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UNIVERSITY of CALIFORNIA
SANTA CRUZ
INTERFACE EVENTS WITHIN THE CALORIMETER OF THEPROTON COMPUTED TOMOGRAPHY HEAD SCANNER
A thesis submitted in partial satisfaction of therequirements for the degree of
BACHELOR OF SCIENCE
in
APPLIED PHYSICS
by
Theodore Geoghegan
20 March 2015
The thesis of Theodore Geoghegan is approved by:
Professor Hartmut F.-W. SadrozinskiAdvisor
Professor David P. BelangerTheses Coordinator
Professor Robert P. JohnsonChair, Department of Physics
Copyright c© by
Theodore Geoghegan
2015
Abstract
Interface Events within the Calorimeter of the Proton Computed Tomography Head
Scanner
by
Theodore Geoghegan
Within the calorimeter of the proton computed tomography head scanner, protons can
sometimes stop close an interface of two scintillators. If the protons stops in the wrapping material
or loses a significant portion of their energy in the wrapping, the signal in the next scintillator can
be below the registration threshold. This causes the protons be reconstructed incorrectly. Seeing
as this scanner is the first of its kind, this problem never existed before. Using beam test data
taken at Loma Linda University, I searched through the data looking for events that stopped near
the scintillator interfaces. I plotted the WEPLs from different beam tests to find a trend within
the data. What I found is that the protons that would stop just before an interface, and not leak
into the next scintillator, would not reconstruct correctly. It did not matter what beam test; the
problem persisted. What I concluded was that the software needs to be revisited so special care is
taken when reconstructing these events.
iv
Contents
List of Figures v
List of Tables vi
Dedication vii
Acknowledgements viii
1 Introduction 11.1 Computed Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Radiation Therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Proton Therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Proton Computer Tomography and Proton Therapy . . . . . . . . . . . . . . . . . . 5
2 The pCT Head Scanner 72.1 Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 The Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Beam Test Data Analysis of Interface Events 93.1 Set Up of Proton Beam Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Defining an Interface Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.3 How to Find an Interface Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.4 Analyzing an Interface Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.4.1 The Pedestal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5 How the Peaks are Separated and WEPLs Evaluated . . . . . . . . . . . . . . . . . . 13
3.5.1 Non-Leaked Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.6 Investigating Correlation Between Upstream Scintillators and WEPL . . . . . . . . . 183.7 Issues in the Reconstruction Software . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.7.1 How to Fix the Issue with the Interface Events . . . . . . . . . . . . . . . . . 22
4 Conclusion 24
A Additional Figures and Plots 25
B Additional Plots and Tables of Data 28
Bibliography 32
v
List of Figures
1.1 Slices of a Head from CT Scan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Relative Doses of X-rays and Proton Radiation. . . . . . . . . . . . . . . . . . . . . . 41.3 Spread Out Bragg Peak (SOBP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Hounsfield Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 Head Scanner Diagram and Coordinate Definition . . . . . . . . . . . . . . . . . . . 8
3.1 Beam Test Step Phantom Degrader Set Up . . . . . . . . . . . . . . . . . . . . . . . 103.2 Plot of Interface Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3 WEPL Plot of Events with Leak into Downstream Scintillator . . . . . . . . . . . . . 133.4 WEPL Plot of Events without Leak into Downstream Scintillator . . . . . . . . . . . 143.5 Reconstructed vs actual WEPL for leaked protons of September data . . . . . . . . . 163.6 Reconstructed vs actual WEPL for non-leaked protons of September data . . . . . . 173.7 ADC Value vs WEPL of an Upstream Scintillator . . . . . . . . . . . . . . . . . . . 193.8 ADC Value vs WEPL of an Upstream Scintillator, Next Step . . . . . . . . . . . . . 193.9 ADC Value vs WEPL of an Upstream Scintillator, One Brick Non-Leaked . . . . . . 203.10 Small Pedestal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.11 WEPL Reconstruction with Threshold of 200 . . . . . . . . . . . . . . . . . . . . . . 223.12 WEPL Reconstruction with Threshold of 40 . . . . . . . . . . . . . . . . . . . . . . . 23
A.1 Sample Diagram of Scintillator Used in Calorimeter . . . . . . . . . . . . . . . . . . 25A.2 Tracker Board Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A.3 Plot of Interface Event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26A.4 Separated Peaks Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27A.5 Separated Peaks Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
B.1 Reconstructed vs actual WEPL for leaked protons of July Data . . . . . . . . . . . . 29B.2 Reconstructed vs actual WEPL for non-leaked protons of July data . . . . . . . . . . 30B.3 Reconstructed vs actual WEPL for non-leaked protons of July, Thicker . . . . . . . . 30B.4 ADC Value vs WEPL of an Upstream Scintillator Zoomed In . . . . . . . . . . . . . 31
vi
List of Tables
3.1 Leaked Proton WEPLs of Steps 26-31 & 32-38 mm . . . . . . . . . . . . . . . . . . . 153.2 Non-Leaked Proton WEPLs of Steps 26-31 & 32-38 mm . . . . . . . . . . . . . . . . 15
B.1 Leaked Proton WEPLs of Steps 26-31 & 32-38 mm . . . . . . . . . . . . . . . . . . . 28B.2 Non-Leaked Proton WEPLs of Steps 26-31 & 32-38 mm . . . . . . . . . . . . . . . . 28B.3 Non-Leaked Proton WEPLs of Steps 13-19 & 20-25 mm . . . . . . . . . . . . . . . . 29
vii
To my parents,
Maria and Patrick Geoghegan,
without them my education would not have been possible.
viii
Acknowledgements
I would like to thank my fellow pCT collaborators: Hartmut Sadrozinski, Robert Johnson, Andriy
Zatserklyaniy, Tia Plautz, and Loma Linda University. They welcomed me into the group and
helped me through my first real research experience. Also, I want to thank my committee, professors,
teaching assistants and most importantly, fellow students, without all of whom, I would not have
gotten through these last four years.
1
1 Introduction
A new form of medical imaging being developed is proton computed tomography (pCT)1.
The focus of this new imaging technique is for use on the brain. The common CT (computed to-
mography) scans create quality pictures of the brain, but use x-rays. The use of protons for imaging
is important because of a newer form of brain tumor irradiation called proton therapy. The drive
behind imaging and irradiating with protons is that proton radiation therapy can be used more
accurately conjointly with images taken with a pCT scan.
A great deal of data are necessary for image reconstruction. These data include the energy
and location of the proton before entering and after exiting the head. The energy before entering
the head is easily obtained because that is the energy of the accelerated protons. The more difficult
part is calculating the exit energy of the protons using a calorimeter.
The scanner is being designed and built from scratch, so each part needs to be tested and
calibrated. The way the calorimeter is designed, it has interfaces that create odd occurrences in
the data that must be attended to. Herein lies the problem that I am addressing and working to
resolve.2,3
1.1 Computed Tomography
Computed tomography (CT), formally called computed axial tomography (CAT), is an
imaging procedure that uses x-rays to produce cross-sectional images, or ”slices”, of the body part
2
Figure 1.1: Slices of a head from CT scan. From the top left the scan is starting at the top of theshoulders and neck. The next slices are successively upwards to the top of the head.4
being examined. The slices are 2-dimensional tomographic images. If many of these are produced
and digitally processed, a 3-dimensional image can be generated. Slices of a head can be seen in
Fig. 1.1. The most common application of CT scans is medical imaging. The cross sectional images,
or ’slices’ can be used to diagnose medical problems. For this case specifically, we use CT scans
to image tumors. CT scans have very good density differentiability, detecting differences smaller
than 1%, making them excellent for imaging tumors. To understand why a different type of CT
scan is needed, when they are already so proficient, the different types of radiation therapy must be
understood.5,6
1.2 Radiation Therapy
Radiation therapy is a type of cancer treatment that uses high-energy radiation to shrink
tumors and kill cancer cells. Different types of radiation used are X-rays, gamma rays and charged
3
particles. The cancerous cells can be irradiated via an accelerator outside the body or via radioactive
material placed inside the body, in and around the tumor. The latter is called brachytherapy, but I
will focus on the beam radiation methods.
Before any person is treated, the radiation therapy needs to be planned. That’s where CT
scans and other type of medical imaging methods come into play. CT scans are the most common
type of imaging for this use. The oncologist creates a simulation using the images of the tumor
and surrounding tissue. After the simulation, the oncologist decides what areas will be treated, the
total radiation dose to be delivered to the tumor, the allowed radiation delivered to the healthy
tissue surrounding the tumor and the safest angles for radiation delivery. At this point it is also
determined what type of radiation will be used to treat the patient.
Radiation kills cancer cells and healthy cells by destroying the DNA which either kills the
cell directly, or stops the cells from dividing. After the cell is dead, they are broken down and
removed from the body through natural processes. Because radiation therapy can kill healthy cells,
as much as possible is done to minimize irradiating healthy tissue. To reduce the negative effect on
healthy tissue, the radiation beams are shaped using lead teeth to the cross section of the tumor,
decreasing damage done to the healthy tissue. It is beneficial that only the cross section is irradiated
with this type of radiation therapy, but healthy tissue is still irradiated whether it is in front of or
behind the actual tumor. Often, this is a sacrifice taken because the healthy tissue also irradiated is
expendable. Not to say it is beneficial that healthy tissue is being irradiated, but it is a side effect
that is worth treatment of the cancer. An area of the body where there is no expendable healthy
tissue is the brain. Irradiating anything but the tumor can have drastic consequences. This was the
motivation behind developing a new form of radiation to treat brain tumors.7
4
Figure 1.2: Relative radiation doses of X-rays and protons. X-rays release most of their energyin the beginning of tissue interaction while protons release most of their energy at the end. Thephenomenon of the proton is called the Bragg peak.8
1.2.1 Proton Therapy
Proton therapy is a radiation therapy developed for sensitive areas of the body, such as
the brain. What separates proton radiation from gamma ray, X-ray and electron radiation is how
it interacts with matter. When the photon and electron radiation enter tissue, they interact fairly
predictably. The deeper the tissue, the less radiation is delivered. The relative radiation dose, for the
most part, tails off the deeper the tissue. On the other hand, protons interact with tissue differently.
When entering tissue, a small amount of the radiation dose is released. As the proton reaches the
end of its path, most of the relative dose is released. As the proton loses energy, its stopping power
becomes greater. Figure 1.2 shows the difference between X-rays and protons. This phenomenon is
called the Bragg peak and all large charged particles have this characteristic.
The reason that the Bragg peak and proton therapy are important is because radiation can
now be localized more efficiently. Before, irradiating a brain tumor would come at the cost of losing
5
Figure 1.3: Photon radiation dose delivery compared to spread out Bragg peak (SOBP) dose delivery.Twelve proton beams’ Bragg peaks are combined to irradiate a tumor. The radiation dose are ofthe SOBP is compared to that of a photon beam.9
vital brain tissue that lay in front of the tumor. Because of the Bragg peak, much more healthy
brain tissue can be saved from unecessary damage. Proton beams can be calibrated so that the
protons stop within the tumor, saving healthy tissue from as much radiation as possible while still
treating the tumor. Figure 1.3 shows how multiple different energies of protons can be combined
to irradiate a tumor. Figure 1.3 also shows that in order to ensure the tumor receives 100% of the
radiation it needs, a large amount of tissue in front of and behind the tumor get irradiated. This is
what proton therapy is going to drastically reduce.
1.3 Proton Computer Tomography and Proton Therapy
Now that computed tomography and proton therapy have both been addressed, the im-
portance of proton computed tomography can now be explained, along with why normal computed
tomography is inferior. Currently, the possibilities of proton therapy cannot be fully taken advan-
6
Figure 1.4: The Hounsfield scale. The scale is set so water has a value of 0 and is half way betweencomplete black and complete white. The units on the numbers are Hounsfield units (HU), which arearbitrary in the sense that they only reference the grey scale.10
tage of because of the conversion of Hounsfield values. A Hounsfield value is the average of the
attenuation value within a pixel compared to the attenuation value of water. This is then displayed
on a scale of arbitrary units that is correlated to a grey scale, Fig. 1.4. When these values are
measure with X-ray computed tomography (CT) to relative electron density values, they are not
always accurate. These uncertainties can lead to errors during the proton therapy treatment up to
more than one centimeter depending on the area being treated. Using proton CT for guiding the
proton therapy can minimize these uncertainties.
7
2 The pCT Head Scanner
2.1 Set Up
The pCT head scanner consists of proton trackers and a calorimeter2. The protons need to
be tracked before entering and after exiting the head. To do this, trackers are placed in front of and
behind the head or phantom being tested. The tracking layer has two silicon strip detectors that
track a certain direction. One layer will track the t-direction and the other tracks the v-direction.
This set up can be seen in Fig. 2.1. I will not go too far in depth about the trackers because they are
not the focus of my research. After the proton is tracked leaving the head, its energy is determined
by the calorimeter. All these instruments are attached to a motherboard for data processing and
recording.
2.1.1 The Calorimeter
The calorimeter lies downstream of the phantom, after the tracker boards. The purpose of
determining the energy after the proton exits the head is to determine how much tissue it passed
through. This is called the water equivalent path length (WEPL). The integral,
L =
∫l
%dl, (2.1)
8
Figure 2.1: Diagram of the head scanner and coordinate definition. The black coordinate axes arethe detector coordinate system while the orange coordinate axes are the reconstruction coordinatesystem. Note, only three of the five scintillators are shown here.11
is equivalent to the WEPL, L, where % is the ratio of the stopping power of the material, Sm, to the
stopping power of water, Sw,
% =Sm
Sw. (2.2)
The layout with the coordinate definitions can be seen in Fig. 2.1. The scintillator is made
of five (channels 0 to 4) successive scintillating plastic blocks. Each block is 50.8 millimeters thick
and wrapped in 65 µm thick 3M VikuitiTM Enhanced Specular Reflector. Each block is touching so
there is no gap between scintillators. Attached to one end of each of these is a photomultiplier . The
principle behind this calorimeter is that when a proton enters a scintillator releasing energy, a fraction
of the energy is re-emitted in the form of visible light. The photons then enter the photomultiplier
creating an electron signal. This pulse then proceeds to an analogue-to-digital converter (ADC) to
be recorded and later changed into WEPL in an offline procedure called calibration. A diagram of
the set up can be seen in Fig. A.1.
9
3 Beam Test Data Analysis of Interface
Events
3.1 Set Up of Proton Beam Test
In order to establish the calibration, the ADC values are determined for known WEPL
values. To do this, a step phantom degrader was used. It consists of four polystyrene (plastic)
bricks, made of the same material and thickness as the scintillators, and one step phantom. A
diagram can be seen in Fig. 3.1. The beam testing was always done with at least the step phantom.
Then, one by one, more bricks were added for more beam tests. The step phantom and degrading
bricks, as seen in Fig. 3.1, do not move from those positions. So if one brick is removed from the
back, the steps and other bricks are not recentered. This way the steps stay in the same position
and the data is kept consistent.
3.2 Defining an Interface Event
The way the calorimeter is designed, five successive scintillators, there will be protons that
do not completely stop in one scintillator. At discrete energies, protons have their peak energy
release in about the last three millimeters of their path. If these three millimeters happen to start at
the end of one scintillator, the proton can leak into the wrapping material and the next downstream
scintillator. This can cause large amounts of energy to be deposited in the first scintillator and little
10
Figure 3.1: The degrader and steps used for the beam tests. For each different beam test run was adifferent number of solid degrading bricks used behind the step phantom.12
or none in the next one. This can cause problems because the data is processed to think a proton
stops in one distinct scintillator. These are the events I look for in the data and to see how they
affect the WEPL that is processed from the ADC counts.
3.3 How to Find an Interface Event
When the proton beam passes through the step phantom, obviously not every proton will be
an interface event. These events will happen at certain thicknesses, or certain steps of the phantom.
To find the certain degrader thickness (degrader step) that creates and interface event, data must be
looked through one step at a time. This is possible because each individual proton is tracked in three
coordinate directions. Events that cross a certain step can be distinguished by setting restrictions
on protons that had certain t coordinates. As seen in Fig. 3.1, the top step of the middle pyramid
is at the coordinate t = 0 mm. To locate the interface events, I start at this step working down the
11
Figure 3.2: ADC count histogram of interface events in upstream scintillator. The ADC count,which is proportional to the WEPL, is on the horizontal axis of the histogram.
pyramid looking at the ADC counts of different scintillators within the calorimeter. The interface
events look like the histogram in Fig. 3.2. They have the two-peak shape, unlike the normal one
peak. This is because some of these protons are releasing all of their energy in the one scintillator,
the higher ADC peak, and others are releasing some of their energy in the first scintillator and some
in the next, the lower ADC peak. What the downstream scintillator ADC count histogram looks
like can be seen in Fig. A.3. The ADC counts that spilled into the next scintillator, Fig A.3, is the
difference between the two peaks in the upstream scintillator.
3.4 Analyzing an Interface Event
These two separate peaks can be treated as two separate classes of events. Even though
the protons are all passing through one thickness, it is clear that something is happening to make it
seem that it is two thicknesses. This is from the scintillator interface issue. As stated before, these
two peaks are a result of some protons leaking into the next scintillator. The leaked events must be
12
separated from the non-leaked events. Protons that stop within the wrapping or lose a significant
portion of their energy in the wrapping are considered non-leaked even though they did technically
leak. They are classified as non-leak because the downstream scintillator either detected no energy
or it was below the registration threshold. To seperate the two types of events, we must make cuts
in the data using the data analysis program ROOT13.
In the data files from the beam tests, there are the data from all of the scintillators and
the WEPL. After the step that leaks into the downstream scintillator is found, we must look to
see which two scintillators the events are stopping in. Using simple data cuts, the two peaks are
separated. If the proton leaked into the next scintillator, obviously there will be a registered ADC
in that downstream scintillator. And if the event did not leak, there will not be an ADC registered.
For example, say the two peaks occur in channel 3 and the leak is in channel 4. If the leaked data
were to be analyzed, a cut would be made, simply put, graph the WEPL if there are ADC counts
in channel 4. Furthermore, if the non-leaked data were to be analyzed, a cut would be made, graph
the WEPL if there are no ADC counts in channel 4.
3.4.1 The Pedestal
To go further and understand more deeply, the pedestal must be explained. The pedestal,
seen in Fig. 3.2, is the tall spike in the data around 0. Because each proton is tracked individually,
they are tracked all the way through, even if they do not make it to a certain scintillator, a ”place
holder” is given to them. So the pedestal is all the events that did not make it to that scintillator,
and in the case of Fig. 3.2, scintillator 4. The pedestal is not at exactly 0, so where ever the pedestal
ends on the plot is the threshold used for determining leaked and non-leaked protons. In the case of
these beam tests, each with a different number of degrading bricks, the threshold ranged from 250
to 400, depending on the test. Later on we will look at the effect of the threshold value.
13
Figure 3.3: Histogram of WEPL values. This shows the WEPL for the step 26-31 mm that hadleaked protons into the downstream scintillator.
3.5 How the Peaks are Separated and WEPLs Evaluated
Now the peaks can be separated. Depending on the beam test and how many degrading
bricks were used, the WEPL can be graphed with threshold cuts. In the example of the two peaks in
Fig. 3.2, the non-leaked WEPL can be graphed by making a cut of scintillator 4, Fig. A.3, having a
threshold less than 200. This means that the only ADC counts are the events below the threshold,
which are the events that did not make it to that scintillator. As for graphing the WEPL for the
leaked data, the cut would be made by choosing events with ADC counts greater than a threshold
of 200 in scintillator 4. This means that there are ADC counts besides the pedestal, saying protons
did reach the scintillator, depositing energy. These two separated peaks can be seen in Figs. A.4
and A.5. Now that the peaks are separated into two distinct groups of data, the WEPLs can be
analyzed and compared. Again using ROOT, instead of graphing the scintillator ADC counts, the
WEPLs are plotted with the same thresholds as before.
These WEPL graphs can be seen in Figs. 3.3 and 3.4. As seen on the plots, Gaussian fits
14
Figure 3.4: Histogram of WEPL values. This shows the WEPL for the step 26-31 mm that had noleaked protons into the downstream scintillator.
are created for the separate peaks and the mean is recorded. After the mean is recorded from the
Gaussian, it is compared to the actual WEPL of the step phantom and degrading bricks. Because
all of these values are water equivalent path lengths and the phantom is not water, the thickness of
the phantom must be multiplied by a density constant. In this case, the plastic is 1.05 times denser
than water, so the thickness of the polystyrene is multiplied by 1.05 to get the ’actual’ WEPL.
Looking above the plots in Figs. 3.3 and 3.4, there is a long ’title.’ These are the specific
selection cuts on the data set being looked at. Reading left to right it first reads ’WEPL’ which is,
obviously, the water equivalent path length, what we have been talking about. After that, each data
filter is separated by &&. Looking above at Fig. 3.4, it is seen the first filter is one that says ’a[4]<200’
which is for no leaked protons. The next ’nt==1’ filters out any events that happened to be more
than one proton. Then, ’T(-101.6)>26&&T(-101.6)<31’ is filtering out all proton protons except
the ones that traveled through the unique step in the phantom. Lastly, ’WEPL<50&&WEPL>0’ is
just setting the horizontal axis in order to see the peak more clearly on our plot above.
15
Leaked WEPLs Only Steps, +1 Brick +2 Bricks +3 BricksActual, 26-31 mm Step 26.67 mm 80.01 mm 132.93 mm 185.85 mmReconstructed, 26-31 mm Step 25.88, 64% 79.02, 97% 132, 80% 179.7, 40%Ratio 0.9704 0.9876 0.9930 0.9669Actual, 32-38 mm Step 20.00 72.92 125.84 180.02Reconstructed, 32-38 mm Step 19.46, 86% 72.69, 98% 125.3, 98% 178.1, 90%Ratio 0.9730 0.9968 0.9957 0.9893
Table 3.1: Leaked Proton WEPLs of Steps 26-31 & 32-38 mm. The reconstructed WEPLs areshown along with the actual value. The ratio shown is the ratio between the two values to show howaccurate the reconstruction is. All units are in millimeters and the ratios are unitless. September2014 beam test data.
Non-leaked WEPLs Only Steps +1 Brick +2 Bricks +3 BricksActual, 26-31 mm Step 26.67 mm 80.01 mm 132.93 mm 185.85 mmReconstructed, 26-31 mm Step 32.34, 36% 81.58, 3% 138.9, 20% 192.7, 60%Ratio 1.2126 1.0196 1.04491 1.0369Actual, 32-38 mm Step 20.00 72.92 125.84 180.02Reconstructed, 32-38 mm Step 53.92, 14% 110.1, 2% 141.1, 2% 211.7, 10%Ratio 2.6960 1.5099 1.1213 1.1760
Table 3.2: Non-Leaked Proton WEPLs of Steps 26-31 & 32-38 mm. The reconstructed WEPLs areshown along with the actual value. The ratio shown is the ratio between the two values to show howaccurate the reconstruction is. These reconstructions are not as accurate as the leaked WEPLs. Allunits are in millimeters and the ratios are unitless. September 2014 beam test data.
Now actual and reconstructed WEPLs are now known, they can be compared to see how
close they are and how many percentage points the reconstructed value is from the actual value. An
example of these data can be seen in Table 3.1 and 3.2. Only two steps are shown because those are
the only two steps, for the number of degrader bricks indicated, where protons leaked into the next
scintillator. The steps are labeled 26-31 mm and 32-38 mm because those are the T coordinates,
see Fig. 3.1, that dictate the unique steps that cause the proton leaks in the calorimeter. The
percentages seen next to the reconstructed WEPL values are the percent of events that either leaked
or did not. Generally, there were more protons that leaked than did not.
16
Figure 3.5: Reconstructed vs actual WEPL for leaked protons of September data. This correspondswith Table 3.1. The y-axis is reconstructed and the x-axis is actual, yielding the slope of the line tobe reconstructed
actual , all in millimeters.
3.5.1 Non-Leaked Events
What is seen in Tables 3.1 and 3.2 is that the protons that leaked into the next scintillator
are more accurately reconstructed to the true WEPL. Through all of the leaked WEPLs, the greatest
difference between the actual and the reconstructed is ±4%. For the non-leaked protons, it is clear
that the ratios between the actual and reconstructed WEPLs are much further apart. There are
some that are within ±10% but many are much further away than hoped for. These are the protons
that did not reconstruct as desired and what are trying to be understood. Figures 3.5 and 3.6
visually show the accuracy gap between reconstruction of leaked and non-leaked protons. One thing
to notice is that the slope of the fitted line is not that far from a slope of one.
More beam tests at Loma Linda University were done with different calibrations of the
software. Each time a test is done, a new calibration is done within the software. Additional data
can be seen in Tables B.1 and B.2.
17
Figure 3.6: Reconstructed vs actual WEPL for non-leaked protons of September data. This corre-sponds with Table 3.2. The y-axis is reconstructed and the x-axis is actual, yielding the slope of theline to be reconstructed
actual , all in millimeters.
Analyzing Larger Steps
One theory I came up with was that the Bragg peak occurring towards the back of the
scintillator caused the problem I was encountering. The protons that did not leak are the ones that
stopped just before leaking into the next scintillator, putting the Bragg peak towards the back of
the previous scintillator, somehow making the ADC to WEPL conversion function fail. This could
explain why the non-leaked protons were not reconstructing accurately. To test this theory, I ex-
amined the non-leaked events of the next two thicker degrader phantom steps. What I saw was
that these steps reconstructed nearly flawlessly, which I think was because the Bragg peaks were far
enough away from the scintillator interfaces. The data from these steps can be seen in Table B.3.
18
3.6 Investigating Correlation Between Upstream Scintilla-
tors and WEPL
The issues with the non-leaked protons continue, so with the help of my mentor, I decided
to look at the ADC data from the upstream scintillators. An upstream scintillator I am referring
to is one that comes before the double peak characteristic. Another way to think about it is if the
proton is stopping near the interface of scintillator 2 and 3, I look at scintillator 1. I wanted to see if
this data had any correlation to the reconstructed WEPL, so I graphed ADC vs WEPL on a scatter
plot with density, as seen in Fig. 3.7
The idea is that if I can find a correlation between the upstream ADC count to the correct
reconstructed WEPL, the poorly reconstructed WEPLs could be filtered out. I use the leaked data
to find a correlation because it reconstructed the best. In Fig. 3.7, the peak is around 78 mm and
4400 ADC counts; see Fig. B.4 for zoomed in on the hot spot. If I could find a ’slope’ that is
constant with ADCWEPL , like 4400
78 , I could use this as a filter for the bad events. I could filter them by
making a restriction, such as only keep the reconstructed WEPLs if the upstream scintillator had
ADC values within a certain range. This range could be determined by the ’slope’ I mentioned.
This filter could be applied to events like the grouping in Fig. 3.7 around 90-100 mm WEPL and
for mis-reconstructed non-leaked events like in Fig. 3.9. As Fig. 3.9 shows, the non-leaked events
with a Bragg peak close to the downstream end of the scintillator are a mixture of events with
reconstructed WEPL close to the actual WEPL and events which have a reconstructed about 30
mm higher and additional artifacts which need to be investigated further.
Next I graphed the next step, 32-38 mm, to see if this correlation follows to this step as
well. But, the similarity between Fig. 3.7 and 3.8 makes it unlikely that the ADC value in the
upstream scintillator can be used find a universal correlation ratio and flag the mis-reconstructed
events.
19
Figure 3.7: ADC Value vs WEPL of an Upstream Scintillator. The y-axis is ADC count of scintillator1 and the x-axis is reconstructed WEPL in millimeters. September data with step degrader plus onebrick step 26-31 mm, leak.
Figure 3.8: ADC Value vs WEPL of an upstream scintillator, next step. The y-axis is ADC countof scintillator 1 and the x-axis is reconstructed WEPL in millimeters. September data with stepdegrader plus one brick step 32-38 mm, leak.
20
Figure 3.9: ADC Value vs WEPL of an upstream scintillator. The y-axis is ADC count of scintillator1 and the x-axis is reconstructed WEPL in millimeters. September data with step degrader plus onebrick step 32-38 mm, no leak.
3.7 Issues in the Reconstruction Software
The software being used to reconstruct the WEPLs for the protons has lines of code written
in it that already takes into account protons near the scintillator interfaces. One of these problems
is that it sometimes uses a threshold for leaked events which is not optimized. Just because I look at
the data and make the cut on the very edge of the pedestal, does not mean the reconstruction code
made that same cut and reconstructed the events accordingly. It could have reconstructed events
that were not in the pedestal as if they actually were, creaing a large error in the reconstruction. So
when I make my data cuts, what I think are non-leaked events, could actually have leaked events
mixed into the reconstruction code, causing issues.
Analyzing the leaked events, all the data runs look very accurate. If what I think is
happening in the code is correct, the leaked proton data are only being affected by having fewer
events. Nothing is happening to the quality of the data, but only the quantity. This is happening
21
Figure 3.10: Pedestal smaller than expected. The pedestal distribution allows a threshold of 40,instead of the overestimation of 200 used in the software.
because the threshold is being constantly over valued at 200, but many times the pedestal is much
smaller than that. One example of a smaller pedestal can be seen in Fig. 3.10. What can happen
to the WEPL reconstruction if the threshold value in the code is incorrect can be seen in Fig. 3.11.
Protons are lumped into the pedestal that do not belong there and get reconstructed to create this
spike on the plot. Now looking at Fig. 3.12, the spike in data is much smaller because of the more
accurate threshold set manually. The spike is still there because the pedestal has a small tail that
is within the threshold. Not coincidentally, the small spike in Fig. 3.12 looks like the edge of a tail.
As seen in Fig. 3.11 and 3.12, the tail continues to the right, registering larger WEPL values.
These large erroneous WEPL values, 15-20% of all events, are due to large energy losses from nuclear
interactions in the phantom or the detector itself. If in the detector, it can sometimes be identified
and filtered out. If the energy loss is caused by prompt gamma production, nuclear excitation,
which mostly happens in the last registered scintillator, the actual WEPL can be recovered using
the upstream scintillator data.
22
Figure 3.11: WEPL Reconstruction with threshold of 200. In this WEPL reconstruction a verynice peak occurs on the actual WEPL value but a spike in the data appears as well caused frommisplaced WEPL threshold.
3.7.1 How to Fix the Issue with the Interface Events
After analyzing many different data sets, all of them have had similar issues with the non-
leaked events. I have played with the threshold cut offs for all the different beam tests and the
same issues keep reoccurring. This leads me to believe the issue is in the reconstruction software.
When the reconstruction software is combining data from two scintillators, because it thinks there
is an interface event, something goes wrong. This something could be where the code believes the
pedestal is or in the way the ADC counts are processed from the two scintillators to produce a single
WEPL. As shown above, using the ADC value in the upstream scintillator does not seem to fix the
problem. In any case, the reconstruction code must be reviewed so it can be recalibrated and retested.
23
Figure 3.12: WEPL Reconstruction with threshold of 40. The spike is noticeably reduced becauseof the more precise threshold set.
24
4 Conclusion
After sifting through all of the data, it is obvious that non-leaked protons stopping close to
or on the interface between two scintillators are having problems with WEPL reconstruction. The
issue is how the reconstruction code handles the events that occur towards the back of a scintillator
and do not leak into the next one. A more serious problem are events which stop in the interface,
lose energy in the wrapping, and thus are reconstructed to having very large WEPL. How these
data are reconstructed need to be looked at more closely. In the simplest terms, the code must be
amended to take special care when handling these specific events and for the threshold values to be
optimized.
25
Appendix A Additional Figures and Plots
Figure A.1: Diagram of the scintillator and photomultiplier used in the calorimeter.14
26
Figure A.2: Diagram of the tracker boards. The tracker layers are the darker lines and each coupleof tracker boards are enclosed in a cassette.15
Figure A.3: ADC count histogram of interface events in upstream scintillator. The ADC count,which is proportional to the WEPL, is on the bottom axis of the histogram.
27
Figure A.4: Separated peak with no spill protons. This is the higher ADC count of the separatedpeaks from Fig. 3.2. Here the pedestal follows the cut.
Figure A.5: Separated peak with spill protons. This is the lower ADC count of the separated peaksfrom Fig. 3.2. There is no pedestal in this cut.
28
Appendix B Additional Plots and Tables
of Data
Leaked WEPLs No bricks +1 brick +2 bricks +3 bricksActual, 26-31 mm Step 26.67 mm 80.01 mm 132.93 mm 185.85 mmReconstructed, 26-31 mm Step 25.97, 60% 79.38, 70% 132.9, 75% 179.7, 40%Ratio 0.9738 0.9921 0.9998 0.9669Actual, 32-38 mm Step 20 72.92 125.84 180.02Reconstructed, 32-38 mm Step 19.92, 80% 72.76, 80% 125.7, 95% 178, 85%Ratio 0.9960 0.9978 0.9989 0.9888
Table B.1: Leaked Proton WEPLs of Steps 26-31 & 32-38 mm. The reconstructed, or plotted,WEPLs are shown along with the actual value. The ratio shown is the ratio between the two valueto show how accurate the reconstruction is. All units are in millimeters and the ratios are unitless.The percentages are the amount of events that were leaked out of the whole run. July 2014 beamtest data.
Non-leaked No bricks +1 brick +2 bricks +3 bricksActual, 26-31 mm Step 26.67 mm 80.01 mm 132.93 mm 185.85 mmReconstructed, 26-31 mm Step 26.54, 40% 83.95, 30% 138.3, 25% 189.6, 60%Ratio 0.9951 1.0492 1.0404 1.0202Actual, 32-38 mm Step 20 72.92 125.84 180.02Reconstructed, 32-38 mm Step 54.79, 20% 107.7, 20% 138.6, 5% 210, 15%Ratio 2.7395 1.3770 1.1014 1.1665
Table B.2: Non-Leaked Proton WEPLs of Steps 26-31 & 32-38 mm. The reconstructed WEPLs areshown along with the actual value. The ratio shown is the ratio between the two value to showhow accurate the reconstruction is. All units are in millimeters and the ratios are unitless. Thepercentages are the amount of events that were not leaked out of the whole run. July 2014 beamtest data.
29
Non-leaked No bricks 1 brick 2 bricks 3 bricksActual, 13-19 mm Step 40.01 mm 93.35 mm 146.69 mm 200.03 mmReconstructed, 13-19 mm Step 40.46 93.88 146.30 198.4Ratio 1.0112 1.0057 0.9973 0.9919Actual, 20-25 mm Step 33.34 86.68 140.02 193.36Reconstructed, 20-25 mm Step 32.84 87.15 139.9 192.1Ratio 0.9850 1.0054 0.9991 0.9935
Table B.3: Non-Leaked Proton WEPLs of Steps 13-19 & 20-25 mm. The reconstructed WEPLs areshown along with the actual value. The ratio shown is the ratio between the two value to show howaccurate the reconstruction is. All units are in millimeters and the ratios are unitless. July 2014beam test data.
Figure B.1: Reconstructed vs actual WEPL for leaked protons of July data. This corresponds withTable B.1. The y-axis is reconstructed and the x-axis is actual, yielding the slope of the line to bereconstructed
actual , all in millimeters.
30
Figure B.2: Reconstructed vs actual WEPL for non-leaked protons of July data. This correspondswith Table B.2. The y-axis is reconstructed and the x-axis is actual, yielding the slope of the lineto be reconstructed
actual , all in millimeters.
Figure B.3: Reconstructed vs actual WEPL for non-leaked protons of July data, thicker steps. Thiscorresponds with Table B.3. The y-axis is reconstructed and the x-axis is actual, yielding the slopeof the line to be reconstructed
actual , all in millimeters.
31
Figure B.4: ADC Value vs WEPL of an upstream scintillator zoomed In. The y-axis is ADC countof scintillator 1 and the x-axis is reconstructed WEPL in millimeters. September data with stepdegrader plus one brick step 26-31 mm.
32
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