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Description
of software for measurement of time of flight, phase
velocity, dispersion, attenuation of sound and impedance
of materials.
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Agnieszka and Wiesław
Bicz
Mieczysław Pluta
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This software package
allows to measure time of flight, sound velocity,
attenuation and frequency dependence of attenuation,
dispersion, phase velocity and impedance (density) of
any material. The software uses ultrasonic pulses and
is based on comparison of pulses achieved with
reference and measured medium.
For each measurement it is necessary to choose
reference signal and compare it with the signal,
coming from the measured medium (reflected or
transmitted through it). This allows to use this
software with almost any kind of samples, containments
etc. For people using this software it is necessary to
have some knowledge about such kind of measurements,
physics of ultrasounds etc. This software package
gives them very good tool for such measurements.
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I. Introduction to the work with the software |
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First
step
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Reference signal should be prepared, the best way to
do it is to use pure (distilled) water. Using markers
in the upper window most important part of the signal
should be chosen. In the bottom window signal between
markers from the upper window can be seen - magnified.
See picture 1.
Picture
1.
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Second
step |
Button “Pattern” should be used. After
pressing this button, chosen signal appears in bottom
screen in white color together with information:
"Correlation pattern". It means this signal from this moment will be
“reference signal”. See picture 2.
Picture
2
From this moment key called "Measure" should
be used – all subsequent operations will use
signal stored before (pattern) as reference for
comparison with
actually measured signal. See picture 3. For time of
flight measurement the display will show 0 –
nothing changed.
Picture
3.
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Third
step |
In
this moment we have to repeat operations described in the
first step. In upper window we choose - using markers
the most important part of signal we are getting from
measured medium. In the bottom window we can see only
signal between markers from the upper window. See
picture 4.
Pay attention on
marker position (it is changed now). It means
now we have another signal (with time offset for
example)
Picture
4
In
this moment we have all information which is necessary for
calculation of time of flight (and another functions
too), and then the button “Measure” should
be used (see picture 5). On the bottom window we can see two earlier prepared signals (white –
reference signal; red - measure signal) in this case
we receive result different from zero.
Picture
5
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II.
The time of flight and sound velocity measurement method. |
In most cases we can
assume, that the signal will change after propagation
- simple geometrical comparison of signals won’t
work properly. This is the reason, why we are using
following algorithm for comparison of two signals with
different time of flight:
a)
FFT
with Hamming window is made.
b)
In
frequency domain, frequency with maximum amplitude is
chosen and using relatively sharp windowing only this
frequency and frequencies from its neighborhood are
taken.
c)
Inverse
FFT is done.
d)
Center
point of achieved signal is taken as time mark,
telling us the moment of “coming” of this
signal
Time
of flight can be measured from zero point (start of
pulse) or from the time of “coming” of
another signal, stored as pattern – as described
above.
If
the path length is known, it is possible to calculate
the sound velocity in the measured material, using
comparison with reference fluid – for example
water.
If
the experimental setup have a containment with
measured fluid, where only a part of the sound
propagation path is in the measured fluid, we can
wrote following formula:
T=T1+T2
Where
T1 is time of propagation outside of
measured fluid and T2 in this medium.
We
can measure time of flight in the whole system (T)
filled with water (TW, that has velocity CW),
or measured fluid TX (velocity CX).
If we know the path length (L) in measured fluid, we
can calculate the velocity of
sound in this medium:
T2w=L/CW
T1=TW-T2W
This
(T1) can be obtained after measurement with
water, and this measurement must be done only from
time to time, since parameters of system doesn’t change quickly.
CX
(sound velocity in measured medium) = L/(TX-T1)
The
user of the software must know the path length (L),
and choose appropriate signals (not only direct
transmission must be chosen, but also multiple
reflections for example).
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| III.
Theoretical basis of material impedance measurement
method |
The measurement of
impedance of an unknown medium can be based on
evaluation of the wave, reflected on the interface of
this medium with another medium (i.e. wall of solid
material - in most cases), eventually transmitted wave
too, and comparison with reflection from another
medium with known impedance.
Meanings
of used variables:
Z
- impedance of
medium (unit is Ns/m3)
R
-
the relation of
reflected and transmitted wave (their intensities)
r
- density of material
(g/cm3)
c
– sound velocity
(m/s)
IR
- intensity of
reflected wave
It
- intensity of
transmitted wave
Geometrical
representation:
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Material
1 (i.e. solid wall) |
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Material
2 (measured medium, water or air) |
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Z1=r1c1 |
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Z2=r2c2 |
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Incident
wave with intensity I |
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Transmitted
wave with intensity IT |
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¾® |
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¾® |
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Reflected
wave with Intensity IR |
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¬¾ |
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In
most cases we are only able to measure the reflected
wave and not the transmitted (this will be disturbed
during propagation in unknown medium). This is the
reason, why it is normally necessary to know the
impedance of the solid wall. But it is also possible to measure it using air as reference
medium (material 2). In this case the measurement
would need following steps:
1)
Measurement
of reflection from the solid wall in contact with air
- result is the intensity of incoming wave. If we know
the impedance of the wall material, this measurement
is not necessary – the intensity can be
calculated from the measurement made in the second
step.
2)
Measurement
of reflection from solid wall in contact with
reference fluid with known impedance (for example
water) – this is only necessary for obtaining
value of wall material impedance. If we know this
parameter, we can calculate R for water and do not
need the measurement with air (we are able to
calculate the intensity of incoming wave).
3)
Measurement
of signal reflected from measured fluid.
If
the setup doesn’t change, measurements from
steps 1 and 2 must be done only from time to time (relatively
seldom). The formulas used here are as follow:
R=IR/IT=
(Z2-Z1)/(Z2+Z1)
I=IR
+ IT=const
I
is the same in each case - with any material, because
it depends only on used transducer and pulser, and can
be also directly measured in comparison with air (which
has almost 0 impedance and thus 100% reflection
– IT»0)
or calculated if we know both impedances (Z2
and Z1 – this is the case, if we know
the impedance of the wall material and are using known
fluid, for example water).
I=IR+IR/R
(if we know R and IR)
We
can measure IR (reflected wave) or IT
(transmitted) wave. If we know only IR, and
the intensity of the incoming wave I, we can calculate
R:
R=IR/(I-IR)
After
comparison with another substance we are able to
calculate the impedance of the measured substance:
Z1=Z2(1-R)/(1+R)
Z2=Z1(R+1)/(1-R)
The
first equation is necessary to calculate the impedance
of wall material (assuming, that Z2 is the
impedance of known material – i.e. water) and
the second for calculation of impedance of measured
material (Z1 is impedance of wall material).
In
the case of impedance measurement only with reflected
signal it is not necessary to measure the signal using
FFT filtration, because it doesn't change the shape (only
in special cases, that are not realistic here). But
this is also not worse, if we do it.
If
we know the impedance and sound velocity of a material,
we are able to calculate the density (r=c/Z).
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IV. Description of method for measurement of phase
velocity, dispersion and attenuation of sound |
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A.
Introduction |
The idea of the
measurement is based on sending and receiving signals
through measured medium. This operation is repeated
many times, after some time period or after some
changes was made (different material, temperature
etc.). Each received signal can be described by
 where
n=1,2,...N. Each signal can be also described using
its Fourier transform:
 (1a)
after
inverse Fourier transform is applied, signal can be
restored from his spectrum   (1b)
The distribution of harmonics of this spectrum shows the transfer function
of the whole unit, where  is
the function of electronics (generator, transducer,
amplifier...), wave propagation  , including diffraction effects  and
influence of the medium  .
 (2)
In
evaluation of material properties the most interesting
thing are changes of medium properties  . Thus it is necessary to design the system in the
way, that all other elements are negligible (at least
in frequency region of interest). This means, that it
is necessary to use:
a – broadband devices (capable of
transmitting and receiving short pulses),
b – transducer with small or
controlled diffraction effects.
In all cases of relative measurements, where measured signal is compared
with reference (index zero), it is allowed to assume,
that the characteristic of electronics  and geometry of the system
 do
not change. Thus:
 (3)
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B.
Measurement with changing distance: |
Measurements
made in two distances  and
 (4a)
 (4b)
Compound factor responsible for propagation
 (5)
we are writing it as
where
 ,
 -
slowness
 - attenuation
coefficient.
For the case without attenuation and
dispersion
(6a)
We are writing it as the superposition of
propagating waves
(6b)
Careful comparison of this both formulas
allows to see, that propagation of wave packet can be
treated as a superposition of harmonic waves with
different slowness
(6b). From (6a) follows, that with the distance
compound amplitudes of harmonics are changing:
Imaginary part of the coefficient 
is responsible for attenuation. Inclusion of this
effect for chosen harmonics allows us to write
compound amplitude after propagation:
Calculation of compound coefficient
is possible after logarithm of formula (5)
 (7)
where
Difference of compound amplitudes
In large distances this difference changes
quickly with frequency and if it is larger than 
we get non continuous phase readings. In this moment,
for the purpose of doing the phase continuous, it is
necessary to be able to estimate the properties of the
medium and try to make a model, that follows the
reality. To calculate the dispersion we describe
slowness as containing two parts – constant and
changing:
where first two parts are describing the
propagation in a medium without dispersion (see (6)).
Phase velocity is calculated from phase difference:
 ,
and from this equation
(8)
The calculation of attenuation using this
method gives realistic results in the central region
of transfer bandwidth, under the condition, that
propagation is going only in one mode (only one path).
If many paths are existing, interference effects occur,
that are causing waves in the attenuation diagram. The
existence of such effects can be shown after
measurements for some distances and comparison of
results. In the border region of transfer function
noise occurs, resulting from division of two small
noise functions.
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C. Measurement with
changing medium parameters.
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We are going back to describing individual measurements using 
and reference signal with
 .
For relative measurements it is necessary to
store reference measurement, made with known medium.
For water solutions the best way could be to use water
as reference medium. Treating attenuation of water as
negligible and taking slowness 
of water as reference, for calculation of attenuation
and dispersion of measured medium we can use modified
formulas (7)
and (8):
 (9)
 (10)
Similar formulas can be used for calculating changes of attenuation and
dispersion of medium. As reference one of the previous
done measurements can be taken.
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| Legends |
Formulas are given for continuous
variable t, but in computing we are using
discrete variable iT, where T is the
sampling period.
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| For
download |
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material parameter
measurement.pdf
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