Document No: SEAFOM
Measuring Sensor Performance
Document – 02 (SEAFOM MSP-02)
DAS Parameter Definitions and Tests
Issue Date: August 2018
1
Table of Contents
1
Introduction .................................................................................................................................... 5
1.1
Objectives and scope of document.......................................................................................................... 5
1.2
Definition of DAS / DVS and its associated elements .............................................................................. 5
1.3
Definition of Terms / acronyms ............................................................................................................... 6
2
Operator Considered Key DAS Requirement Elements ............................................................. 7
3
Definitions ....................................................................................................................................... 8
3.1
Supporting Spatial Parameters ............................................................................................................... 8
3.1.1
Spatial Sample Location / Sample Location Number ...................................................................... 8
3.1.2
Spatial Sampling Interval ................................................................................................................. 8
3.1.3
Fiber Distance .................................................................................................................................. 8
3.1.4
Interrogation Range ........................................................................................................................ 8
3.1.5
Gauge Length and Spatial Resolution.............................................................................................. 8
3.1.6
Fiber Stretcher................................................................................................................................. 9
3.2
Supporting Signal Parameters ................................................................................................................. 9
3.2.1
Output Data Rate ............................................................................................................................ 9
3.2.2
Interrogation Rate ........................................................................................................................... 9
3.2.3
Amplitude Spectral Density ............................................................................................................. 9
3.2.4
Sample Rate .................................................................................................................................. 10
3.2.5
Sample Number............................................................................................................................. 10
3.2.6
Time Series .................................................................................................................................... 10
3.2.7
Response Bandwidth ..................................................................................................................... 10
3.2.8
Nyquist Frequency ........................................................................................................................ 11
3.3
4
Standardization of DAS performance parameter measurement units .................................................. 11
Procedures for Measurement of Performance Parameters ..................................................... 12
4.1
Dynamic Range Test .............................................................................................................................. 13
4.1.1
Stimulus (DR) ................................................................................................................................. 13
4.1.2
Data to Be Collected at each Test Location (DR) ........................................................................... 13
4.1.3
How Data Should be Processed (DR) ............................................................................................. 13
4.1.4
Data Reporting (DR) ...................................................................................................................... 13
4.2
Frequency Response Test ...................................................................................................................... 14
4.2.1
Stimulus (FR) ................................................................................................................................. 14
4.2.2
Data to Be Collected at each Test Point Location (FR) .................................................................. 14
4.2.3
How Data Should be Processed (FR) ............................................................................................. 14
4.2.4
Data Reporting (FR) ....................................................................................................................... 14
4.3
Fidelity Test ........................................................................................................................................... 15
4.3.1
Stimulus (Fidelity) .......................................................................................................................... 15
4.3.2
Data to Be Collected at each Test Location (Fidelity) .................................................................... 15
4.3.3
How Data Should be Processed (Fidelity) ..................................................................................... 15
4.3.4
Data Reporting (Fidelity) ............................................................................................................... 15
4.4
Self-Noise Test ....................................................................................................................................... 16
4.4.1
Stimulus (Self-Noise) ..................................................................................................................... 16
4.4.2
Data to Be Collected at each Test Location (Self-Noise) ............................................................... 16
4.4.3
How Data Should be Processed (Self-Noise) ................................................................................. 16
4.4.4
Data Reporting (Self-Noise) ........................................................................................................... 16
4.5
Spatial Resolution Test .......................................................................................................................... 17
4.5.1
Stimulus (SR) ................................................................................................................................. 17
4.5.2
Data to Be Collected at Each Test Location (SR) ........................................................................... 17
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4.5.3
4.5.4
How Data Should be Processed (SR) ............................................................................................. 17
Data Reporting (SR) ....................................................................................................................... 17
4.6
Crosstalk Test ........................................................................................................................................ 18
4.6.1
Stimulus (Crosstalk) ....................................................................................................................... 18
4.6.2
Data to Be Collected (Crosstalk) .................................................................................................... 18
4.6.3
How Data Should be Processed (Crosstalk)................................................................................... 18
4.6.4
Data Reporting (Crosstalk) ............................................................................................................ 18
4.7
Loss Budget Test .................................................................................................................................... 19
4.7.1
Stimulus (Loss Budget) .................................................................................................................. 19
4.7.2
Data to Be Collected (Loss Budget) ............................................................................................... 19
4.7.3
How Data Should be Processed (Loss Budget) .............................................................................. 19
4.7.4
Data Reporting (Loss Budget) ........................................................................................................ 19
4.8
Sensor Reflection Effects (OPTIONAL TEST) ........................................................................................... 20
4.8.1
Stimulus (Reflection Effects) ......................................................................................................... 20
4.8.2
Partial Reflectors ........................................................................................................................... 20
4.8.3
Data to be Collected for all test configurations (Reflection Effects) ............................................. 21
4.8.4
How Data Should be Processed (Reflection Effects) ..................................................................... 21
4.8.5
Data Reporting (Reflection Effects) ............................................................................................... 21
5
Recommended Test Apparatus .................................................................................................. 22
5.1
Simulated Fiber Sensor to be used for characterization ...................................................................... 22
5.1.1
Recommended standard lengths for Simulated Fiber Sensor ....................................................... 23
5.2
Fiber Stretcher to be used for characterizations ................................................................................... 23
5.3
Signal Generation / Amplification Instrumentation .............................................................................. 24
5.3.1
Recommended Signal Generators and Amplifiers ........................................................................ 24
5.4
Optical Attenuator ................................................................................................................................ 24
5.4.1
Attenuator Requirements ............................................................................................................. 25
5.4.2
Commercial Suppliers.................................................................................................................... 25
5.5
Isolation Chambers / Vibe Isolators ...................................................................................................... 25
5.5.1
Simple Isolation Approach ............................................................................................................ 25
5.5.2
More Exotic Isolation Approach .................................................................................................... 25
6
Reference Appendix (not including test procedures) .............................................................. 26
6.1
Conversion of Optical Phase Measurement to Strain ............................................................................ 26
Table 1 Optical Phase and Strain Relationships ................................................................................................ 28
6.2
Good Quality Data................................................................................................................................. 28
6.2.1 Single Tone stimulus testing for Good Quality Data; Tests 4.1, 4.3, 4.5, 4.6 ................................................... 28
6.2.2
Frequency Response Testing for Good Quality Data..................................................................... 30
6.3
Conformance to Common Parameter Definitions ................................................................................. 31
Table 2 SEAFOM / Energistics Parameter Definition Comparisons .................................................................. 31
6.4
7
What to do if you test tone lines up with a “line” frequency or harmonic ............................................ 31
Appendix (Test Procedures) ....................................................................................................... 32
7.1
Measurement of DAS Dynamic Range .................................................................................................. 32
7.2
Measurement of Frequency Response Test ........................................................................................... 34
7.2.1
Test Approach ............................................................................................................................... 34
7.2.2
Stimulus Waveform Generation.................................................................................................... 35
7.2.3
Processing the Data collected ....................................................................................................... 35
7.2.4
Data Reporting .............................................................................................................................. 37
7.3
Fidelity Test ........................................................................................................................................... 38
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Measurement of DAS SELF-NOISE ......................................................................................................... 38
7.4
7.4.1
Background ................................................................................................................................... 38
7.4.2
Acquire and process the Noise Data ............................................................................................. 39
7.4.3
Process approach for ping domain data. ...................................................................................... 41
7.4.4
Details of the FFT Process that calculates DAS Self-noise ............................................................. 42
8
7.5
Measurement of Spatial Resolution ...................................................................................................... 44
7.6
Measurement of Crosstalk .................................................................................................................... 47
7.7
Measurement of Loss Budget ................................................................................................................ 48
7.8
Sensor Reflection Effects ....................................................................................................................... 48
Appendix FFT Window Functions .............................................................................................. 49
8.1
Flat Top Window used for frequency domain measurements of spectral peaks................................... 49
8.2
Blackman – Harris Window used for frequency domain noise measurements ..................................... 50
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1
Introduction
This document was written by and on the initiative of the SEAFOM Measurement Specifications
Working Group. It is targeted specifically for “Distributed Acoustic Sensing” (DAS).
It is intended to be used as a guide to enable the characterization of performance of DAS interrogator
Units (IU) as defined by the measurement parameters and via the use of a recommended set of
measurement practices contained: including definitions of key parameters, test setups, procedures,
and calculation methods. It is not intended to define any specific acceptance criteria for any given
application, neither to limit the ability for any user to use any brand of DAS with any desired fiber and
cable that is compatible with such system. The recommended equipment that is required to support
these setups and procedures does not require any particular class of performance; however, their
performance parameters will limit the quality of the determination of the various fiber measurement
parameters.
Further, it is intended to have an agreed definition set for the following:1.
2.
3.
1.1
Specification elements and parameters of interest
Vocabulary or metrics used when expressing performance parameters
Measurements to be made to assist operators in determination of suitability for
their requirements
Objectives and scope of document
The objectives of this document are to:1.
2.
3.
Establish key requirement elements in consideration of operator needs
Define these elements with standardized metrics
Provide a recommended set of test approaches to evaluate the specification
elements which are designed to be performed by non-SME resources
Whilst this document does provide a harmonized set of DAS performance testing procedures which
are valid for any brand or model of a DAS system, it does not pose any requirements on the actual
DAS system performance.
1.2
Definition of DAS / DVS and its associated elements
The definition of DAS / DVS and its associated elements is a system including an interrogator and
optical fiber sensor that measures dynamic strain signals at acoustic frequencies at any point along
the fiber, as well as the means to process and archive the interrogation information. Common
abbreviations used include:•
•
DAS = Distributed Acoustic Sensing
DVS = Distributed Vibration Sensing
A typical DAS/DVS system is simply represented in the schematic, see Figure 1 below, and is
comprised of three key elements:1.
2.
DAS Interrogator Unit (IU) – The opto-electronic instrument that is connected to
the sensing fiber and measures and records the dynamic strain along the fiber
Distributed Sensor – The fiber optic assembly, cabled or packaged appropriately
for the sensing application. This may or may not be provided by the same entity
that provides the DAS Interrogator / Processor. Its length is generally considered
to be the linear value if the sensor is stretched-out
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3.
Processor / Data Archive / User Interface – Portrayed as a separate system
element within Figure 1, but could be combined within the DAS IU. It provides
processing functions (standardized or customized), data archiving (usually
standardized), and also provides an interface to control and “set” the Interrogator,
select processing options, and define and implement the data collection options
(triggered, timed, or other).
DAS
sensor length
Interogation
Unit
processor
data archive
user interface
Distributed Sensor
service operator / user
Figure 1. DAS System Elements
1.3
Definition of Terms / acronyms
ASD ............... Amplitude Spectral Data (also known as signal magnitude spectral data)
DAS ............... Distributed Acoustic Sensor
DVS ............... Distributed Vibration Sensor
DR ................. Dynamic Range
FBG ............... Fiber Bragg Grating
FFT ................ Fast Fourier Transform – time domain to frequency domain conversion
FR.................. Frequency Response
IU ................... Interrogator Unit
Length .......... Measured in meters of fiber length (not optical path)
rt-Hz .............. root Hertz = square root (Hz) noise density term
SFS ............... Simulated Fiber Sensor
SME............... Subject Matter Expert
SNR ............... Signal to Noise
SSL ............... Spatial Sample Location
Strain ............ Sensed parameter. Fiber strain (not optical path change)
TFL ................ Total Fiber Length, is equal to the Interrogation Range
THDFT ............ Total Harmonic Distortion for Fidelity Test
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2
Operator Considered Key DAS Requirement Elements
Operational parameters which are typically considered to support an operator’s evaluation of a DAS
system, against technical performance requirements are categorized below:A.
Dynamic Range – Stimulate a “standard” sensor to the point where the maximum
level of stimulation can be attained such that the measured stimulus is not
corrupted when compared to the input stimulus. Considers various locations along
the sensor.
B.
Frequency Response – Stimulate a “standard” sensor over the full required or
specified frequency range. Measurements are made to determine the “transfer
function” magnitude. Considers various locations along the sensor.
C.
Fidelity - Stimulate a standard “sensor” using signal types that are conducive to
determination of distortion or linearity. Considers various locations along the
sensor.
D.
Noise – Place the standard “sensor” in a quiet environment and measure the DAS
system’s self-noise. Considers noise measurements in various ways, such as
broad band “spot” noise and noise densities in pre-determined frequency bands.
Considers various locations along the sensor.
E.
Spatial Resolution - Stimulate a “standard” sensor in a way to realize a measured
response that can be processed to accurately realize the spatial resolution of the
interrogation process. Considers various locations along the sensor.
F.
Cross-Talk – Stimulate a “standard” sensor in a way to realize a measured
response that can be processed to accurately determine the level of residual
signals that appear in locations other than the location of the original stimulus.
Considers various stimulus locations along the sensor.
G.
Loss Budget – Insertion of calibrated point losses to the standard sensor so that
evaluations may be made of other performance parameters which are deemed loss
sensitive. Considers various locations along the sensor.
H.
Reflection Sensitivity – Dead zones are caused by unplanned partial reflections
in the installed sensor fiber where the reflections may temporarily disable the
interrogation process (signal saturation). Insertion of in-line partial reflectors in the
standard sensor which simulate “sensor imperfections” and DAS system response.
Test considerations include both sensor end terminus and in-line reflection
locations.
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3
Definitions
This section provides for definition of terms, units and supporting parameters associated with the
recommended procedures defined in the later sections.
3.1
Supporting Spatial Parameters
A list of supporting spatial parameters is presented. These combined with the definitions provided in
this section sets the nomenclature to be used when defining the measurement processes to assess
DAS performance parameters.
A graphical representation of supporting parameters is provided in Figure 2 to assist the definitions
with further clarifications in Figure 3.
sensor simulator
DAS
Interogation
Unit
0 1 2 3 4 5 6 7
Spatial
Sample
Locations
Sample
Location
Number
Spatial
Sampling
Interval
spatial
resolution
Figure 2. DAS Interrogator Test Arrangement
3.1.1
Spatial Sample Location / Sample Location Number
The DAS IU samples the backscattered light from the sensor at different locations along the sensor
simulator. These locations are defined through the interrogator configuration or setup, and
represented spatially along the fiber as uniformly spaced dots . A numbering system is defined
such that the first Spatial Sampling Location starts at “0”. Successive locations are numbered as
positive integers which increase along the length of the sensor. The term Spatial Sample Location is
also known as SSL.
3.1.2
Spatial Sampling Interval
The physical separation in meters (real number) between consecutive Sample Locations defines the
Spatial Sampling Interval. It should not be confused with ‘Spatial Resolution’.
3.1.3
Fiber Distance
The distance in meters (real number) of fiber length from the connector of the IU to the desired
Sample Location.
3.1.4
Interrogation Range
The Total Fiber Length (TFL) in meters (real number, fiber length, not optical length) from the
connector of the DAS IU to the final end of the Sensor Simulator Fiber. This end is either a
purposefully cut or terminated end of the fiber. See Figure 3.
3.1.5
Gauge Length and Spatial Resolution
The gauge length is a distance (length along the fiber in meters) which the IU manufacturer designs /
implements by hardware / software to affect the IU spatial resolution. It is not necessarily equal to the
spatial resolution, which is a measured performance parameter. It should, for a properly operating IU
be a close approximation. See Figure 3.
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3.1.6
Fiber Stretcher
The basic definition of Fiber Stretcher for the purpose of use in Fiber Sensor Simulator is: 1)
Construction is fiber wound on a piezoelectric cylinder, where electrical stimulus of the piezoelectric
cylinder will cause a linearly proportionally amount of fiber strain uniformly across the fiber length
attached. 2) The length of fiber wound on the fiber stretcher (not including leads) is recommended to
be greater than twice the gauge length of the interrogator being evaluated. Fiber stretcher usage is
depicted in Figure 15.
3.2
Supporting Signal Parameters
DAS Interrogation generally involves continuous sampling of the perturbations of the fiber optic sensor
at each of the Spatial Sample Locations simultaneously. Thus, each Spatial Sample Location would
yield a signal record which can be processed according to the intended application information
desired.
The intent for this sub-section is to define the supporting signal parameters associated with this
sampling to set the nomenclature to be used when defining the measurement processes to assess
DAS performance parameters.
Figure 3 depicts these Supporting Signal Parameters showing how they make up the Time Series data
and how they relate to spatial locations on the sensor fiber. Definitions of these Signal Parameters
follow.
3.2.1
Output Data Rate
The rate at which the IU provides output data for all Spatial Sample Locations. This is usually the
sample rate of the DAQ, and represents the time duration between spatial samples. See Figure 3.
3.2.2
Interrogation Rate
The Interrogation Rate (times per second) is the rate at which the IU interrogates the fiber sensor or
simulator. It is equivalent to the Pulse Rate for interrogators that provide optical pulse interrogation. It
is equal to the inverse of the sample interval. See Figure 3.
3.2.3
Amplitude Spectral Density
Time Series Data is converted to frequency domain data for some of the Performance Parameter
Measurement procedures. These will produce data in units of Amplitude Spectral Density. This is the
square root of Power Spectral Density. This is also known as the signal magnitude spectral data.
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TIME SERIES
Measurement
Start Time
DAS
Interrogation
Unit
Spatial
Sample
Spatial
Resolution
sensor
Fiber
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
sample
number
Sample
Interval
0 1 2 3 4 5 6 7 8
spatial
sample
interval
M
samples
Time Series 2
Time Series 3
Time Series 4
spatial
sample
location
Fiber
distance
N-1
N
TFL Total Fiber Length
= Interrogation Range
Interrogation rate = 1/(Sample Interval)
Figure 3. Signal Parameters relating to Time Series and their Spatial Location Identification
3.2.4
Sample Rate
The sample rate is the rate at which the raw acoustic data is output from the interrogation unit. NOTE:
The maximum sample rate is equal to the interrogation rate. Sample rate applies when the
interrogation rate is reduced (by decimation or other) prior to being output by the IU.
3.2.5
Sample Number
The sequence number of a Sample in a Time Series (see Figure 3) is called the Sample Number..
3.2.6
Time Series
A data set for a particular sample location, which is usually represented as sampled at the
Interrogation Rate, but can also be represented at a sub-sample rate of the interrogation rate. NOTE:
Whatever rate is used, it must be used for all tests in section 4.
3.2.7
Response Bandwidth
The minimum to maximum detectable frequency (3db decay point on frequency response curve).
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3.2.8
Nyquist Frequency
For the purposes of this document Nyquist Frequency is the frequency represented by the time
duration or period of half of the Interrogation or sample rate, whichever is smaller. Example: If the
Interrogation rate is 20,000 samples per second, the Nyquist frequency will be 10KHz.
Conformance to common parameter definitions:
SEAFOM parameter definitions described in Section 3.1 and 3.2 of this document have been
developed with an effort to be common to other standards being developed for DAS. Section 6.3
outlines commonality between SEAFOM MSP-02 and Energistics PRODML v2.0 DAS parameter
definitions.
3.3
Standardization of DAS performance parameter measurement units
In consideration of standardization of the DAS performance parameters, the measurements made that
characterize performance parameters should be represented (or converted to) strain units.
Normalization Considerations: Certain strain measurements are to be modified to accommodate
normalization as needed. For example:
Measurements which are influenced by system noise may be modified by normalizing to a particular
noise bandwidth. Metrics here are “strain per square root Hz” or strain/rt-Hz.
Measurements using stimulus which are influenced by the gauge length are made with the stimulus
being normalized by the gauge length. This includes all required tests except for self-noise and loss
budget.
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4
Procedures for Measurement of Performance Parameters
The performance parameters considered meaningful for characterizing DAS Interrogator performance
are identified below:1.
2.
3.
4.
5.
6.
7.
8.
Dynamic Range
Frequency Response
Fidelity
Self-Noise
Spatial Resolution
Cross-Talk
Loss Budget
Sensor Reflection Effects (optional test)
This section provides for outline procedures for measurement of performance parameters. Details for
some of these processes are provided in section 7 Appendix (Test Procedures).
Baseline Considerations for Test Procedures
The SEAFOM DAS working group endeavoured to develop the test procedures and recommendations
for the anticipated apparatus to perform the testing and data processing to be “within reach” of
practicing organizations resident skill sets and metrology budgets.
Additionally, attempts have been made such that procedures defined are not overly complex in scope
but without compromising the efficacy of the reportable results.
The key objectives followed were:A.
B.
DAS SME not required: One should not need to be a DAS subject matter expert
to be qualified to run the tests and prepare the test results
Single Test Bed for All Procedures: All Procedures have been developed such
that a single test bed is implemented. This is defined as a Simulated Fiber Sensor
(SFS) and is detailed in section 5.1
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4.1
Dynamic Range Test
Stimulate the Simulated Fiber Sensor (SFS, sec 5.1) to the point where the maximum level of
stimulation such that the result signal is not corrupted when compared to the input stimulus. Stimulus
at three different locations TP1, TP2, and TP3 along the sensor as shown in Figure 4.
250
m
IU
TP Stretcher
1
Delay
1
TP Stretcher
2
Delay
2
250
m
TP Stretcher
3
Figure 4. Test Locations for Dynamic Range Test
4.1.1
Stimulus (DR)
Signal Type:
Sinusoidal
Frequencies:
1%, 5%, and 20% and 80% Nyquist
Signal Level (peak):
(0.17 µε to 14 µε) / (gauge length)
Thus if gauge length is 10m, then Signal level range is 0.02µε to 1.4 µε
Stimulus signal should start at lower level than max expected limit and increase level linearly in time to
past max expected limit. See section 7.1 for details.
NOTE: This recommended test is defined at frequencies that are determined to be achievable using
traditional test apparatus (SFS) with somewhat efficient fiber stretchers. It does not prevent vendors /
suppliers to produce data at lower frequencies than what are recommended.
1.
2.
Which can be accomplished using fiber stretchers (higher frequencies)
Which can be accomplished using more substantial means to provide for larger
strain stimuli (lower frequencies)
Stimulation should be applied independently at each test position location.
4.1.2
Data to Be Collected at each Test Location (DR)
Samples per Location:
As needed to cover stimulus range
Time Duration each location:
As needed
Refer to section 6.2.1 to insure good quality data is collected
4.1.3
How Data Should be Processed (DR)
Signal:
Examination of time domain response to determine Dynamic Range
Limit:
Consider this limit to be when signal becomes distorted or experiences its first
discontinuity. Test can be rerun 5 times to obtain the “best” result. This limit is
determined to be the dynamic range.
Details: See Section 7.1, Appendix Dynamic Range
4.1.4
Data Reporting (DR)
Report maximum peak strain attained multiplied by the gauge length. This to be the strain-gauge
length limit. This is for frequencies at 3 positions (12 values). Table format is recommended.
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4.2
Frequency Response Test
Measurement of the frequency response will be made by stimulating the SFS (Sec 5.1) over the IU
functional frequency range as shown in Figure 5. Recommended measurements include the
magnitude of the frequency response at the three locations TP1, TP2, and TP3.
250
m
IU
TP Stretcher
1
Delay
1
TP Stretcher
2
Delay
2
250
m
TP Stretcher
3
Figure 5. Test Locations for Frequency Response Test
4.2.1
Stimulus (FR)
Signal Type:
Frequencies:
Signal Level:
Sequential Tone Sinusoidal Sweep (40 frequency steps). See section 7.2
2% to 80% Nyquist, 40 steps, 2.5 sec each. 100 sec sweep
0.08 µε (peak) / (gauge length in meters) or if needed, at lower levels to produce
monotonic IU Response over the frequency range. This is determined by the test
manager
The stimulus may be applied to all three locations simultaneously, or independently. This will be the
test operator’s choice.
4.2.2
Data to Be Collected at each Test Point Location (FR)
NOTE: Data collected for processing should meet the criteria of Good Quality Data (See 6.2.2).
Repeat tests as necessary to insure this.
Time Duration of Sweep:
Samples Recorded:
4.2.3
100 sec
Sufficient to cover the full 100 sec sweep
How Data Should be Processed (FR)
See Section 7.2.3. Time records are first converted to the frequency domain via FFT with no window
into “magnitude” ASD data. Then the data is further processed to represent the interrogator
(magnitude transfer function) response and used to determine a frequency response plot.
4.2.4
Data Reporting (FR)
Plot 1: Interrogator Response to Stimulus. Three plots from locations TP2, TP3, TP4, Details
described in 7.2.4. Units are dB re strain level vs frequency
Plot 2: Corrected and Normalized Frequency response. Three plots from locations TP2, TP3, TP4,
Details described in 7.2.4. Units are dB (response) vs Frequency
NOTE: This test does not accommodate very low frequencies (below 2% Nyquist). For those
practitioners that wish to also measure lower frequencies, it is recommended that a similar test be
performed, over the desired frequency range, and additionally report that information. Also note,
these tests can be at a higher stimulus amplitude, i.e. if frequency range is restricted to 10% of the
stimulus frequency range of 4.2.1, one can increase stimulus amplitude by 10X.
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4.3
Fidelity Test
Stimulate the SFS (sec 5.1) with sinusoidal tones of varying level. Recommended measurements are
to be taken at the three locations TP1, TP2, and TP3 as shown in Figure 6.
250
m
IU
Delay
1
TP Stretcher
1
TP Stretcher
2
Delay
2
TP Stretcher
3
250
m
Figure 6. Test Locations for Fidelity Test
4.3.1
Stimulus (Fidelity)
Signal Type:
Frequency:
Sinusoidal
10% Nyquist
Note: if frequency coincides with “line interference” it is okay to move by +/- 20%
Signal Levels (peak):
Example:
(0.08 µε, 0.25 µε and 0.8 µε) / (gauge length)
if gauge length is 5m, then levels are 0.016 µε, 0.05 µε and 0.16 µε
The stimulus may be applied to all three locations simultaneously, or independently. This will be the
test operator’s choice.
4.3.2
Data to Be Collected at each Test Location (Fidelity)
Collect time series data at each of the stimulus locations
Samples to record at each selected SSL: one minute duration
4.3.3
How Data Should be Processed (Fidelity)
1.
2.
3.
Parse the one minute time series data records to smaller length time series of
16384 samples long. The objective is to yield 10 sets at each test point location
Transform the Time Series records via FFT magnitude with Flat Top window,
discarding any data which doesn’t meet the criteria of “Good Quality Data” (sec
6.2.1)
Of the remaining data, calculate the total harmonic distortion in percent (equation 1
below) using harmonics 2-5 averaging 10 sets. Vx = signal level (not power level)
where x is the harmonic
THDFT =
(EQ 1)
FT subscript means Fidelity Test
4.3.4
Data Reporting (Fidelity)
Report Total Harmonic Distortion in percent at each of the three levels at each of the three locations.
This becomes 9 data values to report (units are percent). Table format is recommended.
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4.4
Self-Noise Test
The purpose of this test is to evaluate the self-noise DAS Interrogator. Measurements made here are
the Amplitude Spectral Density (ASD, which is the square root of Power Spectral Density) of the noise
response of the IU. The Simulated Fiber Sensor (SFS) should be isolated from room acoustics and
vibration. Tests are to be taken at three different locations along the sensor as shown in Figure 7 and
shown as sections 1, 2, 3 within the two delay coils.
250
m
IU
TP FS
1
sec 1 Delay 1
TP FS
2
sec 2 Delay 2 sec 3
TP FS
3
250
m
Figure 7. Test Locations for Self-Noise
4.4.1
Stimulus (Self-Noise)
None. The fiber sensor simulator should be isolated from acoustics and vibration.
4.4.2
Data to Be Collected at each Test Location (Self-Noise)
Collect data as required per section 7.4.2 step 3 Self Noise (30 seconds). All data may be collected
simultaneously or independently at the section locations. This is the test operator’s choice.
4.4.3
How Data should be Processed (Self-Noise)
Analyze data from three different sections:Section 1: 300 consecutive SSLs in delay 1 (starting 250 SSLs in)
Section 2: 300 consecutive SSLs in delay 2 (starting 100 SSLs in)
Section 3: 300 consecutive SSLs in delay 2 (ending 100 SSLs before the end of delay 2)
Analysis to be performed per Section 7.4
4.4.4
1.
FFT each of the sections 300 time series resulting in “single sided” magnitude
measures, units of self-noise vs frequency
2.
Normalize each of the FFT records to a 1 Hz “noise” bandwidth and convert the
FFT magnitude values amplitude to RMS strain values
3.
Average all of the 300 noise traces in each of the three sections such that result is
one plot or trace for each of the three sections
4.
Convert the averaged magnitude data to dB units (20*Log10 [strain magnitude] ).
Data Reporting (Self-Noise)
Plots Frequency Domain. One plot per test section.
•
•
•
Noise in dB(strain/rt-Hz), units of dB
Frequency in log scale, covering full bandwidth of test (1 Hz – Nyquist)
The gauge length setting of the interrogator will be reported on the test result.
Details: See Section 7.4 Appendix – Self-Noise
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4.5
Spatial Resolution Test
Stimulation to SFS (sec 5.1) is continuous wave, sinusoidal at moderate amplitude, only one frequency
required. Recommended measurements are to be taken at the three locations TP1, TP2, and TP3 as
shown in Figure 8.
250
m
IU
Delay
1
TP Stretcher
1
TP Stretcher
2
Delay
2
TP Stretcher
3
250
m
Figure 8. Test Locations for Spatial Resolution Test
4.5.1
Stimulus (SR)
Signal Type:
Frequency:
Sinusoidal
2% Nyquist Note: if frequency coincides with line interference it is okay to move
by +/- 20%
Signal Level (peak): 0.5 µε / (gauge length)
4.5.2
Data to Be Collected at Each Test Location (SR)
Collect time series data at consecutive Spatial Sample Locations (SSL) that cover the length of fiber on the
fiber stretcher plus two gauge lengths on each side, as shown in Figure 9. The stimulus may be applied to
all three locations simultaneously, or independently. This will be the test operator’s choice.
Samples to record at each selected SSL:
one minute duration
NOTE: collection for both spatial range and crosstalk can be taken at the same time by increasing the
range out to +/-50 GL from stretcher (see sec 4.6).
Fiber Stretcher
“fiber sensor”
gauge length gauge length
-2
-1
“fiber sensor”
gauge length
+1
gauge length
+2
Figure 9. Locations to collect data for spatial resolution test (across fiber stretcher and
including 2 gauge lengths on each side
4.5.3
How Data Should be Processed (SR)
Objective: You want to make accurate measurements of the amplitude of the stimulus signal at each
Spatial Sample Location.
Amplitudes are measured via Flat Top windowed FFT of the time series and extracting the magnitude
value at the stimulus frequency.
Use only Good Quality Data as defined in section 6.2.1. Recommend that each FFT be smaller blocks
than the 1 minute record to increase the probability that data blocks at each SSL have high signal to
noise (fade free).
Details of this process are outlined in appendix section 7.5 “Measurement of Spatial Resolution”.
4.5.4
Data Reporting (SR)
Report: Calculated Spatial Resolution values (in meters) for the three different test locations.
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4.6
Crosstalk Test
Stimulation to SFS (sec 5.1) is a continuous wave, sinusoidal at moderate amplitude. Only one
frequency required. Stimulus is applied at three different locations as shown in Figure 10.
This test makes measurements of the residual signals that occur in locations other than the location of
the original stimulus to make “crosstalk” determinations.
250
m
IU
TP Stretcher
1
Delay
1
TP Stretcher
2
Delay
2
250
m
TP Stretcher
3
Figure 10. Test Locations for Crosstalk Test
4.6.1
Stimulus (Crosstalk)
Signal Type:
Frequency:
Sinusoidal
2% Nyquist
Note: if frequency coincides with “line interference” it is okay to move by
+/- 20%
0.5 µε, / (gauge length)
Signal Level (peak):
The stimulus may be applied to all three locations simultaneously, or independently. This will be the
test operator’s choice.
4.6.2
Data to Be Collected (Crosstalk)
Collect reference stimulus time series data at the location of the fiber stretcher, and time series data at
Spatial Sample Locations at +3 to +50 gauge lengths -3 to -50 gauge lengths or a minimum length of
+/-250 meters as shown in Figure 11.
Time series data to be collected for one minute.
“fiber sensor”
Fiber Stretcher
“fiber sensor”
out to -50 gauge lengths
gauge length gauge length
-4
-3
out to +50 gauge lengths
middle of
fiber stretcher
gauge length
+3
gauge length
+4
Figure 11. Locations to collect data for crosstalk test. +/-50 gauge lengths, don’t analyze
first two gauge lengths on either side of the fiber stretcher
4.6.3
How Data Should be Processed (Crosstalk)
Calculate reference amplitude and crosstalk data as instructed in 7.6. Crosstalk values represent data
elements in the range of +3 to +50, -3 to -50 gauge length. Determine crosstalk by calculating ratio of
crosstalk to reference (in dB).
Details of this process are outlined in section 7.6 “Measurement of Crosstalk”.
4.6.4
Data Reporting (Crosstalk)
Report: Single plot dB level of crosstalk versus SSL at each test point TP1, TP2, TP3. See example
in section 7.6 Measurement of Crosstalk.
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4.7
Loss Budget Test
The loss budget test is intended to evaluate the IU performance for non-ideal sensor installation
conditions. The dominant consideration is that optical loss is caused at the beginning of the sensor, in
the vicinity of the well head exit or other proximal interfaces between the IU and the deployed sensor.
4.7.1
Stimulus (Loss Budget)
The test protocol calls for placing an optical attenuator (as stimulus) between the IU and the input to
the sensor simulator as depicted below. Here we show an input optical attenuator and three
designated test points TP1, TP2, and TP3 in Figure 12, which represent the beginning, middle and
end of the DAS Sensor Simulator.
IU
Atten
250
m
TP FS
1
sec 1 Delay 1
TP FS
2
sec 2
Delay 2 sec 3
TP FS
3
250
m
Figure 12. Test Locations for Loss Budget Test
Test locations are designated as TP2, TP3, and TP4, which represent the beginning, middle and end
of the DAS Sensor Simulator.
Recommended Attenuator Stimulus: (one way attenuation values)
Test 0
Test 1:
Test 2:
Test 3:
0 dB reference data from self-noise test (sec 4.4)
-2 dB
-4 dB
-6 dB
4.7.2
Data to Be Collected (Loss Budget)
A self-noise test is required at the three test points identified for each of the attenuation levels.
4.7.3
How Data Should be Processed (Loss Budget)
Perform self-noise test as defined in section 4.4.
4.7.4
Data Reporting (Loss Budget)
Report: Determine the spot frequency noise level at the 50% Nyquist locations for test 0-3.
This would be a single value in dB strain, normalized to 1 Hz noise band, and citing the gauge length
used.
These values should be reported in two tables. The first table showing the noise levels for four tests
at the three locations. The second table showing the difference (in dB) of the reference test (no
attenuation) and the three tests at the different attenuation levels.
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4.8
Sensor Reflection Effects (OPTIONAL TEST)
Optical point reflections in deployed sensors can cause two unwanted effects:1.
A dead zone (distance) following the reflection location, where no useful
measurement can be made
A performance degradation along part of or the whole fiber length which causes
signal contamination
2.
This test recommends that three separate sensor reflection scenarios be considered. NOTE: This is
an optional test, partial testing is acceptable. The testing involves partial reflectors end, at the
front, or both ends and front of the SFS. The three test arrangements are shown in Figure 13. Here
the partial reflectors are mated to the start and end connectors of the SFS. The SFS is shown
depicting the three sections where self-noise data will be collected, and the three test positions where
Fidelity testing will be performed.
Test 1
IU
250
m
TP FS
1
sec
1
Delay 1
TP FS
2
sec
2
Delay 2 sec
3
TP FS
3
250
m
PR
250
m
TP FS
1
sec
1
Delay 1
TP FS
2
sec
2
Delay 2 sec
3
TP FS
3
250
m
PR
250
m
TP FS
1
sec
1
Delay 1
TP FS
2
sec
2
Delay 2 sec
3
TP FS
3
250
m
Test 2
IU
start
Test 3
IU
start
PR
end
PR
end
Figure 13. Test Configurations for Reflection and Dead Zone Evaluations
4.8.1
Stimulus (Reflection Effects)
A stimulus will also be used to conduct fidelity testing:Signal Type:
Frequencies:
Signal Level
4.8.2
Sinusoidal
10% Nyquist
0.25 µε and 0.8 µε) / (gauge length)
if gauge length is 5m, then levels are, 0.05 µε and 0.16 µε
Partial Reflectors
Partial reflectors need to be in-line fiber elements. They need to provide known partial reflections at
the wavelength(s) of operation of the IU. These can be custom Fiber Bragg Gratings FBG made for
the desired reflectivity or other fiber assemblies. Figure 14 shows examples of other easy to fabricate
partial reflectors.
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20
Tap coupler
PROXIMAL
PARTIAL REFLECTOR
MATED APC
SFS end
easy to fab for
0.1% to 1% reflection
DISTAL PARTIAL
REFLECTORS
cleaved
fiber
~ 3.75% reflection
90+%
Tap
to sensor
FRM
reflector
MATED APC TO PC
attenuation
loop
SFS end
~ 1% reflection
Figure 14. Recommended methods for creating partial reflections for SFS
Proximal reflections can be made by using a “tap” coupler where most of the light passes to the
sensor, and a small portion is directed to a “reflector”. Figure 14 shows a Faraday Reflector Mirror as
these types of mirrors come with pigtail fiber and are easy to implement. Any other pigtailed fiber
mirror should be acceptable.
Distal Reflections can be made by mating connectors as shown in Figure 18 to create the desired
reflection.
The lower left diagram in Figure 14 “MATED APC” shows two angle connectors mated to a pigtail fiber
which is cleaved at 90 degrees. This will provide for an approximate 3.8% reflection which would be
the equivalent of the worst case reflection a DAS sensor could provide.
The lower right diagram in Figure 14 “Mated APC to PC provides for approximately 1% reflection (light
which reflects from the PC connector surface (for 1550 nm light). The pigtail fiber would have a series
of tight loops (say 10 @ 0.5 inch diameter) to attenuate the throughput light to a negligible value.
Recommended Reflections for Testing
This standard does not mandate the start and distal reflection values, but does identify logical value
ranges.
Start Reflection: Consider 0.5% to 1%
End Reflection: up to 3.6%. This is the maximum light that can be reflected from a normal
termination at the end of a fiber
4.8.3
Data to be Collected for all test configurations (Reflection Effects)
A.
B.
4.8.4
How Data Should be Processed (Reflection Effects)
A.
B.
4.8.5
Using Stimulus for Fidelity Test: Per instructions in section 4.3 only testing at
the two stimulus levels of 0.25 µε and 0.8 µε) / (gauge length)
Noise Test: Perform self-noise test as defined in section 6.4
Fidelity Test: Same as in section 4.3 (for the two levels)
Noise Test: Process self-noise test as defined in section 4.4
Data Reporting (Reflection Effects)
Fidelity at Fiber Stretcher: Compare with results from fidelity testing from section 4.3.
THD is presented in percentage values. Up to 18 are provided from reflection tests 1, 2 and
3 to compare with the 6 values from standard fidelity test. This would be best presented in a
table format.
Noise: Compare noise levels measured with data from noise data from 4.4 self-noise test.
Format recommended is to use overlap plots, meaning two data sets on each plot. The
reference data set would be the noise measurement with no reflections. The other data set
would represent the noise data from Tests 1, 2, 3 sections 1, 2, 3. Thus if all tests were run,
9 overlap plots would result.
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21
5
Recommended Test Apparatus
5.1
Simulated Fiber Sensor to be used for characterization
Each of these performance parameters are to be evaluated using a Simulated Fiber Sensor (SFS) of
length defined by the IU’s stated range, or alternatively a range specific to an application. This length
selected becomes the ‘Total Fiber Length’ or TFL.
The Simulated Fiber Sensor will be arranged as shown in Figure 15. It is functionally comprised of
four delay coils and three fiber stretchers which are spliced to represent a contiguous length being the
TFL. In this depiction, they are all shown with pigtail fibers angle terminated with the connector of
choice at the start and end of the TFL.
All elements of the SFS are housed in an isolated container that provides immunity to acoustics and
vibration.
The three fiber stretchers which are each of length Ls located between the four delay coils and
represent test point locations for the many of the performance parameter tests. These are TP1, TP2,
and TP3.
Determinations for the lengths of Delay 1 and Delay 2 are made using the following relationships.
1.
2.
3.
Ls is equal to the fiber stretcher length
TFL’ is set to be equal to TFL- 500 – 3Ls meters
TFL’ / 2 is the length of the Delay 1 and Delay 2
(EQ 2)
(EQ 3)
isolated container
250 m
250 m
Ls
TFL’/2
Ls
fiber stretcher
Delay 1
TP
1
fiber stretcher
TP
2
Delay
TFL’/2
Delay 2
Ls
fiber stretcher
TP
3
Figure 15. Simulated Fiber Sensor and Fiber Stretcher
Three test positions in Figure 15 coincide with the locations of the fiber stretchers and are designated
as follows:TP1: “Start”
Location 1: ................ Before Delay 1
TP2: “Midpoint” Location 2: ................ Between Delay 1 and Delay 2
TP3: “End”
Location 3 ................. After Delay 2
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22
These Three test positions are depicted in Figure 16 and identified as test positions or test points 1-3,
specifically designated as TP1, TP2, TP3, IU refers to DAS IU.
(IU) DAS
Interrogator
250
m
Fiber
Stretcher
TP
1
Delay
1
Fiber
Stretcher
TP
2
Delay
2
Fiber
Stretcher
250
m
TP
3
Figure 16. Test Configurations for SFS showing three test positions
5.1.1
Recommended standard lengths for Simulated Fiber Sensor
The Total Fiber Length (TFL) of the Simulated Fiber Sensor (SFS) may be any length applicable for
the DAS interrogator being evaluated.
The DAS working group did determine that it may also be meaningful to recommend a standard TFL
for the SFS. Such a standard TFL would make it easier for operators to have a common baseline to
make comparisons of different IU offerings.
The DAS working group determined the following:The standard TFL for the SFS = 5 km
In either event, use equations 2 and 3 to determine the lengths for Delay 1 and Delay 2
5.2
Fiber Stretcher to be used for characterizations
The fiber stretcher is used for most of the performance parameter tests that require “stimulus”.
The fiber stretcher is comprised of “sensor fiber” wrapped around a piezoelectric cylinder which is
radially polled. The conditions of this fiber stretcher, in order to be effective for conducting
performance parameter testing are as follows:Cylinder Diameter ................................. > 2 inches (for low macrobend loss)
Fiber Type.............................................. same as SFS fiber
Fiber Stretcher Length ......................... at least two gauge lengths. However, if this length does not
cover at least 10 Spatial Sample Locations, add length for such coverage. Longer lengths acceptable
Sensitivity .............................................. uniform over entire wound section of fiber
Frequency Range ................................. 1% to 80% of Nyquist frequency - see note 1 below
Strain Levels (dynamic) ....................... up to (14 µε peak) / (Gauge Length) - see note 2 below
NOTE 1: Ideally, the “sensitivity” response (strain / volt) of the fiber stretcher should be constant over
the entire frequency range. In practice this is not true and the circumferential resonance of the piezo
cylinder will cause some increased sensitivity at higher frequencies. In order to ensure the accuracies
of Dynamic range (4.1) and frequency response (4.2) tests, one will need to know the frequency
response of the fiber stretcher for data compensation. Insure the supplier provides this information, or
that the fiber stretcher can be calibrated to obtain the information.
NOTE 2: The high strain level indicated is required to satisfy the lowest frequency for the Dynamic
Range test. It may be required (for this one test) that a voltage amplifier will be required between the
signal generator and the fiber stretcher. All other tests in this standard involve much lower dynamic
strain levels and should not need amplification.
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23
Commercial Fiber Stretchers
Known fiber stretcher manufacturers with commercial offerings at the date of publishing this document
are:•
Evanescent Optics, Inc.
•
General Photonics
•
Optiphase - A Halliburton Service
Alternative: Various organizations fabricate their own.
See requirements: see general description for fiber stretcher.
5.3
Signal Generation / Amplification Instrumentation
The fiber stretcher minimally needs a signal generator to produce the drive signals, which is capable
of operating over the ‘Frequency Response’ range specified in section 2. Most fiber stretcher designs
are capable of being driven directly using COTS signal generators.
In regards to the low frequency Dynamic Range tests identified in section 5.2 or 4.1, there will likely be
a need to amplify the signal generator signal to higher voltages to get to the (14µε peak) / (Gauge
Length) levels.
5.3.1
Recommended Signal Generators and Amplifiers
Signal Generator: Many COTS generators are available. One should insure that the generator
produces low distortion sine waves (THD < -54 dB), and has low spurious outputs (< -60 dB) within the
‘Frequency Response’ range.
ARB generation for the frequency response test will require up to 10M sample memory. A partial list
of low price products which satisfy this are as follows:•
•
•
Keysight Models 33511B, 33521B with “Add 16M memory” option
B&K Model 4077B, 4080B (16M memory)
Rigol DG5071, DG5072 (128M memory)
Voltage Amplifier (if needed): This needs to be selected, when mated to the fiber stretcher to
produce a sufficient voltage amplitude to attain fiber strain levels commensurate with the testing
requirements.
It will need to be able to drive a capacitive load (the PZT element) covering the stimulus frequencies
called out in section 5.2 or 4.1. A partial list of known suppliers of such amplifier are listed below:•
•
•
•
•
5.4
TREK, INC. http://www.trekinc.com/
Piezo Systems Inc. http://www.piezo.com/
PiezoDrive http://www.piezodrive.com
Noliac http://www.noliac.com/
AA Lab Systems http://www.lab-systems.com/
Optical Attenuator
A calibrated or optical attenuator approach or attenuator that can be self-calibrated will be required for
the optical budget performance parameter testing.
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24
5.4.1
Attenuator Requirements
Recommended:Calibrated for op wavelength .................. yes or self calibrate with power meter
Attenuation Range .................................. -2 to -6 dB
Step size (settability) .............................. as needed, assume accurate to 0.1 dB
AM modulation ........................................ < -50 dBc
NOTE: above is for tunable attenuator. It is also acceptable to use fixed attenuators.
5.4.2
Commercial Suppliers
Many manufacturers and suppliers for fiber optic tunable attenuators can be found when conducting a
web search for “variable fiber optic attenuator”.
5.5
Isolation Chambers / Vibe Isolators
The Simulated Fiber Sensor (SFS) sec 5.1 uses fiber coils which are sensitive to environmental
disturbances, namely room acoustics and room / benchtop vibrations.
One must take measures to insure such environmental disturbances do not degrade test data for the
measurements of performance parameters (section 6).
Such decisions / implementations will be left to the test staff.
Two isolation approaches are outlined here (5.5.1 and 5.5.2), span the range from simple to thorough
to support those seeking ideas. Neither is required. It does make sense however to provide some
type of isolation when conducting noise tests (sections 4.4 and 6.4) so as to not obfuscate IU selfnoise and environmental noise.
5.5.1
Simple Isolation Approach
A.
B.
5.5.2
Place the elements of the SFS in a thick walled metal container. This will serve to
provide mass and to block airborne room acoustics
Use a bicycle inner tube with a few PSI of air to “suspend” the SFS container. This
will serve to reduce table borne vibrations
More Exotic Isolation Approach
A.
B.
Use a vibration isolation table. Products from Minus K Technology
www.minusk.com/ and others
Place the environmental table (with SFS) inside an anechoic isolation closet /
cabinet. Reference supplier Herzan LLC (southern California) www.herzan.com
and others
Example of a highly capable vibration and anechoic isolation apparatus: Employ an acoustic
enclosure, “Herzan” Silencer model with performance upgrade DE, to provide a thermally stable and
acoustically shielded experimental area. Then within this enclosure the experiment is further
decoupled from the environment with a Minus-K negative stiffness vibration isolation platform, 50BM4. This provides isolation from low frequency vibrations down to of the order of 1Hz. This offers an
experimental working volume approximately 40x40x50cm3.
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6
Reference Appendix (not including test procedures)
This section provides for references, processes, conversion relationships and derivations which
support standardization of data conversions and methods to ensure data quality prior to processing.
6.1
Conversion of Optical Phase Measurement to Strain
Most DAS interrogators considered for use in oil and gas applications implement some methodology
that relies on the determination of an optical phase displacement as the native quantity measured,
relating to the fiber sensitivity.
The conversion of this optical phase measure to standard strain units requires the following:A.
B.
Account for the Poission ratio of the fiber (sensor)
Account for the “double path” nature of DAS backscatter measurements. The
sensed light is based on the folded optical path nature of the OTDR which produces
an optical path length change twice that implied by the linear strain across the optical
gauge length itself, i.e. L is twice the Gauge Length
The following derivation provides for the appropriate conversions:When light travels through a fiber of length of L and refractive index of n, the optical phase is:-
(EQ 4)
Where k is wavenumber (k = 2π/λ), where λ = vacuum wavelength. Changes in phase (of any type)
can be categorized as originating from changes from three different sources, namely length, refractive
index, and wavelength, expressed as:-
.
(EQ 5)
When the fiber experiences strain ε (= dL/L) one may be inclined to assume that the amount of strain
is directly translated to the amount of change in phase delay, as dϕ/ϕ = ε, but this isn’t true as strain
also causes changes in the index of refraction n through the photo-elastic effect 1, and it is necessary
to introduce a scale factor ξ as:-
(EA 6)
Where Pi is the strain optic coefficient (for silica P12 = 0.27, P11 = 0.12), which results in:-
.
1
(EQ 7)
Giallorenzi T G et al “Optical fiber sensor technology” IEEE J. Quantum Electronics, v18 626-65, 1982
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26
Combining equations 7 and equation 4 establishes linear relationship between strain and resulting
change in phase delay as:-
.
(EQ 8)
Accounting for the particular measurement of the IU where the length L, in equation 8 is represented
below by the double transit of a Gauge Length the optical phase is represented as:-
.
(EQ 9).
Where G is the optical Gauge Length of the DAS system
Equation 9 is rearranged to show the strain sensitivity
(EQ 10)
Where the parameters of equation 10 are defined as:-
λ
n
G
ξ
dφ
ε
, the operational optical (vacuum) wavelength of the DAS system
, the refractive index of the sensing fiber (group index)
, the Gauge Length employed by the DAS system
, the photo-elastic scaling factor for longitudinal strain in isotropic material (= 0.78, see eq 6)
, the noise floor of the system in radians
, the noise floor of the system defined as a strain
Calculated Strain / Optical Phase values for given Gauge or Fiber Stretcher Lengths
The Interferometric optical phase-strain relationship from equation 9 is shown in Table 1.
It provides the optical phase level required to attain stimulus strain levels in relation to the amount of
optical fiber wound on the fiber stretcher. Alternatively, it provides the optical phase “accumulated”
across a gauge length for a given strain level.
Thus, it should provide as a handy reference tool to determine the drive level required for fiber
stretchers for the various tests within this document.
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27
Strain
Gauge or
fiber
stretcher
length (m)
1
2
3
4
5
6
8
10
12
15
20
25
30
35
40
45
50
0.025µε 0.05µε
0.1µε
0.25µε
0.5µε
1µε
2.5µε
5µε
optical
phase
radians
0.23
0.46
0.70
0.93
1.16
1.39
1.86
2.32
2.79
3.48
4.64
5.80
6.96
8.12
9.28
10.45
11.61
optical
phase
radians
0.93
1.86
2.79
3.71
4.64
5.57
7.43
9.28
11.14
13.93
18.57
23.21
27.85
32.50
37.14
41.78
46.42
optical
phase
radians
2.32
4.64
6.96
9.28
11.61
13.93
18.57
23.21
27.85
34.82
46.42
58.03
69.63
81.24
92.84
104.45
116.06
optical
phase
radians
4.64
9.28
13.93
18.57
23.21
27.85
37.14
46.42
55.71
69.63
92.84
116.06
139.27
162.48
185.69
208.90
232.11
optical
phase
radians
9.28
18.57
27.85
37.14
46.42
55.71
74.28
92.84
111.41
139.27
185.69
232.11
278.53
324.96
371.38
417.80
464.22
optical
phase
radians
23.21
46.42
69.63
92.84
116.06
139.27
185.69
232.11
278.53
348.17
464.22
580.28
696.34
812.39
928.45
1044.50
1160.56
optical
phase
radians
46.42
92.84
139.27
185.69
232.11
278.53
371.38
464.22
557.07
696.34
928.45
1160.56
1392.67
1624.79
1856.90
2089.01
2321.12
optical
phase
radians
0.46
0.93
1.39
1.86
2.32
2.79
3.71
4.64
5.57
6.96
9.28
11.61
13.93
16.25
18.57
20.89
23.21
Table 1 Optical Phase and Strain Relationships
6.2
Good Quality Data
This element covers tests 4.1: Dynamic Range; 4.2: Frequency Response; 4.3: Fidelity; 4.5:
Spatial Resolution; and 4.6: Crosstalk.
The procedures for the tests indicated require a sufficiently high signal to noise to make a precise
measurement. Considering that DAS systems are influenced by Rayleigh fading statistics, where
highly faded signals have less than sufficient signal to noise, one needs to insure that the “bad” data
sets aren’t used.
The process steps to conduct this Good Quality Data examinations are detailed below:-
6.2.1
Single Tone stimulus testing for Good Quality Data; Tests 4.1, 4.3, 4.5, 4.6
The following is recommended:A.
B.
Take multiple simultaneous time series data of a few Spatial Sample Locations
covered by the fiber stretcher (close to the center, see Figure 17) with the single
tone stimulus on. These sample locations will always be available as the fiber
stretcher is required to cover at least 10 spatial locations (see section 5.2). The
time duration to be recorded should be whatever the specific test calls for
Process each of these time series data by (FFT) converting to the frequency
domain to examine the signal to noise of the stimulus as follows:a.
Select one second of time series data from approximate mid-point of the
time series. Only use 1 second (this normalizes noise bandwidth)
b.
Perform FFT on the one second record. Optional but not necessary to
use data window such as Blackman-Harris
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28
c.
C.
Plot the signal magnitude in units of dB of the frequency domain data
sets (single sided) and examine. Evident should be the single tone signal
superimposed over a noise level for the remaining frequencies
Acceptable time series data would be that which exhibits a signal to noise of 50X
(34 dB) or higher qualifies as “Good Quality Data.” Higher SNR is better
Fiber Stretcher
sensor simulator
DAS
0 1 2 3 4 5 6 7
Interogation
Unit
Spatial
Sample
Locations
few spatial
locations
Fiber Stretcher Range
Figure 17. Fiber Stretcher Spatial Sample Locations
An example plot for examination of data quality is shown in Figure 18. Shown here is a large SNR (~
60 dB)
Figure 18. Frequency Domain Plot of Single Tone Stimulus
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6.2.2
Frequency Response Testing for Good Quality Data
The following is recommended:A.
B.
C.
Section 4.2 identifies the stimulus as a sequential tone sinusoidal sweep lasting
100 seconds. Take multiple simultaneous time series data at each test point
location covered by the fiber stretcher. Ensure the time series captures the full 100
second 40 tone stimulus (go a little longer if needed)
Process each of these time series data (100 second frequency stepped sweep) by
converting to the frequency domain via FFT process to examine the signal to noise
of the stimulus signal for all 40 tones. The specific steps to perform this calculation
are identified in section 7.2
Acceptable time series data would be that which exhibits a signal to noise of 32X
(30 dB) or higher qualifies as “Good Quality Data.” Higher SNR is better
An example plot for examination of data quality is shown in Figure 19. Shown here is a large SNR (~
46 dB).
Figure 19. Frequency Response Plot of Single Tone Stimulus
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6.3
Conformance to Common Parameter Definitions
SEAFOM parameter definitions described in Section 5 of this document have been developed with an
effort to be common to other standards being developed for DAS. During the evolution of this MSP-02
standard, the SEAFOM DAS working group coordinated with Energistics PRODML v2.0 working group
on the naming and definitions of the supporting parameters. Table 2 below outlines the comparisons.
SEAFOM
Spatial Sample
Location
Sample Location
number
Spatial Sampling
Interval
ENERGISTICS
Loci
Comment
Integer value. Represents the particular spatial sample.
Locus Index
Integer value representing location along the sensor fiber
Spatial Sampling
Interval
Sample Location 0
Gauge Length
Locus Index 0
Gauge Length
Total Fiber Length
(TFL) =
Interrogation
Range
Fiber Distance
Fiber End
The separation between two consecutive ‘spatial sample’ points on
the fiber at which the signal is measured. SEAFOM units = meters
of fiber length
Output connector of DAS Interrogator
Represents the design intended spatial resolution of the
Interrogator. SEAFOM units are fiber length in meters. Energistics
Units are meters
Represents the end of the fiber being interrogated.
SEAFOM units = meters of fiber length
Output Data Rate
Output Data Rate
Interrogation Rate
Interrogation Rate
Sample Rate
Sampling Rate
Sample Number
Sample Number
Time Series
Time Series
Fiber Distance
The distance in meters from the connector of the IU to the desired
Sample Location. SEAFOM units are meters of fiber length.
Energistic Units are “Optical Path” distance
SEAFOM: The rate at which the IU provides output data for all
Spatial Sample Locations or Loci (time duration between spatial
samples) ENERGISTICS: similar to Interrogation Rate
The rate at which the Interrogator Unit interrogates the fiber
sensor (can be considered pulse or frame rate)
SEAFOM: is the Interrogation rate or an integer fraction thereof.
ENERGISTICS: is the Output Data rate or an integer fraction
thereof
SEAFOM: The sequence number of a Sample in a Time Series
ENERGISTICS: The index of a particular ‘Sample’ within its parent
‘Time Series NOTE: Both mean the same thing
SEAFOM (for each spatial sample) Energistics (for each Loci)
Table 2 SEAFOM / Energistics Parameter Definition Comparisons
6.4
What to do if you test tone lines up with a “line” frequency or harmonic
If deemed necessary, modify the frequency of stimulus to avoid the overlap.
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7
Appendix (Test Procedures)
7.1
Measurement of DAS Dynamic Range
This appendix outlines a suitable method to determine the Dynamic Range of a DAS system.
Background
The aim of a DAS system is to yield a signal that is directly proportional to the amplitude of applied
time varying acoustic strain acting on the sensing fiber. The dynamic range of the system is a measure
of the range of amplitudes over which the system can accurately represent the acoustic stimulus
applied.
As the magnitude of a sinusoidal stimulus increases, IU induced distortion will begin to occur. Some
practitioners have coined this phenomenon as “slew rate limit” which is applicable only to phase
sensitive DAS interrogators which are designed to implement large angle phase demodulation based
on quadrature measures (“I” and “Q”) of the interferometric return signals.
These measurement approaches usually use inverse trigonometric calculations of the I and Q terms to
determine the optical phase (on the “unit circle”) for each time series sample. The large angle phase
determination involves (as the time series progresses) tracking the optical phase beyond the 0-2π
limits of unit circle. This is accomplished by using “stitching” techniques.
If the rate of change of the signal being demodulated is too fast, the stitching techniques create
mistakes, which can cause an instantaneous jump in phase, which can be some multiple of π radians,
(often 2x). These errors, simply defined represent the slew rate limit of the IU. They also represent
the signal amplitude limit for making linear measurements, and thus is considered in this document to
be the Dynamic Range.
Note, that this dynamic range limit does not consider the range from the noise floor to the maximum
linear operating level. It only considers the maximum linear level.
Example of slew rate limit causing dynamic range limit
This example shows a simulation of an IU measurement of a 100 Hz stimulus signal where it starts at
zero amplitude and is gradually increased over a 30 second time frame. Figure 20 shows both the
stimulus signal (in red) and the IU measured optical phase signal (or dynamic strain signal). At
approximately 17 seconds, the IU experiences a discontinuous transition. This is shown in zoom view
in Figure 21.
The amplitude of the strain stimulus signal (optical phase units converted to strain units per
equation 10) is defined as the Dynamic Range.
Regarding the Dynamic range test (sec 4.1), this test may be taken up to 5 times at each test
frequency / each stimulation point to obtain the reported value.
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Stimulus vs RecoveredSignal
50
Stimulus
Recovered Phase
40
Phase Amplitude (rads)
30
20
10
0
-10
-20
-30
-40
-50
5
0
10
15
Time (s)
25
20
30
Figure 20. Stimulus signal (red) and IU response (blue) showing linear limit at 17 seconds
Stimulus vs RecoveredSignal
Stimulus
Recovered Phase
40
Phase Amplitude (rads)
30
20
10
0
-10
-20
-30
-40
16.92
16.94
16.96
16.98
Time (s)
17
17.02
Figure 21. Zoom view of stimulus signal and IU response showing phase jump at 16.98
seconds
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7.2
Measurement of Frequency Response Test
The frequency response test for the IU represents the accuracy of the IU to measure the sensed
signals amplitude over operational frequency range. This document (MSP-02) only covers the
magnitude and gain “gain flatness” of the frequency response.
It excludes phase response measurement as no simple process for this could be determined.
SEAFOM realizes that the phase response is an important parameter and will strive to include it in a
subsequent revision.
7.2.1
Test Approach
The basic agenda is to stimulate the SFS with a test signal that covers the response bandwidth of the
IU and evaluate its measurement effectiveness. Ideally such a test would be made with a frequency
sweep input that covers all frequencies of interest.
It was determined that the frequency sweep stimulus technique did not provide for sufficient signal to
noise to produce accurate evaluations, so it has been replaced with a frequency stepped sweep
response test using a finite number of frequencies to be tested where each frequency produces
enough energy to provide a sufficient signal to noise level to permit an accurate evaluation.
The stimulus signal is defined as follows
Frequency Range (Interrogation Rate ≤ 20KHz): ................................ 2% to 80% Nyquist Frequency See note FR1
Frequency Range (Interrogation Rate > 20 KHz) ................................. 200 Hz to 8.00 KHz
Number of Frequencies: ....................................................................... 40
Stimulus time for each Frequency ....................................................... 2.5 seconds
Sweep time for Frequency Range ........................................................ 100 seconds
Strain Amplitude ................................................................................... 0.08 µε peak / (gauge length in meters)
With the stimulus signal defined, the Test approach involves the following:1.
2.
3.
Generate the stimulus file for implementation in arbitrary waveform generator
Apply the stimulus to the three test points TP 1, 2, 3 defined in section 6.2.1. Note: this can
be done simultaneously (all three test points) or one at a time
Collect data per section 4.2.2
NOTE FR1: piezoelectric fiber stretchers are sensitive (circumferential resonance) to transient input
signals. In order to minimize transients during the stimulus frequency steps, each frequency
generated should have an integer number of cycles. Thus the 2% to 80% Nyquist definition
should be slightly altered to accommodate that requirement. This is described by the setup algorithm
in the next section.
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7.2.2
Stimulus Waveform Generation
An algorithm using MATLAB commands is provided as an example for generation of the frequency
stepped sweep signal. Methods other than MatLab are applicable.
Sweep signal generation
% Determine Sample rate for arb generator
If Interrogation Rate > 20000
Fs = 100000
else
Fs = Interrogation Rate * 5
% determine start frequency as closest integer to 2 percent Nyquest frequency
ftest = sweep start frequency = (0.8 *Nyquist / 40)
f0 = round(ftest)
% Takes care of Note FR1
sf = step frequency = f0
D = duration of sweep in sec = 100 sec
st = step time = D/40
N = Total number of samples = D*Fs
V = the value which produces the peak output of the arb generator to be a voltage which drives the
fiber stretcher that corresponds to the strain value (Signal Level) defined in 4.2.1.
Create time t as
t = 1/Fs:1/Fs:D;
start at zero seconds increment (1/Fs) seconds, stop at D seconds
NOTE: The frequency stepped sweep assumes the fiber stretcher has a constant sensitivity over all
frequencies. In practice, this is not usually true and usually has a response that increases slightly with
increasing frequency. To ensure the frequency response test is accurate, you will need to modify the
stepped sweep (below) to compensate for the frequency response of the fiber stretcher, or modify step
C in 7.2.3 to compensate the fiber stretcher frequency response.
Create frequency stepped sweep S as
t2 = 1/Fs:1/Fs:st;
for i=1:40
S((i-1)*Fs*st+1:i*Fs*st) = V*sin(2*pi*i*sf*t2);
end
The resulting array S becomes the signal to be created with the arbitrary signal generator which clocks
the output signal at a rate of Fs.
The arbitrary generator output signal should be scaled to signal level to produce a stimulus strain
amplitude recommended in section 4.2.1 or 7.2.1.
7.2.3
Processing the Data collected
The test in section 4.2 requires “Good Quality Data” be collected (see sec 6.2). Once this data
becomes available, the processing to be performed is exemplified using MATLAB constructs.
The data file to be processed is in a file SR. It will be first converted to magnitude frequency domain
data.
Magnitude of Determination
NOTE: The measurement described below involves performing a Fourier transform to determine the
measurement in the frequency domain. This particular data set will not transform correctly if a
window is applied. Do not apply a window.
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A. Perform fft,
Y = fft(SR);
B. Determine Normalization Factor
P = normalization factor = sqrt(2)/N
Note: this normalization factor is used to revert data to the same input referenced
signal level when determining M below.
C. Get abs and multiply P to get magnitude M
M = P*abs(Y);
An example of a plot of M is provided below in Figure 22. Here the interrogation rate was 20 KHz,
and the response shown covers the entire Nyquist frequency range showing the 40 tones occupying
the first 80 percent.
Magnitude response M showing the forty stimulus signals all with magnitude.
Figure 22. Magnitude response M showing the forty stimulus signals all with magnitude
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7.2.4
Data Reporting
Data reporting for the frequency response test shall be a single plot which represents the magnitude
response of the 40 test frequencies. It should be derived from the magnitude (M) data taken and
processed as follows.
1.
Plot 1: Shows the interrogator response M to the test stimulus. Example plot is
shown in Figure 23:a.
Frequency Range: linear from 0 to Nyquist Frequency
b.
Amplitude Scale: dB Peak relative to strain units. Not strain squared
c.
Amplitude Range: 30 dB. Include Indicator of the intended stimulus input
Figure 23. Plot example of Interrogator response to test stimulus, scaled in strain units, shown
in frequency domain
2.
Plot 2: Corrected and normalized frequency response. Example plot is shown in
Figure 24:a.
Correct the response file M to compensate for the (magnitude) frequency
response of the fiber stretcher (see note FR2). Result file is MC and
retain only the 40 values
b.
Calculate the mean value of the 40 MC peak values corrected and
normalize to that level. Result File is MCN
c.
Create Plot 2 of MCN.
i.
Frequency Range is linear from 0 to highest frequency tested
ii.
Amplitude Scale: dB ( 20*Log10 (MCN value))
iii.
Amplitude Range: 9 dB (+3 to -6). Note, if actual data falls
outside of the range specified, then open up the plot range on
either end to accommodate.
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Figure 24. Interrogator normalized frequency response plot example
NOTE FR2: piezoelectric fiber stretcher frequency response may not be perfectly flat over the
frequency range test. Typically, the sensitivity increases with increased frequency as one gradually
approaches the circumferential resonance. If this is the case, then Plot 2 step accommodates
correcting the data from M so that it only relates to the IU response.
7.3
Fidelity Test
Additional Detail for this test is not required.
7.4
Measurement of DAS SELF-NOISE
This appendix outlines a suitable method to determine the noise floor of a DAS system.
7.4.1
Background
The noise floor of a system is a critical specification of the performance of a system and determines
the smallest signal of which the system is capable of detecting and making a measurement.
The measurement approaches assume that the DAS system to be tested and specified employs an
interferometric approach. Thus, the IU fundamentally measures the change in optical path length dΦ
over a defined “Gauge Length”, G. This fundamental output is measured in radians.
In order to present the noise floor in a common form independent of the exact nature of the DAS
sensor methodology and operational wavelength, it is necessary to convert the DAS output to the
physical strain of the optical gauge length employed by the DAS system. The conversion from optical
phase to strain is described in section 8.1 equation 6. This however now makes the noise floor a
function of the employed gauge length and so for direct comparison between specifications the gauge
length must be quoted with the noise floor, when presented as a strain.
Rearranging this equation, we can derive a term that converts from phase to strain as follows, which is
equation 10, section 6.1
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7.4.2
Acquire and process the Noise Data
In order to achieve the noise levels observed by DAS systems installed in real world applications it is
important to ensure that the noise floor of the interrogation process of the IU be measured and not the
environmental noise of the location in which the sensing fiber is placed.
As with a real-world application, the IU should be installed in the laboratory as it would be in the actual
application, not within a shielded enclosure unless such is typical for deployment. The Simulated
Fiber Sensor (SFS) should be placed within the determined shielded environment see section 5.5).
Step 1: Connect the IU to the Simulated Fiber Sensor (SFS) as required, i.e. of the correct length
and fiber type.
Step 2: Setup the DAS system as per the manufacturer’s instructions, again as appropriate for the
fiber configuration with the intended interrogation parameters best suited to the SFS.
Step 3: Acquire Data: Take a data set 30 seconds in duration for the three sections (300
contiguous SSLs per section as described in 4.4.3 and Figure 7. This yields the raw (optical) phase
response of the Simulated Fiber Sensor (SFS). NOTE: data can be taken over the entire SFS and
later process for the three sections.
Step 4: Process SSL “ping” Data: The acquired data set is a 2D field representing the time varying
acoustic field as a function of distance. For simplicity of explanation we define two domains, the
spatial domain, representing the distance along the fiber (a series of consecutive Spatial Sample
Locations or SSLs) and the ping domain, i.e. a 1D data set (Time Series) for each SSL with a
sampling rate equal to the Interrogation Rate. See Figure 26 (Ping Domain Process).
The acquired data is to be processed as described in section 7.4.3 “Process approach for ping domain
data”.
The result here will be Amplitude Spectral Density (ASD) data traces (900 in total, 300 for each of the
three sections) representing the IU noise response, which has been normalized to a 1 Hz resolution
bandwidth and converted to units of strain per root Hertz. This data should not yet be converted to dB
levels.
Step 5: Average the SSL ASD Data: Average the data from Step 4 in three sets representing the
three sections called out in Section 6.4. Thus, the 300 traces from each section are averaged into
one trace per section. The units remain as strain per root Hertz.
Next, convert the data in the three traces to represent as dB re 1 pico-strain / root Hz. This
conversion is 20*Log10 (strain).
Step 6: Plot the noise data
This will be three plots which can be shown independently or all on the same plot. See example
below. The plot will also indicate the gauge length used when the data was collected. Example plot
below for 1550 nm wavelength, 10m Gauge length.
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Figure 25. Example plot of DAS Self-Noise data
Figure 26 System noise floor data processing schematic
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7.4.3
Process approach for ping domain data.
Take each Ping Domain data sets (SSL Time Series) and process them to the frequency domain to
determine the average signal spectral density in rads / √Hz, which will then be converted to units of
strain /√Hz.
There are two options to process the Ping domain data. The first has more computation steps
(preferred by some). The second less so. Either is acceptable
OPTION 1: Process each SSL 30 second Ping Time Series in many segments.
For each Spatial Sample Location (SSL) this would be 900 of them, take the ping domain time series
and split the 30s recording into several overlapping “blocks” each of a chosen FFT length.
If the FFT lengths chosen are 1s in duration, the noise bandwidth will be automatically normalized to a
1 Hz noise band. There can be overlap between the data block if desired. Some experts favour a 25%
overlap.
The FFT should be windowed using a Blackman-Harris window (see section 8.2). The detailed
process steps for the FFT conversion are provided in section 7.4.4 as a MATLAB process. Further,
the resulting frequency domain data should be converted to magnitude and retain only the positive
frequency data (out to the Nyquist frequency).
All of the “Ping” blocks within each SSL (data units of radians per root Hz) should be averaged to
determine a single noise spectrum measurement. After averaging, convert the resultant data (in units
of radians per root Hz) to strain units and normalize to the gauge length using equation 10 (section
6.1).
The result should be three sets of 300 pings (or SSLs) for each of the three segments identified in
section 4.4.3.
OPTION 2: Process each SSL 30 second Ping Time Series in a single segment.
For each Spatial Sample Location (SSL) this would be 900 of them, the chosen FFT length would be
that of the entire 30 second Time Series.
The FFT should be windowed using a Blackman-Harris window (see section 8.2). The detailed
process steps for the FFT conversion are provided in section 7.4.4 as a MATLAB process. Further,
the resulting frequency domain data should be converted to magnitude, normalized to a 1 Hz noise
bandwidth and retain only the positive frequency data (out to the Nyquist frequency).
Next, convert the resultant data (in units of radians per root Hz) to strain units and normalize to the
gauge length using equation 10 (section 6.1).
The result should be three sets of 300 pings (or SSLs) for each of the three segments identified in
section 4.4.3.
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7.4.4
Details of the FFT Process that calculates DAS Self-noise
This process is shown as a MATLAB approach.
1)
Detrend the data to remove DC offset and linear slope. (This step is optional)
Data = detrend (Data)
(this is MATLAB command)
Define the window apodization to multiply the time domain data by (same length as data to Fourier
transform, powers of 2 much faster when using FFT). In MATLAB, a Blackman-Harris window may be
created by calling the ‘blackmanharris’ function and specifying the data length:
Window Coefficients W = blackmanharris(LFFT)
2)
Calculate the window gain, GW:
GW = LFFT/sum(W)
3)
Apply window to data
Windowed Data = GW.*W.*Data
4)
FFT the windowed data
FFT output = fft(GW.*W.*Data)
5)
Normalise fft output by number of samples (FFT length, LFFT)
Normalised FFT = fft(GW.*W.*Data)/LFFT
6)
Convert from double-sided to single-sided equivalent amplitude, accounting for
power split between +ve & -ve frequencies, i.e. single-sideband output SSB =
2*output of +ve power spectrum, or sqrt(2)*amplitude spectrum, as produced by
fft. Also, we are interested in the magnitude of the amplitude spectrum, so take the
absolute values
SSB = abs(sqrt(2).*fft(GW.*W.*Data)/LFFT)
7)
Calculate noise equivalent bandwidth; accounting for FFT resolution and window
noise equivalent bandwidth
FFT resolution fRes = fSample / LFFT, where fSample is the sample rate of the data.
Window noise equivalent bandwidth W NBW, must be looked-up for the specific
window function. MATLAB has a function ‘enbw’ for computing the equivalent
noise bandwidth from the window coefficients.
WNBW = enbw(blackmanharris(LFFT))
NoiseBW = sqrt(WNBW * fRes) % determine the noise bandwidth
Note: sqrt as linear in power, fft data is amplitude based.
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8)
Corrected output normalised to FFT bandwidth (SSBNorm)
SSBNorm = (abs(sqrt(2).*fft(GW.*W.*Data)/LFFT))/ NoiseBW
units of radians per square root Hertz OR rads/rt-Hz OR rads Hz-1/2
9)
SSBNorm needs to be converted to units of “strain noise” This is performed using
equation 10 in section 6.1 where SSBNorm represents the term
Or
λ
n
G
, the operational optical (vacuum) wavelength of the DAS system
, the refractive index of the sensing fiber (group index)
, the Gauge Length employed by the DAS system
, the photo-elastic scaling factor for longitudinal strain in an isotropic
material (= 0.78, see equation 3)
, the noise floor of the system in radians
, the noise floor of the system defined as a strain
Conversion Example:
SSBNorm
G
λ
= 1 radian
= 10m
= 1550nm
= 10690 pico-strain / radian.
The strain noise data is then used to develop the averaged plots described in section 4.4.3, step 3.
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7.5
Measurement of Spatial Resolution
The Spatial Resolution measurement made is a check or verification of the manufacturers
specification of the IU gauge length. This measurement should, for a properly operating IU, be a close
approximation of the gauge length.
Step 1:
Setup an IU as shown in Figure 27 below. Delays 1, 2, and 3 are known lengths and test
points (TP) 1, 2, and 3 are at known Spatial Sample Locations. The length of the fiber
winding on the piezo element of the fiber stretcher should be longer than the IU design gauge
length (recommend at least 2X).
IU
250
m
TP Stretcher
1
Delay
1
TP Stretcher
2
Delay
2
250
m
TP Stretcher
3
Figure 27. Test Arrangement for Spatial Resolution
Optional Time Saving Approach: The IU data that is obtained to conduct the Spatial Range test
(steps 1 to 4) could be defined to cover the needs for both Spatial Range testing and Crosstalk
Testing with all fiber stretchers driven simultaneously. If this is done, then the fiber stretchers would
need to be driven at different frequencies. Recommended frequencies here would be TP2=100 Hz,
TP3=120 Hz, and TP4= 140 Hz
Step 2:
Apply a sinusoidal stimulus to the piezo stretchers. Set the frequency of the stimulation to be
100Hz and amplitude to be 0.5 µε peak / GL. It is not critical that this signal level be precisely
0.5 µε p / GL, which is a useful level for high signal to noise, but rather it be a consistent level
for the entire test.
Step 3:
Begin a Time Series acquisition across the entire fiber span of the Sensor Simulator. The
duration should be long enough to ensure that “good quality data” (see section 6.2.1) are
collected at all the spatial sample locations.
Step 4:
Convert the IU Time Series data (assume optical phase or other “linear” measure of the IU)
into frequency domain.
The Time Series data to be converted for the spatial resolution determination should minimally
cover the Spatial Sample locations depicted in the Figure 28. Here each red dot represents a
Spatial Sample Location, but if one wants to additionally cover the full range for Crosstalk
Test (4.6), the data should be taken out to +/- 50 gauge lengths for each fiber stretcher
location.
Fiber Stretcher
“fiber sensor”
gauge length gauge length
-2
-1
“fiber sensor”
gauge length
+1
gauge length
+2
Figure 28 Spatial Sample locations (highlighted) to be used for Spatial Resolution Evaluation
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This computational approach recommended is to be made as follows:Time series data samples:
Window function for the data:
Frequency Conversion Method:
16384
Flat Top (see section 8.1)
Fast Fourier Transform (FFT)
Recommend that each FFT be small blocks (16384) so that numerous blocks can be processed at
each SSL to eliminate the possibility that faded signals can corrupt the data. Use only amplitude data
that exhibits a high SNR at each SSL as identified in section 6.2.1.
Step 5:
Record the obtained magnitude data at the stimulus frequency (100 Hz peaks) for each
Spatial Sample Location (SSL). Create a plot like that shown in Figure 29. Graphical plotting
approach used to determine Spatial Resolution where the X axis represents SSL locations
and the Y axis shows the magnitude value recorded.
Apply (to the plot) a straight line curve fit as shown (red line) Figure 29. This shows
numerically simulated data for a gauge length of 5 spatial sample units. This figure shows two
different data sets.
The first “Asymmetric Data Set” uses a fiber stretcher which has a range of 10.5 spatial
sample units and is asymmetrically situated with respect to spatial sample locations.
The second “Symmetric Data Set” uses a fiber stretcher which has a range of 11 spatial
sample units and is symmetrically placed with respect to spatial sample locations.
Both data sets are made (simulated) using a 5m gauge length and assume perfect
performance of the IU where gauge length would then be equal to Spatial Range.
The Spatial Resolution is estimated as follows.
Measure Lengths of the range of the left and right downward sloping lines, and designate
them as LL and LR.
Spatial Resolution is estimated to be (LL + LR) / 2
NOTE: These units are in units of Spatial Sample Intervals. Prior to “reporting” they should be
converted to fiber distance in meters.
The data presented should be a single value representing spatial resolution in meters
at each of the three test point locations, TP1, TP2, and TP3.
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45
ε
Spatial
Sample
1
step function strain change
0
Range of Fiber Stretcher
L1 L2 L3 L4
SENSOR
Ln+1 Ln+2
SENSOR
LL = 5
LR = 5
6
Asymmetric Data Set
5
range of stretcher is
non integer length
wrt Spatial Samples
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
LR = 5
LL = 5
6
Symmetric Data Set
5
range of stretcher is
integer length wrt
Spatial Samples and
is centered
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
Figure 29. Graphical plotting approach used to determine Spatial Resolution
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46
22
23
7.6
Measurement of Crosstalk
NOTE: This test is very similar to 4.5 / 7.5 (Spatial Resolution test) taking exception that the data
collected will range +/- 50 gauge lengths (or minimum of +/- 250 meters) from the stimulus fiber
stretcher, as shown in Figure 30.
“fiber sensor”
Fiber Stretcher
“fiber sensor”
out to -50 gauge lengths
out to +50 gauge lengths
middle of
fiber stretcher
gauge length gauge length
-4
-3
gauge length
+3
gauge length
+4
Figure 30. Highlighted points to be sampled for the Crosstalk Test (note includes gauge
lengths +/- 5 to 50 as indicated by the red arrows)
The test arrangement showing placement of the fiber stretchers is shown in Figure 31.
IU
250
m
TP Stretcher
1
Delay
1
TP Stretcher
2
Delay
2
250
m
TP Stretcher
3
Figure 31.Test arrangement for crosstalk measurement
The data collection steps are identical to that defined in section 7.5 (Spatial Resolution test). If all
stretchers are driven simultaneously, then different frequencies should be used for each fiber stretcher
test point. As before, recommend 100 Hz stimulus.
Step 1:
A: Determine Reference Level (RL): Use the phase data from using steps 1-4 defined in
section 7.5 Spatial Resolution Test. Determine the reference magnitude value averaging the
phase data over the flat top portion of the fiber stretcher. Spatial Sample Locations close to
the center of the range of the fiber stretcher.
B: Determine Crosstalk Levels (CL): Use the phase data from using steps 1-4 defined in
section 7.5 Spatial Resolution Test. Determine the magnitudes of the signals (at the
stimulation frequency) for Spatial Sample locations which covers the span +3 to +50 gauge
length and -3 to -50 gauge length from the fiber stretchers (TP2,TP3, and TP4) as indicated in
Figure 31 above.
C: Determine Crosstalk Ratios: Take the ratio of the crosstalk magnitudes to the reference
magnitude for all Crosstalk data and calculate this ratio in dB i.e. 20*Log10 (CL/RL).
Step 2:
Plot the data over the range of +/- 50 Gauge lengths from each fiber stretcher (TP1, TP2 and
TP3) as shown in the example provided in Figure 32, which assumes a 6m gauge length.
The units for each plot should be dB crosstalk versus length (meters) along the Sensor
Simulator Fiber. A conversion of Spatial Sample Location to fiber length is required.
This results in three plots, one for each test point location, TP1, TP2 and TP3.
An example plot is provided in Figure 32. No data is shown within +/- 2 gauge lengths of the stimulus
location.
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47
Figure 32. Example plot for Crosstalk Test Results. Data is shown to cover +/- 50 Gauge
lengths. This example uses a 6m Gauge length
7.7
Measurement of Loss Budget
See Section 4.7.
7.8
Sensor Reflection Effects
See Section 4.8.
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48
8
Appendix FFT Window Functions
This section includes information support of processes recommended in sections 4 (measurement
procedures) and 7 (details of test procedures).
In order to make precise measures of IU response signals, the time series data from certain tests will
be converted to frequency domain via Fourier transform.
Window functions to Time Series data are required prior to some of the Fourier transforms used for the
measurements of Performance Parameters.
8.1
Flat Top Window used for frequency domain measurements of spectral
peaks
The Flat-Top Window function will be used for the following Performance Parameter tests:•
•
•
•
Fidelity
Spatial Resolution
Cross-Talk
Sensor Reflection Effects
The Flat Top window has the best amplitude accuracy of all the smoothing windows at ±0.02 dB for
signals exactly between integral cycles. It is principally used for calibration purposes. The broad peak
produced by the Flat Top window is closer to the true amplitude of the signal than with any of the other
windows. The Flat Top window is therefore a good choice when your top priority is measuring your
signal’s amplitude from the spectrum.
An open reference for the Flat Top window is found on Wikipedia pages with the link below, which
shows the window function and normalized transform magnitude.
https://en.wikipedia.org/wiki/Window_function#Flat_top_window
Figure 33 depicts the characteristics of the Flat Top window (left) for a time series of N samples and
the resulting Fourier transform exhibiting a broad peak across the resulting frequency bins.
Figure 33. Flat-Top Window and Fourier Transform Characteristics
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The generating function with amplitude coefficients are provided below:-
Where
n is the sample index
N is the number of samples
And the coefficients are:ao = 1
a1 = 1.93
a2 = 1.29
a3 = 0.388
a4 = 0.28
8.2
Blackman – Harris Window used for frequency domain noise
measurements
The DAS self-noise test in sections 4.4 and 7.4 are specified to use frequency domain data for the
determination of the IU noise floor. The Fourier conversion of the time series data collected is
specified / recommended to use the Blackman-Harris window function prior to the frequency
conversion.
An open reference for the Blackman-Harris window is found on Wikipedia pages with the link below,
which shows the window function and normalized transform magnitude.
https://en.wikipedia.org/wiki/Window_function#Blackman–Harris_window
Figure 34 depicts the characteristics of the Blackman-Harris (left) for a time series of N samples and
the resulting Fourier transform exhibiting high side-lobe rejection across the resulting frequency bins.
Figure 34. Blackman Harris Window and Fourier Transform Characteristics
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The generating function with amplitude coefficients for the Blackman-Harris window are provided
below.
Where
n is the sample index
N is the number of samples
a0 = 0.35875
a1 = 0.48829
a2 = 0.14128
a3 = 0.01168
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