RTD and fiber.

Coefficient Verification

In order to verify the accuracy of these coefficients, a slow ramp test was carried out with the same

test setup. In this test, the temperature chamber was ramped four times slower from -40Â°C – 200Â°C

and back down, at a rate of 5Â°C per hour. As expected, the quartic fit results in smaller residuals.

The reduction in ramp rate however, results in more obvious humidity effects even on the down

ramp, due to the increased length of time that the sensor spends at low temperatures (< 100Â°C).

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EN-FY1403

Figure 10: Top: Polyimide coated LBL temperature response slow ramp. Dash lines are at 0Â°C and 100Â°C. Top: Temperature

as a function of frequency shift, with a linear fit (left) and quartic fit (right) applied. Middle: Temperature difference between

measured and fit results, as a function of frequency shift, with a linear fit (left) and quartic fit (right) applied. Bottom:

Temperature difference between measured and fit results, as a function of time, with a linear fit (left) and quartic fit (right)

applied.

Up ramp

0 1 R0 1 R

0 0 R0 0 R

A

B

C D

E F

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EN-FY1403

Summary

These tests result in the accurate calculation of temperature coefficients for polyimide coated LBL

within the temperature range -40Â°C – 200Â°C. For a linear fit, a coefficient of -6.38E-1 Â°C /GHz is valid

at any tare temperature, and for a quartic fit tared at 0Â°C, the first through fourth order coefficients

are -7.80E-1Â°C /GHz, -7.96E-4 Â°C /GHz2

, -1.57E-6Â°C /GHz3

, and -1.57E-9Â°C /GHz4

respectively.

As was demonstrated, the presence of humidity has a substantial effect on the error from the fit.

Therefore, the user will obtain best accuracy if temperature testing is conducted in an environment

with very well-controlled humidity, or if the sensor is mounted in a hermetically sealed tube.

may vary from these observations

depending on the degree of humidity change.

Please contact Luna for further technical assistance related to the content discussed in this

Technical Note.

References

sJournal of Lightwave Technology, Vol. 15, No. 8. 1997

t-Optic Strain and Temperature

3 OBR 4600 User Guide

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EN-FY1403 Appendix

can be found by solving the standard Quartic Equation:

as demonstrated below:

such that is real

such that is positive

such that is negative

Coefficients for Quartic Fits of Polyimide Coated LBL Fiber

Linear (Â°C /GHz) 2nd

order coeff.

(Â°C /GHz2

) 3rd

order coeff.

(Â°C /GHz3

) 4th

order coeff.

(Â°C /GHz4

) Tare Temp. (Â°C)

-5.50E-001 -2.45E-004 4.05E-007 -1.57E-009 200

-5.70E-001 -2.09E-004 1.25E-007 -1.57E-009 175

-5.88E-001 -2.11E-004 -1.47E-007 -1.57E-009 150

-6.07E-001 -2.46E-004 -4.11E-007 -1.57E-009 125

-6.29E-001 -3.11E-004 -6.65E-007 -1.57E-009 100

-6.57E-001 -4.03E-004 -9.10E-007 -1.57E-009 75

-6.91E-001 -5.17E-004 -1.14E-006 -1.57E-009 50

-7.32E-001 -6.50E-004 -1.37E-006 -1.57E-009 25

-7.80E-001 -7.96E-004 -1.57E-006 -1.57E-009 0

-8.34E-001 -9.51E-004 -1.77E-006 -1.57E-009 -25

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EN-FY1403 Product Support Contact Information

Headquarters: 3157 State Street

Blacksburg, VA 24060

Main Phone: 1.540.961.5190

Toll-Free Support: 1.866.586.2682

Fax: 1.540.961.5191

Email: 0 1 R0 1 R

Website: 0 1 R

Specifications of products discussed in this document are subject to change

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Â© 2014 Luna Innovations Incorporated. All rights reserved.

Technical Note EN-FY1403