Calibration and GEANT4 Simulations of the Phase II Proton Compute Tomography (pCT) Range Stack Detector

0.82 MB·

by  S. A. Uzunyan

FERMILAB-TM-2617-AD-CD-E
Calibration and GEANT4 simulations of the Phase II
Proton Compute Tomography (pCT) Range Stack
Detector
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January 6, 2016
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t S. A. Uzunyan, G. Blazey, S. Boi, G. Coutrakon,
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d A. Dyshkant, K. Francis, D. Hedin, E. Johnson, J. Kalnins, V. Zutshi,
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s Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA;
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R. Ford, J .E. Rauch, P. Rubinov, G. Sellberg , P. Wilson,
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s Fermi National Accelerator Laboratory, Batavia, IL 60510, USA;
c
i M. Naimuddin, Delhi University, 110007, India
s
y
h
p 1 Introduction
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Northern Illinois University in collaboration with Fermi National Accelerator Laboratory
v
9 (FNAL) and Delhi University has been designing and building a proton CT scanner [1]
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for applications in proton treatment planning. In proton therapy, the current treatment
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0 planning systems are based on X-ray CT images that have intrinsic limitations in terms of
0 dose accuracy to tumor volumes and nearby critical structures. Proton CT aims to overcome
.
1 these limitations by determining more accurate relative proton stopping powers directly as a
0
resultofimagingwithprotons. Fig.1showsaschematicprotonCTscanner, whichconsistsof
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1 eightplanesoftrackingdetectorswithtwoXandtwoYcoordinatemeasurementsbothbefore
:
v and after the patient. In addition, a calorimeter consisting of a stack of thin scintillator tiles,
i
X arranged in twelve eight-tile frames, is used to determine the water equivalent path length
r (WEPL) of each track through the patient. The X-Y coordinates and WEPL are required
a
input for image reconstruction software to find the relative (proton) stopping powers (RSP)
value of each voxel in the patient and generate a corresponding 3D image. In this note we
describe tests conducted in 2015 at the proton beam at the Central DuPage Hospital in
Warrenville, IL, focusing on the range stack calibration procedure and comparisons with the
GEANT 4 range stack simulation.
2 The GEANT 4 model
To verify measurements obtained by the scanner at the CDH proton beam the scanner
response was simulated using a detailed model based on the GEANT-4 software. Fig. 2
1
Figure 1: Four (X,Y) stations measure the proton trajectory before and after the patient.
A stack of 3.2 mm thick scintillator tiles measures the residual energy or range after the
patient.
shows a spherical water phantom between the tracker planes of the scanner model. The
simulated responses of the range stack and tracker stations were analyzed with the same
software as for the data.
Figure 2: The GEANT4 visualization of the scanner model used in the simulations.
3 The CDH test beam
Figure 3 shows the NIU scanner mounted on a cart in a treatment room at Central DuPage
Hospital. The proton beam enters the upstream tracker planes from the right followed by
the downstream tracker planes and finally the range stack. In this note the range stack tiles
are labeled from zero (the tile closest to the tracker) to 95. Data were obtained using proton
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beams of energy in range from 103-225 MeV, equivalent to 8-32 cm proton stopping range
in water.
Figure 3: Fully assembled proton CT scanner at CDH Proton center. From right to left,
beam enters the upstream tracker planes followed by the downstream tracker planes and
finally the range stack. The gap in the middle is the position of the rotation stage for the
head phantom in the horizontal plane.
3.1 Data acquisition (DAQ) system and event selection
The DAQ system of the scanner is described in [2]. The range stack data are collected
by twelve front-end boards. Each board provides the readout of one eight-tile range stack
frame in form of time-stamped records of signal amplitudes in all tiles of the frame. We form
the proton candidate event by combining records with close time-stamps. We remove events
candidates with duplicated frames (overlapped tracks). We then found the frame with a
Bragg peak, or stopping frame, and check that all frames before the stopping frame are also
present in the event.
3.2 Units of measurement
The CDH accelerator control system is tuned to operate with proton beams with energies
expressed inunitsoftheprotonstoppingrangeinwater incm, R (cm). Onecanalsoexpress
w
the protonstopping rangeR , andthus thebeamenergy E , indensity-independent units
w beam
of g/cm2 :
E (g/cm2) ≡ R (g/cm2) = R (cm)×ρ (g/cm3) (1)
beam w w w
To obtain the energy E in MeV we use proton energy-range tables (a.k.a. Janni’s
beam
tables) [4]. A fit of the stopping range R (g/cm2) as a function of E(MeV) is shown in
w
Fig. 4(a). We use
R (g/cm2) = 0.0022×E(1.77) (2)
w MeV
to convert beam energies between MeV and g/cm2 units.
Wecalculate theprotonstopping rangeintherangestackR (g/cm2)using themeasured
rs
proton stopping position as described in Section 5. We compare the R (g/cm2) with the
rs
3
range calculated from the total energy measured by the range stack using the energy-range
dependence in polystyrene shown in Fig. 4(b).
Proton Range vs Energy in water Proton Range vs Energy in polystyrene
2)900 2)900
cm χχ22 // nnddff 220011..44 // 4422 cm χχ22 // nnddff 110022..33 // 4422
1*(g/800 pp00 00..0022115533 ±± 00..00000011332277 1*(g/800 pp00 00..0022006644 ±± 00..00000011779966
e, 0.700 pp11 --11..777733 ±± 00..000011339955 e, 0.700 pp11 --11..7788 ±± 00..000011998899
g g
n n
a a
R600 R600
500 500
400 400
300 300
200 200
100 100
0
10 102 10 102
Proton energy, MeV Proton energy, MeV
(a) (b)
Figure4: a)TheprotonstoppingrangeinwaterR (g/cm2)(blackdots)versusprotonenergy
w
E(MeV), as measured in [4]. The fit R (g/cm2) = 0.0022×E(1.77) conversion function (the
w MeV
red line) is used to find beam energies in MeV that correspond to nominal CDH energies in
cm. b) The proton stopping range in polystyrene R (g/cm2) (black dots) versus proton
poly
energy E(MeV).
4 Stack calibration procedure
Energy deposition in each range stack scintillator tile is measured by two SiPMs connected
to the tile’s single wavelength shifting (WLS) fiber. After passage of a proton, for each of the
two SiPMs the maximum digitized signal, Amax , is collected by the DAQ system. Thus the
SiPM
measured energy deposition in each range stack tile, AADC, is obtained as a sum of Amax
tile SiPM
signals from SiPMs connected to this tile. This measurement varies from tile to tile even
for protons of similar energy due to differences in the SiPM’s properties and the settings of
corresponding readout channels. The following four step procedure is applied to calibrate
the range stack detector.
1) We measure pedestal amplitudes ApdSiPM1, ApdSiPM2 and amplitudes A1peSiPM1,
tn tn tn
A1peSiPM2 of the first photo-electron (PE) peak for all range stack tiles, tn, by collecting
tn
events with no beam. Fig. 5(a) and Fig. 5(b) show these distributions for SiPM1 and SiPM2
of Tile0. The combined SiPM1+SiPM2 no-beam signal in Tile0 is shown in Fig. 5(c).
Figure 6 shows calibration signals for all 16 SiPMs of the first range stack frame. From these
data the ADC to PE conversion coefficients for each SiPM are calculated as
KpeSiPM = A1peSiPM −ApdSiPM
tn tn tn
Ratios of PE conversion coefficients KpeSiPM0/KpeSiPM0 of the first and second SiPM in
tn t0
each tile to the conversion coefficient in the first SiPM in Tile0 are shown in Fig. 7(a) and
Fig. 7(b). Most sensors have a response within 10% of one another.
4
BID= 30, Tile = 0:: Channel 0 BID= 30, Tile = 0:: Channel 16 BID= 30, Tile = 0:: Channels (0,16)
Events/bin 56×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt 55iill1111ee4400232377__0.0.cc1177nn..232355ll00 Events/bin 67×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll 55 ee111100442211__77cc..77nn2277..ll1166556666 Events/bin2.5×103 hhEMREMR22nnMMeeffttiiaattrrSS__iinnee bb ssii dd 33 55 00222244__330077tt77..iill8855ee..88448800
5 2
4 <Pedestal> = 102.84 ADC <Pedestal> = 102.794 ADC <Pedestal> = 205 ADC
<single PE> = 120.971 ADC 4 <single PE> = 119.91 ADC 1.5 <single PE> = 223 ADC
3 PE/ADC = 18.1311 PE/ADC = 17.1159 PE/ADC = 18.0055
3
1
2
2
1 1 0.5
0 80 100 120 140 160 180 0 80 100 120 140 160 180 0180 200 220 240 260 280 300 320 340
ADC counts ADC counts ADC counts
(a) (b) (c)
Figure 5: Measured Tile0 signal amplitudes : a) pedestal and the first photo-electron (PE)
peak in the SiPM1 of Tile 0 in events with no beam. b) pedestal and the first photo-electron
(PE) peak in the SiPM2 of Tile 0 in events with no beam. c) SiPM1+SiPM2 combined.
2) The proton energy deposition in each tile Epe in PE units is obtained via
tn
Epe = (AsSiPM1−ApdSiPM1)/KpeSiPM1+(AsSiPM2−ApdSiPM2)/KpeSiPM2.
tn tn tn tn tn tn tn
Fig. 8(a) and Fig. 8(b) show the PE signals of SiPM1 and SiPM2 in Tile0, Fig. 8(c) shows
the combined SiPM1+SiPM2 signal, Ape, in Tile0.
t0
3)WemeasuresignalsEclbExp ofallrangestack tilesintheregionfaraway fromtheBragg
tn
peak. We conducted two calibration runs at an energy of 32 cm (225 MeV). For the second
run, the assembled scanner was turned 180 degrees to expose the back tiles to the beam first.
The “front” run is used to calibrate the first front 48 tiles of the stack, while the “back” run
is used to calibrate the 48 back tiles. We assume that the “true” EclbTrue amplitudes of the
tn
tile signals follow energy profiles calculated from proton energy-range tables for polystyrene
(the material used for the range stack tiles).
Figure 9(a) shows the tabulated proton dE/dx dependence. Fig. 9(b) and Fig. 9(c) show
energy profiles calculated for protons entering the range stack with energies of 30.6 cm in
the “front” run and 31.4 cm in the “back” run (corrections to the nominal CDH accelerator
energy were applied to account formaterial inthe tracker which isonly present inthe “front”
run configuration and material in the CDH beam transport line, as discussed in Section 5.3).
All “true” EclbTrue,tn = 0,95 amplitudes are normalized to the signal EclbExp of the Tile0
tn t0
in the “front” run. That is, we take the observed energy in Tile0 as to be correct.
The comparison of signals observed in Tile0 in runs of different energies and expected
signals obtained by integration of the tabulated proton dE/dx dependence are shown in
Fig. 10. The expected signals are normalized to the mean Tile0 data signal in the 32 cm
run. The measured and calculated amplitudes are in good agreement, however the data
signals are about 5% higher at low proton energies.
4) We extract normalization coefficients Kclb ≡ EtcnlbTrue and use them in all data runs to
tn EclbExp
tn
correct the observed signals inthe rangestack tiles. Figures 11(a) and(b) show the corrected
energy deposition profiles (the mean number of photoelectrons fromabout 10000 protons per
tile as function of tile number) for 200 MeV protons. Corrected energy profiles for different
beam energies are shown in Fig. 12 through Fig. 14. Slight variations are attributed to
5
BID= 30, Tile = 0:: Channel 0 BID= 30, Tile = 0:: Channel 16 BID= 30, Tile = 1:: Channel 1 BID= 30, Tile = 1:: Channel 17
Events/bin 56×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt 55iill1111ee4400223377__00..cc1177nn..223355ll00 Events/bin 67×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll55 ee111100442211__77cc..77nn7722..ll1155666666 Events/bin 789×103 hEMRhEMR22nnMMffeeiitttt__aarrSSbbiinneeii dd ss33 00 __ tt55 iill11 ee44 1100 7711__..cc116600nn338899ll11 Events/bin 67×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll 55 ee111111442211__77cc..88nn7766..ll1199883377
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4 <Pedestal> = 102.84 ADC <Pedestal> = 102.794 ADC 6 <Pedestal> = 101.784 ADC 5 <Pedestal> = 103.964 ADC
<single PE> = 120.971 ADC 4 <single PE> = 119.91 ADC 5 <single PE> = 117.05 ADC 4 <single PE> = 123.659 ADC
3 PE/ADC = 18.1311 PE/ADC = 17.1159 PE/ADC = 15.2661 PE/ADC = 19.6951
3 4 3
2 3
2 2
2
1 1 1 1
0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180
ADC counts ADC counts ADC counts ADC counts
BID= 30, Tile = 2:: Channel 2 BID= 30, Tile = 2:: Channel 18 BID= 30, Tile = 3:: Channel 3 BID= 30, Tile = 3:: Channel 19
Events/bin180×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt55ii llee11113322111155__44..cc6611nn..559944ll22 Events/bin 89×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll55 ee111122331111__55cc33..nn6699..ll1155777788 Events/bin 56×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt55 iill1111ee4433222277__00..cc7777nn..882244ll33 Events/bin 56×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt iill 55 ee111133441133__77cc88..nn4477..ll5511998899
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<Pedestal> = 105.081 ADC 6 <Pedestal> = 102.78 ADC 4 <Pedestal> = 104.807 ADC 4 <Pedestal> = 103.7 ADC
6 <single PE> = 122.451 ADC <single PE> = 121.203 ADC <single PE> = 123.872 ADC <single PE> = 123.669 ADC
PE/ADC = 17.3698 5 PE/ADC = 18.4234 3 PE/ADC = 19.0649 3 PE/ADC = 19.9687
4 4
3 2 2
2 2 1 1
1
0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180
ADC counts ADC counts ADC counts ADC counts
BID= 30, Tile = 4:: Channel 4 BID= 30, Tile = 4:: Channel 20 BID= 30, Tile = 5:: Channel 5 BID= 30, Tile = 5:: Channel 21
Events/bin 6×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt 55ii ll88ee114444..118877__77cc7777nn..556688ll44 Events/bin 7×103 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll55 ee 1111444411__2277cc66..nn7700..ll2266441100 Events/bin 89×103 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt55ii llee11114455111177__33..cc7777nn..779944ll55 Events/bin 78×103 hhEMREMR22ffnnMMiieett__ttaabbrrSSiiiinnddee 33 ss 00 __tt ii 55 llee88 441155..__114477cc111177nn..ll7777221111
6
5 7 6
4 <<sPinegdlees tPaEl>> == 111243.2.70548 A ADDCC 5 <<sPinegdlees tPaEl>> == 110230..153326 A ADDCC 6 <<sPinegdlees tPaEl>> == 110222..939711 A ADDCC 5 <<sPinedglees tPaEl>> = = 1 10122..576844 A ADDCC
PE/ADC = 9.55459 4 PE/ADC = 17.4045 5 PE/ADC = 19.3804 4 PE/ADC = 10.2202
3 3 4 3
2 2 23 2
1 1 1 1
0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180
ADC counts ADC counts ADC counts ADC counts
BID= 30, Tile = 6:: Channel 6 BID= 30, Tile = 6:: Channel 22 BID= 30, Tile = 7:: Channel 7 BID= 30, Tile = 7:: Channel 23
Events/bin112400 hhEMREMR22nnffMMeeiitt__ttaarrSSbbiinniieedd 33 ss 00 __ ttii 1111llee1122226622__..00cc3399..nn229977ll66 Events/bin112400 hhEMREMR22ffiinnMMttee__ttbbaarrSSiiiiddnnee 33 ss00 __ tt ii ll ee111111661122__2288cc..33nn77..ll3322221122 Events/bin116800 hhEMREMR22nnMMffeeiitttt__aarrSSbbiinneeiidd 33ss 00 __ tt55 ii ll11ee114477001177__..33cc8877nn..003366ll77 Events/bin114600 hhEMREMR22ffnniiMMeett__ttaabbrrSSiiiinnddee 33 ss00 __tt ii ll55ee 11117744__113377cc88..nn8822ll..2200111133
120
100 100 140
80 <<siPnegdlee sPtaEl>> == 112013..11615 A ADDCC 80 <<siPnegdlee sPtaEl>> == 112002..38459 A ADDCC 120 <<sPinedglees tPaEl>> = = 1 10116..790046 A ADDCC 100 <<sPinegdlees tPaEl>> == 110243..244721 A ADDCC
PE/ADC = 18.0555 PE/ADC = 17.4982 100 PE/ADC = 15.2019 80 PE/ADC = 19.2292
60 60 80 60
40 40 60 40
40
20 20 20 20
0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180 0 80 100 120 140 160 180
ADC counts ADC counts ADC counts ADC counts
Figure 6: No beam signals used for PE calibration for the first eight tiles of the range stack.
6
E(t0) 2 E(t0) 2
P P
N)/1.8 N)/1.8
E(t E(t
P1.6 P1.6
1.4 1.4
1.2 1.2
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90
Tile number Tile number
(a) (b) hfill
Figure 7: a) The ratio of PE conversion coefficients KpeSiPM0tn/KpeSiPM0t0 for the first
SiPMs. b) The ratio of PE conversion coefficients KpeSiPM1tn/KpeSiPM0t0 for the second
SiPMs.
statistical effects.
5 Range and energy measurements
The NIU image reconstruction software uses the WEPL of a scanned object, wepl . For
obj
each proton the wepl can be obtained from WEPL of the range stack, wepl ,
obj rs
wepl = E (cm)−wepl ,
obj beam rs
To find wepl one need calibrate the total energy E or the stopping range R measured by
rs rs rs
the range stack detector using a set of phantoms with known WEPL [3]. Here we compare
the accuracy of R and E to choose what measurement is preferrable for the WEPL
rs rs
calibration.
To find the total energy E deposited in the range stack we first search for the frame
rs
with a stopping tile (the “stopping” frame), then sum signals (in PE units) from all tiles
and all frames including the stopping frame. Only events with no missing frames before the
stopping frame were selected. Figure 15(a) shows the total E in PE measured in a run
rs
with E = 26 cm.
beam
To find R we use the Z-position of the tile with the maximum signal (the “stopping”
rs
tile, labeled as nt ). We calculate R as
stop rs
R = (nt +1)×(tileW ×tileD +alW ×alD +mlrW ×mlrD)+
rs stop
nframe×(alW ×alD +mlrW ×mlrD),nt = [0,95];nframe = [0,11]
stop
where (tileW,alW,mlrW) = (3.2,0.00022,0.00625) mm are the widths of scintillator and
wrapper (aluminized mylar) layers, and(tileD,alD,mlrD) = (1.011,2.700,1.397)g/cm3 are
the densities of these materials. The second term accounts for the extra layer of the wrapper
in the end of each range stack frame.
Note, thestopping rangesinpolysterene andmylar expressed ing/cm2 areapproximately
equal to the proton stopping range in water R :
w
7
BID= 30, Tile = 0:: Channel 0 BID= 30, Tile = 16:: Channel 16 BID= 30, Tile = 0:: Channels (0,16)
Events/bin 78×103 hhEMREMR22ffiinnttMMeeBBttSSaarrSSppiinneeee __ ssbb iidd 33 00 66__8383tt22iill....ee14140000__030322ccnn525244ll00 Events/bin1102×103 hEMRhEMR22ffnnMMiieettBBttSSaarrSSppiinneeee __ bbss iidd 3300 __ 66tt2244iill22ee....00333300__cc220022nnll1188554466 Events/bin 56×103 EMRχEMRχhh22nn22MMee //ttffaa rrSSiinniittnneeBB dd ss ffSS ppee__bbiidd 33446600 66.. __4444 22 tt..4411ii3300ll 22ee6622// ..0066447744
6 8 4 MMSSCCiiooeeggnnaammssnnaatt aa nn tt 44 11..5522119933..5544775566 ±± ±±±± 00 0033..00..880055..334411
5
4 6 3
3 4 2
2
2 1
1
00 5 10 15 20 25 30 35 00 5 10 15 20 25 30 35 00 10 20 30 40 50
PE counts PE counts PE counts
(a) (b) (c)
Figure 8: Measured signal amplitudes (PE units) in Tile0 at a beam energy of 26 cm (200
MeV) after subtracting pedestals : a) in SiPM1; b) in SiPM2; c) sum of SiPM1 and SiPM2.
The means of Gaussian fits of combined signals away from the Bragg peak at a beam energy
of 32 cm (225 MeV) were used to extract the normalization coefficients for the range stack
tiles.
Rm
R (cm) = RSP dL (3)
w Z m
0
where RSP is the proton stopping power of the medium relative to water and L is the
m
physical proton path length along the calorimeter and R is the physical depth at which
m
the proton stops in the range stack. Then, neglecting small variations ( < 0.5%) in mean
ionization potential between water, polystyrene and mylar, as used in the Bethe Bloch
equation, the water equivalent range of the proton becomes
Rm Rm
R (cm) ≃ ρ /ρ dL,and,forρ = 1.0 g/cm3,R (g/cm2) ≃ ρ dL
w Z m w w w Z m
0 0
Thus we expect R to have linear dependency on the beam energy, E , expressed in cm.
rs beam
Figure 16 shows R in a run with E = 26 cm.
rs beam
We also can find the R from the total energy E using Janni’s range-energy tables This
rs rs
method requires expression of E in MeV, and we use the conversion coefficient calculated
rs
as the ratio of the mean amplitude of the data signal (in number of photoelectrons) to the
mean amplitude of the estimated MC signal (in MeV) in Tile0, in 26 cm runs. Figure 15(b)
shows the proton stopping range in the range stack Rconv(g/cm2) calculated from E via
rs rs
the Rconv = 0.0021 × E(1.78) conversion function obtained from Janni’s tables. Finally, we
rs rs
can find wepl directly, from the WEPL of a scanned object calculated from E using the
rs rs
Bethe-Bloch equation. Howewer, this will also require calibration, as the measured E only
rs
includes the visible part of deposited energy. Figure 15(c) shows the WEPL of the range
stack weplcalc(cm) calculated from E via
rs rs
Ers 1
weplcalc = E (cm)− dE (4)
rs beam Z S(E )
Ebeam p
where S(E ) = −dE/dx is a water stopping power for proton with energy E .
p p
8
Proton Energy loss in polystyrene
dE/dX, MeV/(g/cm2) 456789000000 ppppppχpχp2222131300 // nn dd ff 00--..0000 ..00 2288--..33114499118833991188 558877.. 8822±±±±..99 ± ± ±±000000 ....8811662020 ....3131//5500 16163300669999666611 mplitude, number of photoelectrons1116802400000 CDDoeepprrooessciittteeeddd CeennDeeHrr ggeyyn::e 21rg1797y.1:2 .368089. 6PM1Ee6V cm mplitude, number of photoelectrons1116802400000 CDDoeepprrooessciittteeeddd CeennDeeHrr ggeyyn::e 21rg2719y.0:5 .386173. 4MP4Ee1V cm
30 Signal a40 Signal a40
20
20 20
10
0 10 102 00 20 40 60 80 100 00 20 40 60 80 100
Proton energy, MeV Tile number Tile number
(a) (b) (c)
Figure 9: a) The proton dE/dX dependency in polystyrene as tabulated in Janni’s proton
energy-range tables. b) The “true” front run signal profile used for calibration of tiles (0-47)
of the range stack. c) The “true” back run signal profile used for calibration of tiles (48-95)
of the range stack.
We fit peaks of the R and E distributions with a Gaussian and use the mean and σ
rs rs
parameters of the fits to study the linearity (R and E as functions of the beam energy)
rs rs
and resolution (σ(E )/E and σ(R )/R as functions of E and R ) of the range stack
rs rs rs rs rs rs
detector. The linearity and resolution plots for the proton stopping position R are shown
rs
in Fig. 17 and the linearity and resolution plots for the energy measurement are shown in
Fig. 18. The good linearity with a non zero intercept of the R shows there is material in
rs
front of the range stack at all energies. The energy measurement has lower accuracy (energy
resolution ranges from 5.5% to 3.5% , compared to 2.2-1.2% for R ) and also shows an
rs
unexpected suppression at beam energies of 27 cm and 28 cm. Additionally, Figures 15(a)
and (b) show that if we try to extract the stopping range or WEPL in the range stack from
the direct energy measurement, the Rconv and distributions with σ(Rconv) = 11.7 mm and
rs rs
σ(weplcalc) = 11.8 mm are significantly wider than R distribution with σ(R ) = 3.3 mm.
rs rs rs
Thus, the direct R measurement is preferred for the WEPL calibration.
rs
5.1 Comparison with GEANT 4 simulations
A GEANT 4 simulation of the pCT detector was used to obtain the energy deposition Eg4
tn
in the range stack tiles for different beam energies. We converted the range R to energy E
p p
using the inverse of the Janni fit:
E = (R /0.0022)(1/1.77).
p p
To compare energy profiles and total energy deposition in the range stack, the G4 signals in
the tiles were expressed in the number of photoelectrons by normalizing to the data signal
in Tile0 in the 26 cm beam run.
5.2 Smearing of simulated tile signals
To account for photo-statistics and SiPM readout, smearing of the G4 signals in each tile
was done as:
Sg4 = G(< Sped >)+P(Eg4)− < Sped > ,
tn tn tn tn
where < Sped > is a mean sum of SiPM pedestals in tile n from calibration runs, Eg4 is the
tn tn
9
s χχ22 // nnddff 00..11663311 // 1111
n
electro 24 pppp1100 --00..006655 77228822 ±±..55 00 ±±..00 0000..3333336688338844
hoto 22 pp22 99..118866ee--0055 ±± 77..553311ee--0066
p
of
er 20
b
m Data
u
n
0, 18
e Janni’s tables
Til
n
e i 16
d
u
mplit 14
a
al
n
Sig 12
10
0 50 100 150 200 250 300 350
Proton Energy, 0.1*(g/cm2)
Figure 10: Measured signal amplitudes (blue crosses) and expected amplitudes calculated
from Janni’s tables (red line) in Tile0 of the range stack for different proton energies. The
expected signals normalized to the mean (over 10000 protons) Tile0 data signal in the 32 cm
run.
energy deposition in tile n obtained from GEANT, and G(Sped) and P(Eg4) are the sum of
tn tn
SiPM pedestals smearing using Gaussian and Eg4 smeared using Poisson distribution. The
tn
effect of smearing is shown in Fig. 19, where the left plot shows the total energy deposition
in the range stack at a beam energy of 26 cm (or 200 MeV) in data; the center histogram
shows the unsmeared simulated signal, and the right histogram shows the smeared signal.
Comparison of data and simulated signals from 200 MeV protons in Tile0 and in Tile74 (the
stopping tiles with the maximal signal for this energy) are shown in Fig. 20.
5.3 Beam energy correction and smearing for the MC simulations
The total stopping range of all material along the proton path, R , before the proton
total
stopping position is equal to the nominal beam energy of the accelerator in g/cm2, R ≡
total
Ebeam. In our test beam configuration, the total stopping range can be expressed as:
total
R = R +R +R +sft const,
total rs beamline tracker
where R , R , R are the proton ranges in the range stack, any material in the
rs beamline tracker
accelerator beam line, and the tracker, respectively.
The sft const is the systematic shift of the range measurement due to initial and arbi-
trary origin of the range calculation. We extract the stopping range using the position of
the tile with the maximum signal and the total width of scintillator and wrapping layers
including this stopping tile. The definition of stopping position is arbitrary and for con-
sistency estimated with the MC. We estimate the sft const using simulations of the range
stack response in configuration with no tracker. In the GEANT model we do not have any
other material before the range stack, and the sft const can be obtained from the fit of the
proton stopping positions at different beam energies, as shown in Fig. 21(a). Evaluation
of the fit function at zero beam energy results in sft const=0.7 ± 0.4 mm in water (the
−p0 parameter of the fit). From the fit of the measured proton stopping position R in
rs
10