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A New Calibration Method and Device for Certified Flow Measurements With
Laser Velocimetry
Conference Paper · November 2012
DOI: 10.1115/IMECE2012-93100
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Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition
IMECE 2012
November 9-15, 2012, Houston, Texas, USA
IMECE2012-93100
DRAFT: A NEW CALIBRATION METHOD AND DEVICE FOR CERTIFIED FLOW
MEASUREMENTS WITH LASER VELOCIMETRY
Katsuaki Shirai∗†, Lars Büttner, Jürgen Czarske
Laboratory of Measurement and Testing Techniques
Carsten Kykal
TSI GmbH
Faculty of Electrical and Computer Engineering
Technische Universität Dresden
Email: juergen.czarske@tu-dresden.de
52068 Aachen, Germany
Email: carsten.kykal@tsi.com
ABSTRACT
We aim to establish traceability at calibration and hence to enable a certified flow measurement with a calibrated measurement system. A new calibration method is presented for laser
velocimetry. We develop a simple, unique method which establishes traceability of its uncertainty. The device is transportable
and calibratable by any users for their own instruments on-site.
Our new method requires only a rotating disk and a precision linear stage providing positional information. In former calibration
methods, the uncertainty of the orbit radius of a scattering object
was dominant due to the diffficulty of accessing the true center of
the rotation. The diffuculty was solved in our new method. The
new method provides an accurate estimate of the orbit radius and
hence the velocity of the calibration object through a linear regression. The calibration constant is obtained even without the
need of direct access to the rotation radius. The uncertainty budget is examined throughout the calibration procedure. The traceability chain is established once the traceabilities are maintained
to the translation stage and the motor used for rotating the calibration disk. The new method has been realized with three different calibration setups and their performances were investigated.
We demonstrate that the new calbration method can achieve reasonable uncertainty values.
NOMENCLATURE
A
B
C0
d
f
frot
M
N
r
u
ucal
x
x0
xj
z
α
δ
Λ
λ
ω
σ
σj
ξ
c
∗ Address
all correspondence to this author.
† Present affiliation: Laboratory of Energy-Conversion Technology,
Kobe University, Rokkodai 1-1, Nada, 657-8501, Kobe, Japan,
Email: shirai@mech.kobe-u.ac.jp
cal
j, k
sc
1
slope of the linear fit [1/(m·s)]
intercept of the linear fit [1/s]
constant
fringe spacings [m]
Doppler frequency [Hz]
rotation frequency [Hz]
number of locations for local Gaussian fit [m]
number of scattering objects
radius or radial coordinate [m]
velocity of tracer particle [m/s]
calibration velocity [m/s]
stage coordinate [m]
offset of the stage coordinate [m]
constanc in the Gaussian fit [m]
axial coordinate (optical axis) [m]
half-angle between the two laser beams of LDV [rad]
parameter variation
value defined in Eq.(21) [m2 ]
laser wavelength [m]
angular velocity of rotation [rad/s]
uncertainty (standard deviation)
constant in the Gaussian fit [m]
SNR or amplitude of Doppler signals
center values
calibration values
j, k-th values
stage-coordinate values
c 2012 by ASME
Copyright ⃝
INTRODUCTION
Quality control gains more attentions in production fields, which
leads to the rapid increase of sensor developments and applications. Sensor technologies are expected to play a major role
in the future and the sensor market will show futher growth in
industry [1]. Measurement is the basis for production control
together with tolerance. Tolerance values are managed through
quantitative measurements using various sensors. Nowadays, the
interexchange and combination of tolerance values are required
between different components produced in different places even
beyond borders and continents with the globalization of modern
economy. Hence, establishment of traceability in measurements
obtains higher attentions in production field.
Flow measurement is not an exception. Many different techniques are available for knowing flow velocities. Modern laser
diagnostics allow nonintrusive measurements without inserting
a physical probe into a flow such as the location behind rotator
blades in turbomachinery. Laser Doppler velocimetry (LDV) has
been widely used as a well-established diagnostic tool in fluid
mechanics [2] since it was invented by Yeh and Cummins [3].
LDVs are used for measurements requiring relatively high resolutions of time and space without disturbing the flow. They are
capable of measuring multiple velocity components with exceptionally high dynamic ranges in unsteady flows. Developments
of laser Doppler techniques is continued toward achieving high
spatial resolutions into the range of micrometers [4]. LDV is also
known to have small measurement uncertainty when it is properly used. Besides, LDVs are even set for transferring velocity
standard of gas flowrate in some countries because of their wide
ranges of linearity.
In this paper, we propose a new calibration method toward establishing a traceability of uncertainty in flow measurements using
laser velocimetry such as an LDV. The calibrated velocimetry
is applied to flow measurements. Our challenge is to establish
measurement traceability at the calibration. The new calibration
method is based on the linear relationship between the Doppler
frequency and the orbit radius of scattering object attached on
a disk rotating at a constant angular velocity. Calibration uncertainty of the method is examined based on the Guide to the
expression of Uncertainty in Measurement (GUM) [9]. We show
the measurement uncertainty is traceable with this new method
as long as the traceabilities are achieved for the two fundamental elements required in the system. Three different setups of the
new calibration are realized and their experimental results are
examined.
Measurement Volume
x
time
u
d
α
α
z
1/f
Doppler Burst Signal
Laser Beams
(wavelength: λ)
Tracer Particle
FIGURE 1.
Schematics of the measurement volume and Doppler signal of a laser Doppler velocimetry (LDV).
particles are seeded into the flow in advance or naturally existing
particles may function as tracer particles. The local flow velocity
is measured by evaluating the Doppler frequency shifts of the
particles.
Fig. 1 depicts schematics of the measurement volume and a
Doppler burst signal of a typical differential LDV. The measurement volume is formed at the intersection of a pair of coherence
laser beams. The resulting interference fringes become nominally parallel in the direction of optical axis when the beams intersect at their focal points. The fringe spacings d of this nominally parallel fringes can be described as
d=
λ
,
2 sin α
(1)
being λ and α are the wavelength and the half crossing angle,
respectively. When a tracer particle passes through the fringes,
it scatters the incident laser beams. The scattered light generates
modulated signal called Doppler burst such as in the right side of
Fig. 1. The beat frequency f of the Doppler signal is proportional
to the physical velocity u perpendicular to the bisector plane of
the fringes
u
f= .
d
(2)
Hence, the velocity of the particle is obtained by measuring the
Doppler frequency. As long as the tracers follow the fluid motions, the local flow velocities in the measurement volume are
obtained.
Calibration of LDV
The calibration can be carried out using a scattering object which
has a constant, well-defined local velocity. With a known velocity ucal of the scattering object, the nominal value of the fringe
spacings d is precisely determined from the measured Doppler
frequency as
LDV AND ITS CALIBRATION
Laser Doppler velocimetry (LDV)
The principle of an LDV is based on the fact that the Doppler
beat frequency of the scattered light by a small tracer particle
is proportional to its velocity of the physical movement. The
d = ucal / f,
2
(3)
c 2012 by ASME
Copyright ⃝
which is called as a calibration factor. In other words, the calibration of an LDV is equivalent to obtain the nominal value of the
constant fringe spacings d in Eq.(2). Hence, velocity measurement is identical to the reproduction of the calibration velocity.
The uncertainty originating from the calibration induces systematic contribution to the total uncertainty budget of the velocity
measurements. Indeed, the calibration uncertainty is crucial for
laser velocimetries, especially when the traceability is demanded
in the measurement. Ultimately, the calibration eventuates the
realization of a constant known velocity ucal of a scattering object.
In the metrological field, LDV has been set as a primary velocity
standard for gas flows in seveal countries such as the USA, Japan
and Germany [5–7]. They are all based on a nominally constant
velocity realized by a scattering object attached on a rotating system. The tangential velocity of the scattering object is expressed
as
ucal = rω = r2π frot .
Scattering Object
(e.g., Pinhole)
True Center
(not known in advance)
r
Disk
( ∂d
σf
x=0
FIGURE 2.
Principle of the new calibration method using multiple
scatterin objects (r: orbit radius, x: stage coordinate).
(4)
uncertainty as systematic one. The estimate uncertainty of the
frequency can be described based on the theory of Crámer-Rao’s
lower bound (CRLB) [10], depending on the sample rate, the
record length of the signal and the signal-to-noise ratio (SNR).
The fractional uncertainty of Doppler frequency σ f / f becomes
usually around in the order of 10−4 ∼10−3 with a typical set of
conditions of the parameters. The uncertainty of the calibration
velocity σucal appearing in the second term is further decomposed
into
√
( ∂u
)2
)2 ( ∂u
cal
σ frot +
σr
∂ frot
∂r
√
( σ )2 ( σ )2
frot
r
+
.
= ucal
frot
r
σucal
=
ucal
(6)
(7)
The uncertainty of the calibration velocity becomes from 0.6 %
to 1.7 % as a sense of single standard deviation σucal in conventional calibration methods using a single scattering object [8].
This large uncertainty value originates from that of the orbit radius of the scattering object. The uncertainty comes from the
difficulty to access the true rotation radius under the fabrication
tolerances and the plays required between some elements such as
the one between the disk and the rotating shaft. Compared to the
radial uncertainty, the disk rotation and frequency estimate typically ranges around 0.05 %, which are one order of magnitude
smaller the radial one. The motor rotation can be stablized by a
phase-lock-loop and an encoder, while the estimate uncertainty
of the frequency is limited by the bound mentioned in the above.
Hence, the reduction of the radial uncertainty at the calibration is
the most effective strategy in order to reduce the total uncertainty
of the calibration.
)2 ( ∂d
)2
σucal
+
∂ucal
∂f
√
)2 (
)
1 (
ucal σ f + σucal 2 .
=
f
x
xj
Unknown Offset: x0
Calibration Uncertainty
The calibration uncertainty, which is equivalent to the relative
uncertainty of thre fringe spacings σd /d, is analyzed along the
GUM. In the latest version of the GUM, the uncertainties are
classified into type A in the form of a standard deviation, and
type B such as a tolerance or a worst case estimate with a lower
and an upper limit bound. Eq.(3) already shows that the calibration depends on two sources of uncertainties – the velocity of a
scattering object and the frequency estimate of Doppler signals.
The uncertainty of the fringe spacings can be expressed by following the law of uncertainty propagation being the uncertainty
elements assumed to be independent,
√
uj =rjω
fj
rj
being r , ω, frot the orbit radius, angular velocity and rotation
frequency, respectively. The calibration devices in the national
metrology insitutes tend to become bulky and not designed to be
transported for on-site calibrations. Outside of national metrology institutes, a limited number of sysmtems have been tested
and used for calibrating laser velocimetries. Such methods with
their performance evaluations are summarized by Shirai (2011)
[8].
σd
=
d
f
(5)
The first term in the square root of the right-hand side of the
equation is the statistical uncertainty but it contribute to the final
3
c 2012 by ASME
Copyright ⃝
NEW CALIBRATION METHOD
We propose a new calibration method for accessing the inaccessible orbit radius of a scattering object. The new method provides the calibration constant even without the need of accessing
the radius.
Principle
The new method is based on the linear relationship between
the tangential velocity and the true orbit radius as schematically
shown in Fig. 2. We use multiple, pointwise scattering objects
(i.e., pinholes) attached on a single rotating disk. The angular
velocity of the disk is assumed to be constant. Each of the multiple scattering objects can act as a single scattering object with
the Doppler frequency depending on the orbit radius. A linear
precision stage is utilized to mechanically shift the pinholes in
the radial direction (see Fig. 3). The radial shift between the successive scattering positions is known with relatively small uncertainty from the displacement of the precision stage. As long as
the disk rotates at a constant angular velocity, the tangential velocity of the pinholes linearly increases depending on the radial
position from the rotation center. Hence, it provides the exact
rotation radius of a scattering object with a simple linear extrapolation. This is possible because the unknown value is included
commonly. Even without knowing the commonly included unknown value, the differential distance between respective orbits
can be precisely recorded using a linear precision stage with either an encoder or a displacement sensor.
The mathematical expression of the calibration method is described as following. We use N pieces of single scattering objects ( j=1,. . .,N) and the resulting Doppler frequency f j at j-th
object is proportional to the orbit radius r j
fj =
2π frot
r j.
d
FIGURE 3.
Schematic of the new calibration method with a combination of rotating disk and a linear precision stage.
The offset x0 is an unknown but it is commonly included in the
stage coordinate. The Dopppler frequencies of the scattering objects are acquired while their locations are recorded in the stage
coordinate. The resulting position-frequency pairs are fitted with
a linear regression using Eq.(9). The linear fit provides the unknown constants A and B, and hence the initially uknown offset
x0 . Once the offset value is known, the actual radius r is known
r j = x j − x0 ,
The fringe spacings d is obtained as
d=
2π frot
,
A
Uncertainty of New Method
The uncertainty of the new method is examined in the following.
The calibration velocity is written as
(9)
The constants A and B are
ucal = rcal ω = (xcal + x0 )ω,
2π frot
,
d
2π frot
B=
x0 .
d
B
where x0 = − .
A
A=
(14)
where the rotational frequency frot is known. Since the constant
A is the slope of the linear regression, the fringe spacing is obtained even without the need of knowing the offset value. The
stage coordinate can be known with a relatively small uncertainty
by means of a position sensor or an encoder embedded in the linear stage.
(8)
In fact, the true orbit radius is inaccessible. Instead, we have
the radial displacements from the linear precision stage. Since
the linear stage is traversed in the radial direction, the relationship between the Doppler frequency and the stage coordinate x j
becomes linear
f j = Ax j + B.
(13)
(10)
(15)
with rcal and xcal being the radius and stage coordinate values at
the calibtation. Hence, the radial uncertainty becomes
(11)
σrcal =
(12)
4
√
(
σ xcal
)2 ( )2
+ σ x0 ,
(16)
c 2012 by ASME
Copyright ⃝
being σ x the uncetainty of the stage coordinate, equivalent to
the positional uncertainty such as unidirectional/bidirectional repeatability. The stage coordinate and the offset are assumed to
be statistically independent here. The offset uncertainty is further expressed as
Mounted Pinholes
Rotating Disk
Nomial Center of Rotation
√
(
σ x0
)2 (
)2
∂x0
∂x0
σA +
σB
=
∂A
∂B
√
(
)2
)2
(B
1
σA + − σ B .
=
A
A2
Pinhole
(17)
FIGURE 4.
Multiple pinholes attached on the chopper blade of a commercial optical chopper in the first experiment.
(18)
The estimation uncertainty of the fit constants are provided as
[11]
√
σA = σ f
σB = σ f
√
N
,
Λ
(19)
Σx j 2
,
Λ
(20)
where Λ = N
N
∑
j=1
2

N

∑
x j 2 −  x j  .
Optical Chopper Blade
(21)
j=1
Rotating Disk
(Pinholes clamped inside)
where the σ f is the uncertainty of the Doppler frequencies being
in the order of 10−4 ∼10−3 at a typical condition. The remaining
is the uncertainty σ x j of determining the respective scattering
location. It depends on the realization described in the second
experiment. The resulting uncertainty of the claibration velocity
follows Eq.(7) in the same way as the single scattering object
σucal
= ucal
ucal
√
(σ
rcal
rcal
)2 ( σ )2
frot
+
.
frot
FIGURE 5.
The rotating disk in the second experiment. It contained
five pieces of unmounted pinholes clamped inside. The white labels
with numbers indicate the pinhole number 1–5 from inside to outside.
whose rotation was regulated using a phase-lock-loop. A simple LDV was built using a laser diode as a laser source and a
diffractive grating for splitting beams. The nominal value of the
fringe spacings was 4.5 µm with the working distance of 50 mm.
A non-automated manual linear stage was employed and a laser
triangulation sensor (Micro-Epsilon: ILD1700-10) was used together. The position sensor monitored the displacement of the
linear stage with a precision of 0.5 µm. The feature of this experiment was the determination of the scattering location using an
oscilloscope with visual inspection of the signals by the experimentalist. This half manual method caused certain ambiguity,
which would be improved in the second experiment. The resulting variation of the fringe spacings regarded as the uncertainty
became 0.24 % [8].
(22)
Finally, the calibration uncertainty is obtained through Eq.(5).
Feasibility Experiments
The new calibration method was realized with three different setups. Calibration experiments were carried out in order to examine their feasibilities and performances.
First Experiment The first setup was built only for checking the fundamental feasibility of the method. Five pieces of
mounted pinholes with an aperture diameter of either 2 µm or
5 µm (Edmund Optics: mounted precision pinholes) were attached to a specially fabricated disk such as shown in Fig. 4. The
disk was attached to an optical chopper (Thorlabs: MC1000),
Second Experiment The second experiment had two improvements compared to the first one – in terms of axial uncertainty of the pinholes and the scattering locations. In constrast
to the mounted pinholes, unmounted pinholes of 2 µm aperture
diameter (Edmund Optics: unmounted precision pinhole) were
5
c 2012 by ASME
Copyright ⃝
Linear Actuator with
an Integrated Encoder
Rotating Disk attached
with 5x Pinholes
Self-Made LDV System
Detection Optics
(Forward Scattering)
Measurement Volume
FIGURE 6. The second calibration experiment using multiple pinholes and motorized lienar precision stage.
FIGURE 7.
Local Gaussian fit for determining the accurate, reproducible scattering point inside the measurement volume.
clampted flush to the flat inner surface of the disk as shown in
Fig. 5. This way of mounting pinholes eliminated the axial ambiguity of the scattering locations. The other improvement was
the determination method of the scattering location in the stage
coordinate. In order to determine the precise location of every
scattering object, a stable referece point is required inside the
measurement volume. We chose the center of the measurement
volume as the refernece point, since the optical intensity becomes
maximum and hence the resulting Doppler signals always exhibit
the largest amplitude and the highest signal quality at the center.
Taking into account of these features, we recorded both the SNR
and the amplitude values of the Doppler singals in time domain.
The radial traverse was done at small steps of the stage coordinate around each pinhole such as shown in Fig. 7. Either the
recorded SNR or amplitude values were fitted with the stage coordinate values assuming the Gaussian distribution
(
ξ = C0 exp
x j − x jc
σj
δξ =
(24)
The first two terms can be neglected since the variation of the
first two terms should be sufficiently small compared to that of
the parameter x j in the third term. Hence, the variation of the x j
becomes
δx j =
δξ
∂ξ
∂x j
.
(25)
The variation is calculated for all the local points around j-th
scattering object (k=1,. . .,M) and the resulting uncertainty for the
x j is obtained as an average
)2
,
∂ξ
∂ξ
∂ξ
δC +
δσ +
δx .
∂C0 0 ∂σ j j ∂x j j
√
(23)
σx j =
where ξ is either the SNR or the amplitude values of the Doppler
signals. The parameters C0 and σ j are constants. Both the SNR
and the signal amplitude should take maximum value at the center of the measurement volume. Hence, the scattering center of
the j-th object x jc is the position where the Gaussian distribution becomes locally maximum. The maximum point is obtained
through an interpolation either nonlinear Gaussian fit or simple
three-point parabolic fit in natural logarithmic domain commonly
used for Doppler frequency estimate of an LDV [2]. This Gaussian fit provides very precise locations of the scattering points
in the final calibration and hence reduced the umbiguity of the
procedure in the former visual method. The determination uncertainty of the scattering center is calculated through a linear
approximation, neglecting the higher order terms
∑M
k=1 (δ x j )
M
2
.
(26)
Once this uncertainty of the scattering position is determined, the
uncertainty of the calibration radius is obtained through Eq.(16).
Further details of the other potential uncertainty sources not mentioned in the present paper are discussed in Shirai (2010) [8].
Fig. 6 shows the setup of the second experiment. Four pieces of
the pinholes out of the five functioned properly during the experiment. We used a motorized linear precision stage with an integrated encoder (Newport Corportation: CONEX TRA25CC).
The positional uncertainty of the stage was σ sc =2µm according
to the specification sheet of the manufacturer. The typical result
of Gaussian fit for the SNR and the amplitude are shown in Fig. 8.
The SNR was expected to be more robust than the amplitude of
the signal in time domain. In contrast to this expectation, we
6
c 2012 by ASME
Copyright ⃝
(a) SNR
18
original data
Gaussian fit
fitted center
17
16
AMP
SNR [dB]
TABLE 1. List of the relative uncertainty values for respective pinholes 2–5 (pinhole 1 did not function) based on SNR and amplitude
(AMP) values of the signals.
(b) Amplitude
original data
Gaussian fit
fitted center
15
14
13
12
11.58 11.6 11.62 11.64 11.66 11.68 11.7 11.72
0.24
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
11.58 11.6 11.62 11.64 11.66 11.68 11.7 11.72
x [mm]
σr /r [%]
x [mm]
FIGURE 8.
Comparison of the Gaussian fit in the second experiment,
(a) SNR, (B) amplitude.
σd /d [%]
pinhole♯
SNR
AMP
SNR
AMP
2
0.767
0.190
0.961
0.190
3
2.501
0.183
0.910
0.183
4
0.256
0.172
0.912
0.172
5
0.980
0.144
0.843
0.144
1.35
f [MHz]
1.3
four pinholes
initial linear fit
iterative linear fit
1.25
1.2
sult. However, this way of the realization is the simplest and may
be the most realistic without complication, because an off-theshelf LDV system with a backward-scatter detection mode can
be directly applied without any modification to the system. A
commercial LDV system with a fiber-optic probe (TSI: TR260)
with an air cooled Ar laser for two velocity-component measurement was used for this experiment (see Fig. 10). A blackpainted disk was attached to a DC motor (Maxon Motor: ECmax 30). Only the blue-beam pair (λ=488 nm) was used in this
experiment and the scattered light was detected with a photomultipleier unit. The Doppler frequencies were direclty caliculated by an equipped hardware processor (TSI: FSA3500). One
of the typical results is shown in Fig. 11. Not all the measurement points are aligned on the perfect linear line, hence only the
points on the line were used for the linear fit. The selected points
seem to be on an almost perfect linear line. An iterative procedure included in the fitting algorithm has slightly improved the
fit result but the improvement is hardly discernible in comparison with the simple linear fit. The calibration was done with the
optical chopper operated at frot =20 Hz and the working distance
of the probe at 261 mm. The resulting fringe spacing from this
condition (Fig. 11) was d=2.52±0.06 µm, which indeed covers
the specification value of d=2.55 µm for this probe. The relative
uncertainty becomes 2 % in the sense of single standard deviation in this case. This relatively large uncertainty was attributed
to the scattering which took place at multiple locations. All the
illuminated locations inside the measurement volume scattered
the light, so the scattering locaton was not fixed to a single point
such as in the case of the second experiment in which pinholes
were used as single scattering objects. Hence, the scattering location was determined with a large uncertainty around the half
diameter of the laser beams at the measurement volume. In spite
of the uncertainy, the realization of the third experiment was the
simplest compared to the other ones and its feasibility was confirmed accordingly.
1.15
1.1
39
40
41
42
43
44
45
r [mm]
FIGURE 9.
Linear fit of the Doppler frequency to the stage coordinate of the four pinholes in the second experiment. The local scattering
positions were determined by using the signal amplitudes in this figure.
observed that the amplitude provided more reliable center in the
present experiment (compare the two plots in Fig. 8). The resulting linear fit of the Doppler frequency to the stage coordinate of
the four pinholes is shown in Fig. 9. Based on the determined orbit radii of the four pinholes, calibration was done for the respective pinholes based on the SNR and the amplitude, respectively.
The radial uncertainty σr /r was determined and the fringe spacings were caliculated with their uncertainties σd /d. The results
are summarized in Tab. 1. The resulting fringe spacings value
were consistent each other between the ones determined based
on the SNR and the other on the amplitude (AMP), although the
ones based on the SNR has larger scatters of the measurement
points in Fig. 8. The resulting uncetainty values of the fringe
spacings have been reduced into 0.14 %–0.19 %. This improvement is achieved by the local Gaussian fit for determining the
scattering locations with small uncertainty.
Third Experiment The scattering object is not limited to pinholes. The third calibration setup was built in a more simple way.
The pinholes were replaced with the surface roughtness of a disk.
The scatteirng may occur everywhere on the illuminated area and
hence the resulting Doppler signal may be the superposition of
multiple scaterings. This would increase the ambiguity of the
positional determination as we would see in the uncertainty re7
c 2012 by ASME
Copyright ⃝
Rotating Disk (The surface
was painted black color.)
ACKNOWLEDGMENT
This work was partly supported by the Deutsche Forschungsgemeinschaft (CZ55/20-1,2). The authors thank Mr. Janarthanan
Gnanaprakasam for his work in the second experiment. The calibration method and the devices reported in the present document is patent pending in the world wide. Please contact with
the Knowledge and Technology Transfer (GWT) at TU Dresden
for your further interest on technology transfer.
Optical Chopper
(Thorlabs Inc.: MC1000)
Measurement Volume
DC Servo Actuator (Newport
Corpotation: CONEX TRA25CC)
Commercial LDV Probe
(TSI Inc.: TR260)
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[7] Müller, H., Kramer, R., Strunck, V., Mickan, B., Dopheide,
D., 2001. “Laser-Doppler-Anemometer zur Darstellung
und Weitergabe der Einheit, Strömungsgeschwindigkeit
(in German)”, 9. Fachtagung, Lasermethoden in der
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[8] Shirai, K., 2010. “Development and application of novel
laser Doppler velocity profile sensors for high spatially resolved velocity measurements in turbulent shear flows”.
Dissertation, Dresdner Berichte zur Messsystemtechnik,
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[9] BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, 1995.
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[11] Taylor, J.R., 1997. An Introduction to Error Analysis (2nd
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FIGURE 10.
The third calibration experiment using a commercial
LDV system and the surface scattering of a rotating disk.
1.6
f [MHz]
1.4
1.2
original points
points used for analysis
initial polyfit
iteration
1
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
r [mm]
FIGURE 11.
Typical result of the lienar fit with the surface scattering
in the third experiment.
Conclusion
We developed a new calibration method for laser velocimetry
such as an LDV toward establishing the traceability of uncertainty in measurements. As the measurement is equivalent to reproduce the calibration velocity influenced by the accompanying
systematic uncertainties, an eatablishment of the uncertainty at
the calibration is required. The principle of the new method was
described and its uncerainty was analyzed along the GUM. The
analysis showed that the measurement uncerainty can be traced
throughout the caliration. Hence, it is possible to realize a qualified measurement with this new method as long as the traceabilities are maintained to the translation stage and the motor. The
new calibration system was tested in the three experiments with
the differnet realizations. The experiments indicated that the calibration uncertainty of down to 0.14 % can be achieved with one
of the setups. It was demonstrated that the new method was also
compatible with an off-the-shelf commercial LDV without any
modification. Development is continued toward the automation
and the improvement of the system with a further smaller uncertainty. This new portable calibration method provides measurement traceability to the end-users of laser velocimetries for their
own measurements which requires low effort but still establishes
tracerable uncertainty.
8
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