Lund university
BACHELOR DIPLOMA WORK
Developments of detection of X-ray
scattering in combustion
- characterization of noise levels of an A/D sampling device
Björn Annby-Andersson
Supervised by Frederik Ossler
Department of Physics
Division of Combustion Physics
May 2016
Abstract
A simple investigation about the noise of the acquisition cards NI PXI-4495, provided
by National Instruments, was performed. Standard deviations were calculated for data
acquired from a signal generator, a constant voltage source and when the input channels
were grounded, to estimate the noise. The obtained noise is in the order of a few millivolts
when acquiring signals from the devices while the noise when grounding the system is in
the order of microvolts. The device’s ability to resolve the presence of graphite in a simple
model of a graphite/air mixture is presented. Possible situations in which the acquisition
device can be utilized are when measuring single event processes. Measurements on
combustion engines or chemical reactors are two proposed situations.
2
Acronyms and abbreviations
SAXS Small angle X-ray scattering
WAXS Wide angle X-ray scattering
RPM Revolutions per minute
A/D Analog to digital
SD Standard deviation
RMSD Root-mean square difference
3
Contents
Abstract
2
Acronyms and abbreviations
3
Populärvetenskaplig sammanfattning
6
1 Introduction
7
1
Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3
The work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Experimental
1
Test of acquisition cards . . . . . . . . .
1.1
Signal generator . . . . . . . . . .
1.2
Grounded input channels . . . . .
1.3
Pre-amplifier or constant voltage
2
Signal analysis and interpretation . . . .
3 Results
1
Standard deviations . . . . . . . . . . .
1.1
Signal generator . . . . . . . . .
1.2
Grounded input channels . . . .
1.3
Standard deviations when using
age source . . . . . . . . . . . .
2
Signal analysis and interpretation . . .
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a
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4 Discussion
1
Comments on the result . . . . . . . . .
1.1
Signal generator . . . . . . . . . .
1.2
Grounded input channels . . . . .
1.3
Pre-amplifier or constant voltage
1.4
Signal analysis and interpretation
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5 Outlook
25
Acknowledgements
26
Self reflection
27
References
28
4
Populärvetenskaplig sammanfattning
Under förbränningsprocesser bildas mycket
små partiklar av storleksordningen 1-100
nanometer och kallas därför nanopartiklar.
Nanopartiklar utgör beståndsdelarna i det
vi känner som sot. En nanometer är en etthundramiljontedels meter. Detta är svårt
att föreställa sig. Istället kan man jämföra
längden av ett par centimeter med längden
av en resa runt ekvatorn.
Nanopartiklar är så otroligt små att de
är omöjliga att se med blotta ögat. Istället måste speciella tekniker användas för att
detektera dem. En metod som används i dagens forskning är baserad på röntgenspridning. Som namnet föreslår, är det röntgenstrålning som används, alltså samma typ av
strålning som används för att ta röntgenbilder av skelettdelar. När undersökningar
kring nanopartiklar inom förbränning ska
genomföras skickar man röntgenstrålningen
in i en (brinnande) flamma. Strålningen
sprider sig sedan av sot- och nanopartiklar
i olika riktningar. Den spridda strålningen
som samlas in kan ge svar på vilka partiklar som faktiskt finns inne i flamman, vilken
storlek och struktur de har och i vilken koncentration de förekommer.
En fråga som bör ställas är; hur kan
kunskapen om sot- och nanopartiklar utnyttjas? Partiklar av nanostorlek kan å ena
sidan vara skadliga för hälsan och miljön
men å andra sidan vara viktiga inom industrin. Hälsobesvär kan uppkomma vid
inhalation av nanopartiklar då de fastnar i
våra luftvägar. Väl inne i kroppen tar de sig
lätt igenom biologiska vävnader och orsakar
skador på inre organ men även på cellmembran. Sotpartiklarna som befinner sig i at-
mosfären absorberar solljus och värmer upp
den omgivande luften. Sot kan också deponeras på is och ge ytterligare smältning av
glaciärer och isar. Jordens temperaturökning är en aktuell fråga och forskningen kring
sot- och nanopartiklar kan bidra till en reducering av temperaturökningen.
Hur kan då dessa små, små partiklar vara användbara? I ett samhälle där
tekniska apparater blir mindre och mindre krävs metoder för att tillverka material som har speciella mikroskopiska egenskaper. Om mekanismerna bakom bildandet av nanopartiklar och deras aggregation
kartläggs kan nanomaterial tillverkas genom
kontrollerade processer i, till exempel, flammor. Dessa material kan sedan användas
i industrier som medicin och elektronik.
Inom medicin används redan nanomaterial
för att transportera aktiva substanser inom
kroppen.
Under detta kandidatarbete har ett datoriserat insamlingssystem för röntgenspridningsdata testats. Systemet är utrustad
med hårdvara som skall registrera signaler
upptagna av detektorer.
Datainsamlingen sker parallellt i 64 kanaler, där varje
kanal representerar en viss spridningsvinkel
i datainsamlingen. En undersökning av
insamlingssystemets prestanda har gjorts
med hjälp av en signalgenerator för att
bestämma de signalnivåer som man kan
vänta sig att upplösa. Dessa nivåer ger då
en uppfattning av vilka koncentrationer av
små nanopartiklar som kan detekteras. I
detta arbete har nanometerstora grafitpartiklar i luft valts som teoretiskt exempel.
6
Chapter 1
Introduction
1
Motivation
Soot and nanoparticles are formed during combustion with rich fuel/air mixtures. The
formation and properties of these particles are especially interesting from different points
of view.
First of all, there exist serious health issues that are related to nanoparticles. They can
provoke cancer and can cause respiratory problems. For example, inhaled nanoparticles
deposit with high efficiency in the entire respiratory tract due to diffusion [1]. Membranes
and biological barriers can easily be penetrated by nanosized particles where they cause
damage on cellular membranes and inner functions [2].
Another important issue is the impact of nanoparticles on the environment. Air pollution and biological damage on plants or animals are of considerable interest. Soot particles
are believed to contribute to climate change. They absorb sun light and transfer heat to
the surrounding air in the atmosphere, the warmer air later contributes to the melting
of, for example, glaciers [3]. The increasing temperature of the earth is currently of great
concern and needs to be dealt with.
Studying the formation of nanoparticles in hydrocarbon flames can reveal the mechanisms responsible for the formation and theoretical modeling can be developed. Emissions
of dangerous particles can be reduced and better controlled manufacturing of nanostructured materials can be achieved if the key mechanisms are known. The manufacturing of
nanosized material are already ongoing in fields as medicine where, for example, active
substances are encapsulated in nanostructured capsules for transportation inside the body
[4]. Other fields where nanoparticles are used are in confection and electronics. In combustion, the production of nanostructured particles have already been performed. Silica,
titania and iron oxide have been manufactured in hydrocarbon flames [5-8].
To probe the dynamics and structures of soot particles, detection systems as the one
presented in [9] can be used. Detector noise and deviation are important to keep in mind
when performing measurements, in particular for single events, when possibilities for time
averaging gets difficult. A too high noise level would make it impossible to distinguish
characteristic signals originating from events that is supposed to be measured. The performance of the detector system, in terms of dynamic range and signal level resolution
becomes very important to detect rapidly changing signal levels. The evaluation of the
real performance of the system will be necessary to understand the range of application
it can be used for. In this work, the results form an investigation of the performance of
a multi-channel data sampling device are reported. The instrument is a newly upgraded
7
version of the device used for X-ray scattering reported in [9].
Previous investigation related to single event dynamics of a burning match was performed in [9]. What is interesting to know is in what situations, besides flame measurements, the acquisition device can be utilized. Single event processes such as explosions,
measurements in flames or chemical reactions are of interest because of the fast sampling
rate of the device (204800 S/s). Two possible measurement situations are presented below:
• All four strokes of a 4-stroke engine can be probed with the system. Especially
interesting would be to examine the soot/nanoparticle formation during the combustion stroke. It would be possible to examine the dynamics for different fuel/air
mixtures. A comparison between what particles that are formed using different
ignition techniques could be investigated. Other interesting research could be in
which particles are formed as a function of rpm (revolutions per minute) or temperature. The high pressure achieved during the compression stroke could launch
reactions yielding nanoparticles. Species and the species’ concentrations are interesting parameters during the exhaust stroke. Mapping out the toxic and dangerous
nanoparticles in the exhaust gas is one of the first steps of improving particle filters. The temperature’s impact on nanoparticle formation during the intake stroke
is another area to investigate.
• Measurements on formation and dynamics can be performed in chemical reactors.
Formation rates could be examined for different conditions such as; temperatures,
pressures or stirring velocities. The development of reactors can be performed using
the results of previously mentioned experiment proposals to enhance the efficiency
of reactors to reach the highest possible yield of a product.
2
Background
X-ray scattering is a non-intrusive measurement technique that is performed in-situ. This
measurement technique does not affect temperature, species concentration or flow fields
that strongly influences dynamics. Methods that is preformed ex-situ results in local
disturbances on temperature and flow conditions, information about formation dynamics
and concentration is lost. X-ray scattering is a technique that is used to probe information about size, structure and concentration of nanostructured particles in, for example,
combustion. The scattered intensity, I(q(λ, θ), θ, φ), is measured, [10]
I(q(λ, θ), θ, φ) =
I0 cre2 p(θ, φ)N
m
X
x̂j
j=1
dσ(q)
dΩ
∆Ω(θ)∆V (θ)
(1.1)
j
where I0 is the irradiance of the source, c is a calibration factor, re is the classical electron
radius, also known as the Thomson scattering length, and ish 2.82i· 10−15 m, N the total
number of species, x̂j the mole fraction of species j and dσ(q)
is the corresponding
dΩ
differential scattering cross-section, ∆Ω(θ) the solid angle corresponding to the scattering
angle θ and ∆V (θ) is the measured volume at θ. The momentum exchange, q, in the
scattering process between particle and X-ray is [11]
q=
4π
sin(θ/2)
λ
8
(1.2)
where λ is the wavelength of the X-ray and θ is the scattering angle, which is, the angle
that emerge between the X-ray beam and the scattered X-ray. In Fig. 1.1 a simple image
of the scattering process is depicted. A X-ray beam traveling in the x direction is scattered
by the particle, the plane spanned by the scattered X-ray and the X-ray beam is called
the scattering plane. φ is the tilting angle of the scattering plane with respect to the xy
plane, which corresponds to the plane of polarization of the beam.
Figure 1.1: Simple imaging of the process where a X-ray is scattered by a particle.
The polarization factor, p(θ, φ), in equation 1.1 is [10]
p(θ, φ) = 1 − cos2 φ sin2 θ.
(1.3)
For convenience the ratio, γ(q), of the scattering signals to a reference signal is calculated,
[11]
γ(q) =
I(q, θ, φ, t)
I(q, θ, φ, t0 )
(1.4)
where t0 is the starting time for collecting data. This representation is preferable to use
when studying dynamic objects in order to detect modifications in the system with respect
to known initial conditions [9]. This ratio can also be given as relative to a steady state
condition, e.g., air, if one wants to compare changes with respect to conditions of pure
air.
Especially two X-ray scattering techniques have been utilized in [9-13] to probe characteristics of soot particles in flames, namely small- and wide-angle X-ray scattering (SAXS
and WAXS) [14-19]. Data recorded with WAXS includes information about the structure of small nanoparticles and soot [10] while SAXS provides information about size
distribution of particles in the 1-100 nm range [11]. The detector system developed in
[9] included a 20-channel SAXS detector and a 6-channel WAXS detector able to acquire
data for hours every 5 µs.
The differential cross-section, dσ/dΩ (later denoted with σ), mentioned earlier, quantifies the intrinsic rate of an event. In a flame where hundreds of species are present it
requires a lot of work to calculate the differential cross-section for every species. Instead,
one deals with three groups of particles; atoms and small molecules, particle precursors
or poly-cyclic aromatic hydrocarbons (ca 100 carbon atoms) and small structural species
like small nanoparticles or larger particles with 100 or more carbon atoms [10].
9
Calculated differential cross-sections for graphite constructed out of graphene layers
are dependent of the number of layers and the inter-layer organization [10].
3
The work
A first-level evaluation of a newly upgraded version of the acquisition device used in
previous work [9-13] was done in this project. The upgrades included increased processor
capacity and number of channels. The setup is presented in Fig. 1.2. A X-ray beam is sent
through a flame. X-rays scatter in different directions by nanoparticles in the flame. The
WAXS or SAXS detector detects X-rays dependent on the angle they scatter. The X-rays
that enter the detectors is transformed to electrical signals through the scintillators/PMT
or diode installations. A pre-amplifier converts the current output of the PMTs to voltage
and the signal is acquired by the A/D cards in the acquisition device. Previously, 26
channels have been utilized during measurements, but, with the increase in number of
channels, 64 detectors can be used for simultaneous data acquisition. New detectors
can, hence, be added to the detection system. Placing detectors in scattering angles
corresponding to values of q that have not been measured in previous work, an increase
in the measurable q-range can be achieved. Structures which have been non-measurable,
due to the lower number of channels, in previous work can in the future be measured.
Also, the resolution of already known structures can be enhanced due to the increase of
channels.
The influence noise has on measurements is discussed. A theoretical case is given for
different concentrations of small graphite nanoparticles in air.
The work includes implementation of LabVIEW software for acquiring data on multiple channels simultaneously.
10
Figure 1.2: Setup used for X-ray scattering measurements carried out in flames using
N channels. The circle represents the flame which the X-ray beam intersects. Each
channel has either a scintillator/PMT or diode installation. The pre-amplifier transform
the signals from current to voltage and the sampling device acquires the signal. The Xrays scatter with different angles and, hence, the detector channels need to be placed at
different locations.
11
Chapter 2
Experimental
The computer used for the acquisition of data, a NI PXI-1042 from National Instruments,
was equipped with 4 acquisition cards (named Dev1, Dev2, Dev3, Dev4) of the type NI
PXI-4495, see Fig. 2.1. Each acquisition card had 16 input channels. A junction splitting
a signal into 16 equivalent signals was used in order to measure the same signal in all 16
channels of one acquisition card at the same time. The maximum sampling rate of the
acquisition cards was 204800 Samples/s (one sample each 5 µs). This sampling rate was
used for all acquisitions carried out during the experimental work.
Figure 2.1: The NI PXI-1042 acquisition device. The parts of the device are; (1) CPU,
(2) Dev1, (3) Dev2, (4) Dev3 and (5) Dev4.
1
1.1
Test of acquisition cards
Signal generator
A signal generator, Rigol DG1022A, was used to produce a known sinus signal, this signal
was split by making use of the junction mentioned earlier. A known signal was recorded
on 16 channels using one acquisition card at a time. Acquisitions for sinus signals with
12
0.1, 1, 10, 50, 90 and 100 kHz frequency and 2.5 V amplitude were made. The standard
deviation was calculated in every measurement point for each acquisition card in order to
evaluate if there was any strong deviations in the acquisition. The deviation was estimated
as noise. The standard deviation was calculated with
v
u
n
u 1 X
(µi,k − µ̄k )2
(2.1)
SDk = t
n − 1 i=1
In the equation above, k is the index of measurement point, n is the number of channels,
i.e. 16 in this thesis, µi,k is the acquired value for the i:th channel at the k:th measurement
point and
Pn µ̄k is the mean value for the k:th measurement point, which is defined as
1
µ̄k = n i=1 µi,k .
A sinus function, F (tk ), was fitted to the mean data, µ̄i , of the acquired sinus signal
for several frequencies.
F (tk ) = A sin(2πf tk + φ) + B
(2.2)
where A is the amplitude, B is an offset parameter, f is the frequency, t is time and φ is
the phase.
To fit the sinus function to the mean data, the root-mean square difference sum
(RMSD) was minimized by hand, modifying the parameters of F (tk ).
v
u
N
u1 X
|F (ti ) − µ̄i |2 ,
(2.3)
RM SD= t
N i=1
in the equation above µ̄i is the mean value of the signal required in every measurement
point, N is the number of measurement points. The acquisitions were performed over a
few seconds which generated values of N around a few hundred thousand.
1.2
Grounded input channels
A 50 Ω resistor was connected to the end of the splitting junction to ground the inputs
to the data acquisition cards and data was acquired on every channel on each of the
acquisition cards. The standard deviation was calculated for each acquisition card in the
same manner as explained in the previous section. This measurement was an estimation
of the inner noise of the acquisition device.
Frequency spectra was studied for every channel to evaluate if the input channels would
pick up or generate any noise showing up as disturbing frequency components during the
acquisition.
1.3
Pre-amplifier or constant voltage
A pre-amplifier was connected to the splitting junction. Data acquisition was performed
simultaneously on every channel for one acquisition card at a time. Two sets of data were
recorded for each acquisition card, either the pre-amplifier was turned ON or OFF. The
standard deviation was calculated for every moment in time for each data set.
A simple device with a 9 V battery, an ON/OFF switch and an output was connected
to the splitting junction. Data acquisitions were done simultaneously on every channel for
each acquisition card. The standard deviation was calculated for every sampling event.
13
2
Signal analysis and interpretation
Knowing the theoretical differential cross-sections for air and graphite gives the opportunity to calculate the differential cross-section for a mixture of air and graphite. The
graphite used in this work was of a 4 layer structure, each layer separated by 3.4 Å and
shifted 1.42 Å with respect to the neighboring layers. The number of carbon atoms in the
structure was 352. The differential cross-sections used in this work were numerically calculated, with φ = 50◦ , from reference [3]. To calculate the total differential cross-section,
σtot , for a mixture of air and graphite the following equation was used,
σtot ∝
σL + xσG
NL σL + NG σG
=
NL + NG
1+x
(2.4)
where x = NG /NL , NL and NG are the number of air and graphite particles in the mixture,
respectively, σL and σG are the differential cross-sections for air and graphite, respectively.
The total differential cross-section was plotted for different values of x and compared with
the individual differential cross-section for air and graphite.
The standard deviation obtained for the acquisition made with a constant voltage
source was simulated as noise to get an estimation of how large concentrations of graphite
in air that is needed to distinguish a structure representing the one for graphite. The
following equation was used to plot the mixture’s differential cross-section, σsig , including
simulated noise, normalized to the differential cross-section of air σL ,
σtot (1 + noise)
(2.5)
σL
where noise represents the simulated noise in shape of the standard deviation obtained
using a 9 V constant voltage source. Any noise from the measurements done in this thesis
could have been used but the interesting part is to see what happens with measurement
data when noise is included. A crude estimation of how much graphite is needed in a
graphite/air mixture to be able to detect the presence of graphite in the mixture was
done. This was done by plotting γsig for varying values of x to see for which x the shape
of γsig would retain features that could be evidenced above the level of noise.
γsig =
14
Chapter 3
Results
1
Standard deviations
The standard deviations were calculated for each sampling event for each measurement.
The measurements were performed for four cases; (1) with a signal generator, (2) with
grounded input channels, (3) with a pre-amplifier connected to the system and (4) with
a 9 V constant voltage signal.
1.1
Signal generator
An example of the sinus signal acquired is presented in Fig. 3.1. The signal seen in
the plot was acquired with Dev4 on channel 6. In the case presented, the signal has a
frequency of 1 kHz and a 2.5 V amplitude.
Figure 3.1: Example of the acquired sinus signal, here, recorded with channel 6 on Dev4
with 204.8 kS/s. The amplitude of the signal is 2.5 V and has the frequency 1 kHz.
In Table 3.1 the maximum standard deviations obtained for each acquisition for 5
different frequencies are shown. The numbers in the table can be seen as an upper
limit which the standard deviations do not exceed. The standard deviation is frequency
dependent, as can be seen in the table. From the measurement carried out with the signal
generator the standard deviations are in the order of a few mV.
15
Dev1 and Dev2 show similar patterns in the standard deviation. This is also the case
for Dev3 and Dev4, they exhibit similar behavior. Fig. 3.2a and b show zoom-ins of
the standard deviations for Dev1 and Dev4, respectively. The standard deviations are
calculated with a 100 Hz sinus signal. Results showed that the patterns for 0.1, 1 and 10
kHz were of the same nature as the ones presented in Fig. 3.2. Dev1 and Dev2 exhibit
more noisy patterns of the standard deviations whereas the patterns for Dev3 and Dev4
are less noisy.
(a) Dev1.
(b) Dev4.
Figure 3.2: Zoom-ins of the calculated standard deviations for two acquisition cards, the
signal acquired to calculate the standard deviation was a sinus signal of 100 Hz.
Fig. 3.3a and b are plots of the calculated standard deviations, for Dev1 and Dev3,
when a 50 kHz sinus signal was acquired. As was observed for the previous frequency,
the pattern in Dev1 is noisier than the pattern for Dev3. The pattern in Dev3 has a clear
beat character, the pattern for Dev1 also shows a similar beat character but it is harder
to distinguish because of the noise present.
(a) Dev1.
(b) Dev3.
Figure 3.3: Zoom-ins of the calculated standard deviations for two acquisition cards, the
signal acquired to calculate the standard deviation was a sinus signal of 50 kHz.
Zoom-ins of the standard deviations obtained for Dev2 and Dev4 when acquiring a 90
16
kHz sinus signal can be seen in Fig. 3.4. The standard deviation for Dev4 is less noisy
than for the case with Dev2, this is a behavior that is consistent, Dev1 and Dev2 exhibit
more noise than Dev3 and Dev4.
(a) Dev2.
(b) Dev4.
Figure 3.4: Zoom-ins of the calculated standard deviations for two acquisition cards, the
signal acquired to calculate the standard deviations was a sinus signal of 90 kHz.
Table 3.1: Maximum standard deviation obtained when acquiring a sinus shaped signal,
with five different frequencies, with a 2.5 V amplitude.
f [kHz]
0.1
1
10
50
90
Dev1 [mV]
1.5
1.6
1.6
3.5
4.5
Dev2 [mV]
2.0
2.2
2.3
4.5
6.5
Dev3 [mV]
0.7
0.7
0.7
1.4
2.6
Dev4 [mV]
0.5
0.47
0.5
1.2
2.2
Fitting a sinus function to the mean data recorded by the acquisition cards by minimizing the root mean square deviation resulted in the numbers presented in Table 3.2.
Interesting to notice is that the fitted amplitude, A, is reduced when the frequency increases. For 90 kHz, the amplitude still agrees well with the amplitude set on the signal
generator. Increasing the frequency further results in a smaller amplitude. The offset
parameter, B, however, is not affected by the increase of the frequency. The frequency, f ,
agrees well with the frequency set on the signal generator. There is a phase shift observed
when performing the fit.
An example of the fit is presented in Fig. 3.5, the experimental data is a 50 kHz sinus
signal with a 2.5 V amplitude and are represented by the blue stars in the plot. The red
circles represents the fit model.
17
Figure 3.5: The mean of the experimental data, collected with Dev4, is represented by the
blue dots. The signal acquired was a sinus wave with the frequency 50 kHz and amplitude
2.5 V. The red circles are a sinus function fitted to the experimental data.
Table 3.2: Parameters obtained when fitting a sinus function to the mean of the acquired
sinus data, four frequencies are presented in the table.
f [kHz]
50
90
99
100
1.2
RMSD
0.0111367
0.0053312
0.0027972
0.0014990
A [V]
2.4955
2.4885
2.1617
1.9283
B [V]
-0.0120
-0.0121
-0.0123
-0.0120
f [Hz]
50000.23
90000.25
99000.29
100000.3
φ [rad]
-44.77
-1.470
-2.744
1.293
Grounded input channels
Grounding the channel inputs, with a 50 Ω resistor, and calculating the standard deviations of the data acquired results in the maximum standard deviations presented in Table
3.3. As can be seen in the table, the standard deviation does not exceed 110 µV for Dev1
- Dev3, Dev4 however, has a higher maximum standard deviation, 120 µV. Also presented
in Table 3.3, are the channels which have an overtone structure in their frequency spectra.
An example of the overtone structure is shown in Fig. 3.6 where the frequency spectrum
for channel 7 in Dev1 is presented. The same structure is observed for channel 8 in Dev1
and for channels 1 and 6 in Dev2. For low frequencies there are several peaks separated
by 1000 Hz. A stronger peak is also observed between 40 kHz - 60 kHz.
18
Table 3.3: Maximal standard deviation obtained using a 50 Ω resistor. Channels that
exhibited structure in their frequency spectrum are also presented.
Acquisition card
Maximal standard deviation [µV]
Channels with
structure in
frequency spectrum
Dev1
110
Dev2
110
Ch7
Ch8
Ch1
Ch6
Dev3
110
Dev4
120
Figure 3.6: Frequency spectrum of the inner noise of the system, calculated with Fourier
transformation. Here is channel 7 in Dev1 presented. A clear overtone structure can be
seen for lower frequencies.
1.3
Standard deviations when using a pre-amplifier or a constant
voltage source
A zoom-in of the standard deviation obtained having a pre-amplifier connected to the
system is presented in Fig. 3.7. In the plot, the standard deviation for when the preamplifier was turned off is shown. It turned out that the standard deviation was not
affected whether the amplifier was turned on or off. The standard deviation plot does not
have any clear structure but is rather random in its nature. In Table 3.4 the maximum
standard deviations calculated for the pre-amplifier modes ON and OFF are stated. As
can be seen, the standard deviations are the same for both the ON and OFF state, 2.3
mV.
19
Figure 3.7: Zoom-in of the standard deviation calculated with data acquired with a preamplifier connected to the acquisition device. The amplifier was turned off when the data
used in this plot was acquired. The data was acquired on 16 channels with Dev4.
Table 3.4: The table contains the maximum standard deviation obtained using a preamplifier in the system for two cases, one with the pre-amplifier in ON mode and one in
OFF mode. The data was recorded with Dev4.
Preamp mode
OFF
ON
Max. standard deviation [mV]
2.3
2.3
Calculating the standard deviation for the data acquired when connecting a 9 V battery to the input channels results in the plot in Fig. 3.8, the pre-amplifier was not
connected to the system during these measurements. As can be seen in the figure, the
standard deviation is random in its nature. The maximum standard deviations for Dev1
- Dev4 are specified in Table 3.5, they are in the range of a few mV.
Table 3.5: Maximum standard deviations obtained when acquiring a constant 9 V signal.
Max. standard deviation [mV]
Dev1
1.0
20
Dev2
1.3
Dev3
2.3
Dev4
1.6
Figure 3.8: Standard deviation, for Dev4, calculated with data recorded on 16 channels
with a constant voltage signal of 9 V.
2
Signal analysis and interpretation
In Fig. 3.9, the differential cross-sections for graphite, air and a mix of air and graphite
are plotted for two different ratios of x. A structure for the mixed differential cross-section
can be seen in Fig. 3.9a when x = 0.01. The differential cross-section for air and the
mixture are overlapping for x = 0.0001 and cannot be distinguished from each other.
(a) x = 0.01.
(b) x = 0.0001.
Figure 3.9: The differential cross-sections for graphite, air and a mix of graphite and air
as functions of q are presented in the plots. (a) Differential cross-sections with the ratio
x = 0.01, (b) the differential cross-sections for x = 0.0001.
When x → 0 the differential cross-section for the mixture takes the same shape as
21
the differential cross-section for air. Including noise to the graphite/air cross-sections and
normalizing against the cross-section of air can be acquired under steady state conditions
in principle almost excluding noise, we can use eq.(2.5). The results are shown in Fig.
3.10 where the standard deviation measured in the previous sections was used as noise
generator. In the plots, γsig − 1 is presented. In the four graphs the ratio x goes from
10−7 to 10−4 . It can be seen that for small x, only the noise is present. As x is increased
the structure of the differential cross-section becomes more apparent. Including other
standard deviations than the one obtained for the constant voltage results in similar
graphs. In Fig. 3.10c an interval is marked, indicating how to distribute the detectors to
measure the peak inside the interval. By choosing detector angles corresponding to the
interval, the peak can be measured. The interval-window can be placed over the entire
plot or selected regions of the plot. An interval over the entire plot would result in a
measurement with lower resolution of the structure.
(a) x = 10−7 .
(b) x = 3 · 10−7 .
(c) x = 10−6 .
(d) x = 10−4 .
Figure 3.10: The total differential cross-section normalized to the differential cross-section
of air. In the plots, the standard deviation retrieved for the measurements with the constant voltage is included. The plots are made for four different ratios of x. Also marked
in (c) is an interval, for which all 64 channels of the acquisition device can be used to
measure.
22
Chapter 4
Discussion
1
Comments on the result
The standard deviations should not be considered as standard deviations of the signal
related to the probed volume in a real experiment.
1.1
Signal generator
The noise, given as the standard deviation, obtained from data collected from the signal
generator is in the order of a few mV. The zoom-ins showing patterns of the standard
deviations presented in Fig. 3.2-3.4 retail the behavior of each acquisition card. From the
results a clear distinction can be observed between the patterns for Dev1 and Dev2 towards
Dev3 and Dev4. The different patterns obtained cannot, at this point, be explained.
However, the standard deviations should include noise from both the signal generator,
the acquisition system and most probably background. Reasons why a beat structure
observed is not yet known.
The fit that was made to the mean data indicates that the system cuts the amplitude
for frequencies > 90 kHz. This is important to keep in mind when performing measurements, a pre-amplifier could be needed in order to actually obtain useful data. The source
to the offset parameter can originate either from the acquisition device or the signal generator, further investigation would be needed to find the mechanism responsible for the
offset. Future tests could include investigations on possibilities to adjust the device to
eliminate the offsets. The phase shifts observed do depend on when the data acquisition is
started, and should be of no concern for the applications. The frequency parameters were
very exact, there were only small deviations from the values set on the signal generator.
They were on the order of 0.1 Hz, which is a relatively quite small value. The goodness
of the fits were never estimated but should be investigated in further work.
To summarize, a clear distinction was observed between Dev1 and Dev2 with respect
to Dev3 and Dev4, this might be due to attrition of the acquisition cards, Dev1 and Dev2
have been used over a longer time than the other two. National Instruments specify that
their acquisition cards are worn out over time.
1.2
Grounded input channels
The small deviations obtained are most probably due to the inner noise of the system.
Dev1 and Dev2 show different results from Dev3 and Dev4 also in this experiment. The
23
reason why an overtone structure is observed is not known. However, it might be due to
attrition of the acquisition cards. The mechanism behind the randomly distributed peaks
present in the frequency spectrum are not yet known.
1.3
Pre-amplifier or constant voltage
Adding the pre-amplifier to the system resulted in higher deviations than the ones observed when grounding the input channels. Adding components to the system resulted
in higher noise levels. This is very important to take into account when performing measurements where important measurement data can be drowned in too high noise levels.
If this happens, important information may be lost.
The noise/standard deviations obtained with the 9 V constant voltage source was
higher than for the case when the input channels were grounded. The noise may depend
on the amplitude of the signal, since it was higher than for the grounded case, but should
be further investigated.
1.4
Signal analysis and interpretation
One important aspect is how to interpret noise and signals and to determine detection
limits. The results give information about the ratio x = NG /NL , i.e. the ratio between
number of nanometer-sized graphite particles to air molecules in an aerosol. What can be
read out is the minimum amount of graphite that is needed, to detect it in a graphite/air
mixture for a certain level of noise. This analysis can stand as a starting point for more
developed studies in flames.
In the results section, the case where the standard deviation for the constant voltage source was presented. One could of course also examine what ratios that the other
standard deviations would give. The results of such a simulation exist but is not very
interesting here, the interesting part is instead to tie together how the standard deviation
of the acquisition device affect the physical data that is about to be measured.
What is presented, is the results of a simplification of a measurement carried out in a
flame. The simulated flame, or rather the mixture, only consists of air and graphite. From
the results section it can be seen that the main features of the graphite differential crosssection can be seen when there exists one graphite particle per one million air particles.
Consequently, a too high level of noise in the detector system reduces the ability to
distinguish patterns in the measurement data that originates from physical processes.
24
Chapter 5
Outlook
Further work should include a more thorough evaluation of the detection system. Noise
from the complete setup, including a well-defined radiation source, detectors, scintillators,
PMTs and pre-amplifiers, could be performed since the setup was only simulated with a
signal generator or a constant voltage source in this thesis. Such an evaluation would give
an estimation of the minimum detectable signal that can be recorded by the system.
An interesting investigation would be to evaluate how noise is dependent on the temperature of the acquisition device. An experiment where the device is cooled down could
be performed. If the device was placed in a cooling container where the temperature
can be controlled, data could be acquired for different temperatures. Calculations of the
standard deviation could be compared for different temperatures.
Further studies in the field of soot/nanoparticle formation could be carried out at MAX
IV, a 4th generation synchrotron radiation facility in Lund, Sweden. The 4th generation of
synchrotron radiation will have photon fluxes that will increase the signal-to-noise ratios.
Better detection limits will result in higher spatial resolution to study the in-homogeneity
in connection to soot particles [10].
25
Acknowledgements
I would like to acknowledge and thank my supervisor, Frederik Ossler, for the opportunity
to this bachelor thesis. He has supported me throughout the project, both during his
working hours and free time, and given me interesting tasks to perform.
A big thank you should also be sent to Payman Tehrani, from National Instruments, for
introducing me to LabVIEW and Igor Buzuk for providing me with technical equipment
during the project.
26
Self-reflection
During the project I have learnt a lot about X-ray scattering, especially about detection of
X-rays and the devices used to acquire signals generated by scattered X-rays. I have learnt
about concepts connected to detection and layouts that may limit the detectors/detection.
The physics-related knowledge that I have accumulated are concepts important in the
field, such as; momentum exchange, differential cross-sections, scattered intensities and
some fundamental theory about X-ray scattering.
Most of the problems I have encountered have been related to programming. During the thesis work I have done a lot of programming in LabVIEW and MATLAB. In
LabVIEW I have learnt how to design acquisition programs able to acquire data on several channels simultaneously. In MATLAB I have improved my skills, especially skills in
handling data and computing with large data sets.
27
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