AN ALGORITHM FOR DOSE ESTIMATES USING LiF THERMOLUMINESCENT DETECTORS
Submitted by Michel ATIEH
Department of Civil and Industrial Engineering School of Nuclear Engineering
In partial fulfillment of the requirements For the Degree of Master of Science
University of Pisa Pisa, Italy Fall 2019
Advisor: Prof. Eng. Francesco D’ERRICO Co-Advisor: Prof. Eng. Riccardo CIOLINI
2
Abstract
The purpose of the thesis is to find algorithms that can be used to get the perosnal dose equivalents Hp(d) using TL dosimeters. To do so, the plan was to irradiate dosimeters with different filters, in air and on a phantom using monoenergetic radioisotopes of low, medium and high Gamma rays energies. In this manner, we can conclude if it is right to calculate the Hp(10) for the UniPi dosimeters as it was done previously, and try to create an algorithm for the four-element dosimeter in a way to conclude the deep, shallow and eye lens doses. In addition, we can see the effect that the phantom has on the dose received by the dosimeter. We also irradiated the dosimeters with protons of different energies therefore analyzing the response of the dosimeters at different energy levels, filters, and their response to charged particles.
241Am (Americium) was our low energy radioisotope because it emitted gamma rays at 49 keV, 137Cs (Cesium) was chosen to be our medium energy radioisotope as it emitted gamma rays at 662 keV, and finally 60Co (Cobalt) was used to cover the high range of energy as it emitted gamma rays at 1.17 MeV and 1.33 MeV.
The irradiations with 60Co were done at Bruno Guerrini Laboratory, as for the irradiations with 241Am and 137Cs, they were made at the SSDL (Secondary Standard Dosimetry Laboratory) at C.I.S.A.M. (Joint Research Center for Military Applications). Lastly, the irradiations with protons were done at INFN – LNL (National Institute of Nuclear Physics – National Laboratories of Legnaro).
At the end of this work, we were able to find different algorithms for the University of Pisa dosimeter, and for the four-element dosimeter.
3 Table of Contents
Abstract ... 2
Acknowledgments ... 9
CHAPTER 1 DOSIMETRY FUNDAMENTALS ... 10
1.1 Introduction to Radiation Dosimetry ... 10
1.2 What is a Dosimeter? ... 10
1.3 Simple Dosimeter Model in Terms of Cavity Theory ... 11
1.4 General guidelines on the Interpretations of Dosimeter Measurements ... 12
1.5 Advantages of Media Matching ... 13
1.6 Media Matching of w and g in Photon Dosimeters ... 13
1.7 Correcting for Attenuation of Radiation ... 16
1.8 Importance of Dosimeter Wall Thickness... 17
1.9 Charged Particles ... 17
1.9.1 Dosimeter Size ... 17
1.9.2 δ - Ray Equilibrium ... 18
1.10 General Characteristics of Dosimeters ... 19
1.10.1 Absoluteness ... 19
1.10.2 Precision and Accuracy ... 19
1.10.3 Dose Range ... 20
1.10.4 Stability ... 23
1.10.5 Energy Dependence ... 24
1.11 Integrating Dosimeters ... 26
1.11.1 Thermoluminescence Dosimetry... 26
ii. Basis for Calibration ... 39
CHAPTER 2 EXPERIMENTAL PART ... 46
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2.1.1 University of Pisa Dosimeter ... 46
2.1.2 Four-element dosimeter ... 47
2.2 Preparation of Dosimeters and Reader ... 49
2.2.1 Choosing Calibration Dosimeter ... 50
2.2.2 Calculating the RCFs ... 50
2.2.3 Calculating the ECCs ... 50
2.3 Dosimeters Preparation and Calibration of UniPi ... 52
2.4 Irradiations ... 52
2.4.1 60Co irradiation at Bruno Guerrini Laboratory ... 52
2.4.2 241Am, and 137Cs irradiations at SSDL Multicurie Laboratory at CISAM (Marina Militare Centro Interforze Studi Applicazioni Militari) ... 63
2.4.3 Dosimeter identification ... 68
2.4.4 Irradiation of four-element dosimeter, and its badge holder ... 73
2.4.5 Protons irradiation at INF – LNL (National Institute of Nuclear Physics – National Laboratories of Legnaro) ... 75
2.5 Relationship between the Energy and the Intensity of a beam ... 79
2.6 Personal Dose Equivalents Hp (0.07), Hp (3), and Hp (10) using the University of Pisa Dosimeter ... 81
2.7 Personal Dose Equivalent Hp (0.07) and Hp (10) using the four filters Dosimeter ... 82
2.8 Personal Dose Equivalent Hp (3) using the the four filters Dosimeter ... 83
CHAPTER 3 COMPARISON OF ANALYTICAL AND EXPERIMENTAL DATA ... 84
3.1 Aluminum ... 84
3.2 PTFE (Polytetrafluoroethylene) ... 85
3.3 Copper ... 86
3.4 Mylar ... 87
3.5 Copper + ABS ... 88
CHAPTER 4 ALGORITHMS GENERATION ... 89
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4.1.1 in Air ... 89
4.1.2 on Phantom ... 91
4.2 Generation of an algorithm for the four element dosimeter ... 94
4.2.1 in Air ... 94
4.2.2 on Phantom ... 95
4.4 Relative Response of TLD crystals to 137Cs... 96
CONCLUSION ... 97
6 Table of Figures
Figure 1: Schematic depiction of a dosimeter as a sensitive volume V containing medium g, surrounded by a wall of medium w and thickness t ... 11 Figure 2: Illustrating a double-valued dose-response function resulting from a decrease in the dosimeter sensitivity at high doses... 23 Figure 3: Typical energy-dependence curves in terms of the response per unit exposure of x- or 𝛾-rays ... 25 Figure 4: Energy-level diagram of the thermoluminescence process: (A) ionization by
radiation, and trapping of electrons and holes; (B) heating to release electrons, allowing luminescence production. ... 27 Figure 5: (a) Glow curves vs. time obtained with a CaF2: Mn TL dosimeter at eight linear heating rates. The dose to the phosphor was adjusted to be inversely proportional to the heating rate in each case. ... 29 Figure 6: (b) Glow curves vs. temperature recorded simultaneously with the curves in a. .... 30 Figure 7: the components that form a TLD reader ... 32 Figure 8: TLD reader at the Nuclear Measurements Laboratory at University of Pisa ... 33 Figure 9: Figure showing the lenses inside the TLD to magnify to light output of the crystals ... 33 Figure 10: Typical programmed readout cycle in a modern TLD reader, consisting of a
“preheat” period without light integration to discriminate against unstable low-temperature traps, a “read” period spanning the emission of the part of the glow curve to be used a “preheat” period without light integration to discriminate against unstable low-temperature traps, a “read” period spanning the emission of the part of the glow curve to be used as a measure of the dose, an “anneal” period during which the remainder of the stored energy is “dumped” without light integration, and the cooling-down period after the heater-pan power is turned off ... 35 Figure 11: Glow curves vs. temperature (upper scale) and time (lower scale) for four
thermolnminescent dosimetry phosphors. Heating rate: 40 ℃/min. The amplitudes are
arbitrary. (Gorbics et al., 1969. Reproduced with permission from Pergamon Press, Ltd.) ... 38 Figure 12: Glow-peak-area response vs. 60Co 𝛾-ray exposure for several TL phosphors. The relative TL output of the phosphors is arbitrary (see Table 2)- The LiF: Mg, Ti curve was
7 taken from Cameron et a1. (1967); Li2B4 : Mn, from Wilson and Cameron (1968); CaSO2:
Mn, from Bjarngard (1967); CaF2:Mn, from Gorbics et al. (1973). ... 39
Figure 13: LET response of BeO, Li2B4O7:Mn, and LiF. The curves give values of kCo/kLET as a function of LET in water, in keV/𝜇m. The inset indicates the types of radiation sources and particles used. (Tochilin et d., 1968. Reproduced with permission from E. Tochilin) ... 42
Figure 14: Thermoluminescent response of LiF per roentgen and per rad for photon energies from 6 to 2800 keV. (Tochilin et al., 1968. Reproduced with permission from E. Tochilin.) 43 Figure 15: Thermoluminescent response of Li2B4O7:Mn per roentgen and per rad for photon energies from 6 to 2800 keV. Tochilin et al., 1968. Reproduced with permission from E. Tochilin.) ... 43
Figure 16: Dosimeter configuration of Thermo-Fischer's brochure ... 47
Figure 17: Beta-Gamma Dosimeter assembly configuration ... 48
Figure 18: Dosimeter configuration figure from "The essential Physics of Medical Imaging" book ... 49
Figure 19: Irradiation of all dosimeters on the rotary radiator to generate the reader calibration factor (RCF) at the Bruno Guerrini laboratory ... 53
Figure 20: The Aluminum (1 mm thcikness), filters that were used for the irradiation ... 55
Figure 21: Figures showing the rotary radiator that was used to irradiate in air ... 56
Figure 22: Image showing the 30×15×15 cm plexiglass phantoms that were used in the Bruno Guerrini Laboratory ... 59
Figure 23: irradiations at the SSDL Laboratory at CISAM ... 64
Figure 24: irradiations at the SSDL Laboratory at CISAM ... 65
Figure 25: irradiation of dosimeters at the Nuclear Measurements Laboratory ... 73
Figure 26: irradiation at CISAM with the dosimeter in the badge holder and using the water phantom 30 × 30 × 15 cm ... 74
Figure 27: irradiation at CISAM with the dosimeter in the badge holder, on phantom ... 75
Figure 28: SRIM & TRIM simulation of shooting a Hydrogen atom of energy 0.75 MeV into a LiF target of thickness 0.8 mm ... 76
Figure 29: SRIM & TRIM simulation of shooting a Hydrogen atom of energy 6 MeV into a LiF target of thickness 0.8 mm ... 77
Figure 30: curves showing the intensity of different energy beams passing through different filters ... 79
Figure 31: curves showing the intensity of different energy beams passing through different filters (60 keV to 6 MeV) ... 80
8 Figure 32: different materials and thicknesses used to get a personal dose equivalent Hp(10) known as “Deep dose” ... 81 Figure 33: Intensity vs Energy curves for Hp (0.07), and Hp (10) estimation ... 82 Figure 34: Intensity vs Energy curves for Hp (3) estimation ... 83 Figure 35: Analytical curve of aluminum with experimental data when irradiated with 241Am, 137Cs, and 60Co radioisotopes in Air, on a 30 × 15 × 15 cm plexiglass phantom with error bars of 14 % (Phantom). ... 84 Figure 36: Analytical curve of aluminum with experimental data when irradiated with 241Am, 137Cs, and 60Co radioisotopes in Air, on a 30 × 15 × 15 cm plexiglass phantom with error bars of 20 % (Phantom) ... 85 Figure 37: Analytical curve of aluminum with experimental data when irradiated with 241Am, 137Cs, and 60Co radioisotopes in Air, on a 30 × 15 × 15 cm plexiglass phantom with error bars of 20 % (in Air and Phantom)... 86 Figure 38: Analytical curve of aluminum with experimental data when irradiated with 241Am, 137Cs, and 60Co radioisotopes in Air, on a 30 × 15 × 15 cm plexiglass phantom with error bars of 18 % ... 87 Figure 39: Analytical curve of aluminum with experimental data when irradiated with 137Cs on a 30 × 15 × 15 cm plexiglass phantom with error bars of 10 % ... 88 Figure 40: the average relative response of the University of Pisa dosimeter to 1 mGy dose at different energies, and the analytical values of Soft Tissue at 0.07 mm and 10 mm thickness, in air ... 89 Figure 41: the average relative response of the University of Pisa dosimeter to 1 mGy dose at different energies and the analytical values of Soft Tissue at 0.07 mm and 10 mm thickness, on phantom ... 91 Figure 42: the average relative response of the four-element dosimeter to 1 mGy dose at different energies, in Air ... 94 Figure 43: the average relative response of the four-element dosimeter to 1 mGy dose at different energies, on phantom ... 95 Figure 44: the relative response to 137Cs of Al2O3:C, LiF:Mg,Ti, and Lif:Mg,Cu,P TLD crystals at different photon energies from Thermo Fisher brochure. ... 96
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Acknowledgments
During the making of this thesis, numerous individuals bigheartedly gave their time and expertise. Without their help, it would not have been possible to be where I am today.
I would like to express my deepest appreciation to Prof. Francesco D’ERRICO, Prof. Riccardo CIOLINI, Eng. Alessio ONORATI, Tech. Fabio PAZZAGLI, and Tech. Renato SANDRINI.
I would like to extend my sincere thanks to my dear family Jean, Ramza, Mario ATIEH, and my love Stéphanie KALKACHE for their constant support on all levels during my time abroad.
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CHAPTER 1 DOSIMETRY FUNDAMENTALS
1.1 Introduction to Radiation Dosimetry
Radiation dosimetry (or simply “dosimetry”) is the measurement of the absorbed dose or dose rate resultant from the interaction of ionizing radiation with matter. In general terms, it is the determination (i.e., by measurement or calculation) of these quantities, as well as any of the other radiologically relevant quantities such as exposure, kerma, fluence, dose equivalent, energy imparted. We usually measure one quantity (usually the absorbed dose) and derive another from it through calculations based on the previously defined relationships. Energy spectrometry of ionizing radiations is a separate task, but is often carried out in parallel with a dosimetry problem, and may then be considered an integral part of it.
1.2 What is a Dosimeter?
A dosimeter can be defined normally as a device that has the capability of providing a reading r that is a measure of the absorbed dose Dg, deposited in its sensitive volume V by ionizing radiation. If the dose is not homogeneous throughout the sensitive volume, then r is a measure of some kind of mean value D̅g. In an ideal world, r is proportional to Dg and each volume element of V has equal effect on the value of r, in which case D̅g is just the average dose throughout V. This idealization is most of the times well approximated in practical dosimeters. Most dosimeters do exhibit some degree of nonlinearity of r vs. D over at least some part of their dose range, or there may be poor coupling of the dose-measuring signal to the readout reader. For example, an ion chamber may have regions from which the ions are not completely collected, or all segments of a large scintillator may not deliver light homogeneously to the photomultiplier therefore affecting its efficiency.
This discussion of course is as well valid to dose-rate measuring devices by substituting dD̅g
dt for D̅g.
Usually we are interested in measuring the absorbed dose in a dosimeter’s sensitive volume as a means of determining the dose (or a related quantity) for another medium in which direct measurements are not possible. Interpretation of a dosimeter reading in terms of the desired quantity is the main problem in dosimetry, generally exceeding in difficulty the actual measurement.
11 Sometimes, the dosimeter can be calibrated directly in terms of the desired quantity (e.g., exposure, or tissue dose), but this kind of calibration is generally energy dependent unless the dosimeter strictly simulates the reference material.
1.3 Simple Dosimeter Model in Terms of Cavity Theory
A dosimeter can normally be described as formed of a sensitive volume V filled with medium g, surrounded by a wall (or envelope, package, container, capsule, buffer layer, etc.) of another medium w having a thickness t ≥ 0, as shown in Fig. 1.
A simple dosimeter can be treated in terms of cavity theory, the sensitive volume being identified as the “cavity”, which may contain a gaseous, liquid, or solid medium g, depending on the type of dosimeter.
Cavity theory is one of the most powerful tools of interpretation of dosimeter readings. The dosimeter wall can serve a number of functions simultaneously, including:
i. being a source of secondary charged particles that contribute to the dose in V, and provide charged-particle equilibrium (CPE) or transient charged-particle equilibrium (TCPE) in some cases.
ii. shielding V from charged particles that originate outside the wall.
iii. protecting V from “hostile” influences such as mechanical damage, dirt, humidity, a. light, electrostatic or RF fields, etc., that may alter the reading.
iv. serving as a container for a medium g that is a gas, liquid, or powder.
v. containing radiation filters to modify the energy dependence of the dosimeter.
Figure 1: Schematic depiction of a dosimeter as a sensitive volume V containing medium g, surrounded by a wall of medium w and thickness t
12 The dosimeter wall has many functions, of which: being a source of secondary charged particles that contribute to the dose in V, and provide charged-particle equilibrium (CPE) or transient charged-particle equilibrium (TCPE) in some cases, shielding V from charged particles that originate outside the wall, protecting V from “hostile” influences such as mechanical damage, dirt, humidity, light, electrostatic or RF fields, etc., that may alter the reading, serving as a container for a medium g that is a gas, liquid, or powder, and containing radiation filters to modify the energy dependence of the dosimeter.
1.4 General guidelines on the Interpretations of Dosimeter Measurements
For Photons CPE D = Kc = ψ ( 𝜇𝑒𝑛 𝜌 ) (1.1) and TPCE D = Kc (1 + μ’𝑥̅) ≡ Kcβ = ψ ( 𝜇𝑒𝑛 𝜌 )β (1.2)
Consider a dosimeter with a wall of medium w, thick enough to discount all charged particles generated anywhere , and at least as thick as the maximum range of secondary charged particles generated in it by the photon. The dosimeter reading r will give us a measure of the dose Dg in the dosimeter’s sensitive volume. If the sensitive volume is small enough to assure the Bragg-Gray (B-G) condition of nonperturbation of the charged-particle field, and pressuming that the wall is homogeneously irradiated, CPE occurs in the wall near the cavity. B-G or Spencer cavity theory is consequently used to determine the dose Dw there from that (Dg) in the sensitive volume. Then Eq. (1.1) allows the calculation of ψ or ϕ for the primary field from the value of Dw. Furthermore, the dose Dx in any other medium x substituting the dosimeter and given an identical irradiation under CPE conditions can be gotten from
CPE Dx = Dw (𝜇𝑒𝑛⁄𝜌) 𝑥 ̅̅̅̅̅̅̅̅̅̅̅̅̅ (𝜇𝑒𝑛⁄𝜌) 𝑤 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅ for photons (1.3)
The exposure C(C/kg) for photons can subsequently be derived from the absorbed dose Dair (for x = air) through this relation:
CPE X = Dair
(
𝑒
13 For higher-energy radiation (hν ≥ 1 MeV), where CPE fails but TCPE takes its place in dosimeters with walls of enough thickness, Eq. (1.2) replaces Eq (1.1). Relating Dw to ψ or ϕ then necessitates evaluation of the ratio β = D/Kc for each case. Nevertheless, the value of β is usually not much greater than unity for radiation energies up to a few tens of MeV, and it is not very dependent on atomic number. Therefore, for media w and x not differing significantly in Z, Eq. (1.3) is still roughly valid. If the dosimeter’s sensitive volume is too large for the application of B-G theory, Burlin theory can be replaced to calculate the equilibrium dose Dw in the wall medium at the point of interest, from the value of D̅̅̅̅ specified by the dosimeter g reading. Therefore, the preceding equation (1.1) is still operational. However, the sensitive volume-size parameter d is required to be known in this case, and it may not follow exactly the simple forms suggested by Burlin and others, leading to uncertainty in dosimetry interpretation.
1.5 Advantages of Media Matching
There are strong advantages in matching a dosimeter to the medium of interest x, and also matching the media composing the wall (w) and sensitive volume (g) of the dosimeter to each other. Atomic composition is the most apparent matching parameter, but the density state (gaseous vs. condensed) effects the collision-stopping power ratio of w to g for electrons by the polarization effect.
If the wall and sensitive-volume media of the dosimeter are similar.
w = g
with respect to composition and density, then Dw = D̅g for all homogeneous irradiations.To the extent that w and g are at least made similar to each other with respect to composition and density state (i.e., gaseous vs. condensed), the influence of cavity theory is kept minimal. Subsequently, the information required regarding the radiation energy spectrum to consent precise evaluation of the terms in, for example, the Burlin cavity relation is lowered, allowing the use of suitable estimates without noteworthy loss of precision in determining Dw from D̅g.
1.6 Media Matching of w and g in Photon Dosimeters
Since it is not always feasible to try to devise a homogeneous dosimeter to make w and g actually similar in atomic composition, it will be useful to mention the important parameters involved. The Burlin cavity relation (1.5) is useful in this connection:
𝐷𝑔 ̅̅̅̅ 𝐷𝑤 = d ∙ m𝑆̅𝑤 𝑔 + (1 – d)(𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤 𝑔 (1.5)
14 It can be seen that the average dose D̅̅̅̅ in the dosimeter’s sensitive volume will be equivalent g to the equilibrium dose Dw in the wall medium if
m𝑆̅𝑤𝑔= (𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤 𝑔 = 1 (1.6)
independently of the value of d, which differs with the size of the dosimeter’s sensitive volume. In other quarters, the matching criteria between the media w and g call for the respective matching of their mass collision stopping powers and their mass energy- absorption coefficients. When those parameters are each the same for the wall as for the medium in the sensitive volume V, the need to evaluate d in the Burlin equation is eliminated as it is a considerable simplification.
Additionally, since D̅̅̅̅ then remains equal to Dg w. which is the CPE dose value in the wall medium at the point of interest, Eq. (1.3) may be used to calculate the dose in medium x from the observed value of Dw measured by the dosimeter.
The requirements given in Eq. (1.5) are still quite strict and difficult to attain, especially for a material w that its atomic composition is not identical to g. A more practicable matching relationship between media w and g is the following:
m𝑆̅𝑤𝑔= (𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤 𝑔 = n (1.7)
where n is some constant, no longer required to be unity. In other words, the ratio of mass collision stopping powers for g/w is only required to be equal to the corresponding ratio of mass energy absorption coefficients. Under these conditions the Burlin equation simplifies to
𝐷𝑔
̅̅̅̅
𝐷𝑤 = dn + (1 - d)n = n (1.8)
regardless of the value of d, as was the case for Eq. (1.8). Nevertheless, now we see that D̅̅̅̅ is g n times as large as Dw.
To further understand how the value of Dw depends on n, we write the following Burlin equations for two dosimeters containing the same sensitive volume medium g, and given the
15 same photon irradiation. One is enclosed in wall w1 and obeys Eq. (1.5), while-the other is enclosed in w2 and obeys Eq. (1.6):
𝐷̅𝑔1 𝐷𝑤1 = d ∙ m𝑆̅𝑤 𝑔 + (1 – d)(𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤1 𝑔 = 1 (1.9) 𝐷̅𝑔2 𝐷𝑤2 = d ∙ m𝑆̅𝑤2 𝑔 + (1 – d)(𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤2 𝑔 = 1 (1.10)
But Dw1 and Dw2 are equilibrium absorbed doses in media w1 and w2, and are linked by
CPE 𝐷𝑤1 𝐷𝑤2 = ( 𝜇𝑒𝑛 𝜌 ̅̅̅̅) 𝑤2 𝑤1 = n (1.11)
the last equality having been derived from Eqs. (1.3) and (1.6). Comparison with Eq. (1.9) shows that
Dg2 ̅̅̅̅̅ = Dw1
and Eq. (1.11) then provides the equality
𝐷𝑔1
̅̅̅̅̅ = 𝐷̅̅̅̅̅ (1.12) 𝑔2
This proves that the dose in the dosimeter’s sensitive volume is independent of the value of n so long as Eq. (11.9) is satisfied. This is because, under these conditions, the equilibrium dose in the wall is inversely proportional to n, thus maintaining D̅̅̅̅ constant. Thus, the reading of g the dosimeter gives a value of D̅̅̅̅ that is the same as if the wall were perfectly matched to g. g
The practical case to which this approach is applicable occurs where photons interact only by the Compton effect in g and w. Then μen/ρ is nearly proportional to the number of electrons per gram, NAZ/A. To a first approximation so is the mass collision stopping power of the secondary electrons. Consequently Eq. (11.6) is approximately satisfied, with
16
1.7 Correcting for Attenuation of Radiation
We should pay some attention to the difference in the attenuation of uncharged radiation in penetrating into the dosimeter and into the medium of interest, based on the geometry. For example, if the dosimeter shown in Fig.1 were immersed in a water medium (x) and irradiated with a γ-ray beam, the broad-beam attenuation could be calculated by applying μen/ρ in the straight-ahead approximation, to the wall thickness t plus the radius r of the sensitive volume. That is, the photon energy fluence ψdos reaching the center of the dosimeter, given ψ0 incident on its outer periphery, would be gotten from
Ψdos ≅ ψ0 exp [− (𝜇𝑒𝑛 𝜌 )𝑤 𝜌𝑤𝑡 − ( 𝜇𝑒𝑛 𝜌 )𝑔 𝜌𝑔𝑟] ≅ ψ0 [− ( 𝜇𝑒𝑛 𝜌 )𝑤 𝜌𝑤𝑡 − ( 𝜇𝑒𝑛 𝜌 )𝑔 𝜌𝑔𝑟] (1.13)
where ρw and ρg are the densities of media w and g, respectively. However, the corresponding ψwat reaching the center of the sphere of water that would replace the dosimeter if it were removed, and assuming the same ψ0 value, would be:
𝜓𝑤𝑎𝑡 ≅ ψ0 exp [− (𝜇𝑒𝑛
𝜌 )𝑤𝑎𝑡 𝜌𝑤𝑎𝑡(𝑡 + 𝑟)] ≅ ψ0 [1 − ( 𝜇𝑒𝑛
𝜌 )𝑤𝑎𝑡 𝜌𝑤𝑎𝑡(𝑡 + 𝑟)] (1.14)
Clearly if the dosimeter wall and sensitive volume were exactly water-equivalent with respect to μen
ρ and ρ, Eqs. (1.12) and (1.13) would be equal, signifying cancellation of attenuation effects. Else, the dosimeter reading should be multiplied by ψwat/ψdos to correct for the difference of attenuation in determining the dose to water at the dosimeter midpoint. Where TCPE is present in place of CPE, the attenuation correction factor becomes βψwat/βψdos ,which simplifies to ψwat/ψdos if β can be presumed to have roughly the same value in both media.
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1.8 Importance of Dosimeter Wall Thickness
Deciding in advance of making a measurement what its goal will be will surely be helpful: To measure a quantity that depends on (a) the characteristics of the local photon, or (b) the characteristics of the local secondary charged-particle field.
If (a) is the objective, then the dosimeter should have a wall at least as thick as the maximum range of the charged particles present, to provide CPE or TCPE. On the other hand, if (b) is the objective, then the dosimeter wall and sensitive volume should both be thin enough not to interfere with the passage of incident charged particles.
The two situations provide themselves to fairly direct dosimetric interpretation. For the thick-wall case, the dose in other media can be obtained through the ratio of mass energy-absorption coefficients factor, as shown in Eq (1.13). For a thin wall and thin detector, the dose in other media can be derived through B-G or Spencer cavity theory, i.e., stopping-power ratios.
1.9 Charged Particles
The absorbed dose at a point in a medium is obtained as the product of the charged-particle fluence (not the energy fluence) and the mass collision stopping power, assuming that CPE exists for the δ-rays. This product is to be summed over all energies in the primary (i.e., non-δ ray) charged-particle spectrum.
The practical application of this declaration is usually restricted by a lack of information about the fluence and its spectrum, even though transport calculations (especially Monte Carlo) are helping to remedy that deficiency. Nonetheless, to verify the calculations dosimeter measurements are necessary at least to validate the calculations, and measurements are often easier and less expensive to carry out to a given level of precision.
Following are some important considerations in charged-particle dosimetry:
1.9.1 Dosimeter Size
For measuring the dose at any point in a medium, a dosimeter needs a sensitive volume small (or thin) enough to satisfy the B-G conditions, i.e., nonperturbation of the charged-particle field, and all dose to be deposited only by crossers. Furthermore, the dosimeter wall should be thin enough so the dosimeter as a whole does not significantly disturb the field, but thick enough to serve any essential functions (e.g., containment) required by the dosimeter. Thin flat pillbox- or coin shaped dosimeters, oriented perpendicular to the particle-beam direction, are often used to satisfy these requirements as closely as possible.
18 One may take as a rule of thumb that neither the wall thickness nor that of the sensitive volume should exceed ~ 1 % of the range of the incident charged particles.
1.9.2 δ - Ray Equilibrium
One of the functions of the dosimeter wall is to produce δ rays to take the place of those that are generated in, and escape from, the sensitive volume.
Table 1: Approximate CSDA Ranges of Electrons and Protons in Water
Otherwsie speaking, the wall should offer δ-ray CPE for the sensitive volume. This will be accomplished if the wall matches the sensitive volume almost with respect to atomic number and density state, is at least as thick as the maximum δ-ray range, and is homogeneously irradiated throughout by the primary charged particles.
The significance of the wall as a δ-ray generator is highest when the dose in free space is to be measured. In that case the escaping δ-rays are not replaced at all except if the wall or other ambient media (including the air) deliver them. The thinner the sensitive volume is, the more its dose is decreased by δ-ray losses, and the more reliant on it becomes on the wall to supply δ-ray equilibrium. For heavy charged-particle beams the maximum δ-ray energy T’max is almost equal to β2/(1 – β2), in MeV. Therefore, 10-MeV protons for example, generate 6 rays of maximum energy T’max = 20 keV, with a range in water of 9 × 10−4 g/cm2, or 8 mm of air. The proton’s range in this case is over 100 times greater. Therefore, δ-ray CPE is simply achieved for heavy-particle beams.
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1.10 General Characteristics of Dosimeters
1.10.1 Absoluteness
An absolute dosimeter can be assembled and used to measure the absorbed dose deposited in its own sensitive volume without necessitating calibration in a known field of radiation. Nevertheless, it may need some sort of calibration not involving radiation, like electrical-heating calibration of a calorimetric dosimeter.)
Three types of dosimeters are now commonly regarded as being capable of absoluteness: i. Calorimetric dosimeters.
ii. Ionization chambers.
iii. Fricke ferrous sulfate dosimeters
These are not at all times considered as absolute dosimeters, nevertheless, because calibration gives certain advantages: A calibration can be specified in terms of some quantity of interest other than the absorbed dose in the sensitive volume, e.g., tissue dose or exposure. It can also offer traceability to an authoritative standardization laboratory such as the National Bureau of Standards.
Note that the absoluteness of a dosimeter is independent of its precision or its accuracy, characteristics to be discussed next. Nevertheless, to be useful, an absolute dosimeter must be reasonably accurate and precise as well.
1.10.2 Precision and Accuracy
The concept of the precision or reproducibility of dosimeter measurements is related to random errors due to fluctuations in instrumental characteristics, ambient conditions, and so on, and the stochastic nature of radiation fields. Precision can be assessed from the data obtained in repeated measurements, and is usually specified in terms of the standard deviation. High precision is associated with a small standard deviation.
The standard deviation mentioned should be stated for a set of measurements refers to the precision of individual readings or of their mean value. The precision of a single measurement indicates how closely it is likely to agree with the expectation value of the quantity being measured. Similarly, the precision of the average value of a group of repeated measurements expresses the likelihood of its agreement with the expectation value. For a sufficiently large number of readings, their average value coincides with the expectation value.
20 The accuracy of dosimeter measurements demonstrates the closeness of their expectation value to the true value of the quantity being measured. Thus, it is impossible to evaluate the accuracy of data from the data themselves, as is done to assess their precision. Accuracy is a measure of the collective effect of the errors in all the parameters that influence the measurements. Estimation of the accuracy of an experimental determination is a tedious process, based mainly on “educated guessing”. It is better done by the experimenter than by some later reviewer who lacks knowledge of the details. Note that in experiments that are limited to relative measurements, only the precision, not the accuracy, is important.
Although parametric errors are not random, but represent biases either up or down from their true values, their estimated magnitudes are usually combined as random errors if their direction is unknown and is believed to have equal probability of being too high or too low.
Clearly precision and accuracy are separate characteristics. Measurements may be highly precise but inaccurate, or vice versa, or may be strong in both or neither of these virtues. If one speaks of a dosimeter as being a high-precision instrument, one means that it is capable of excellent measurement reproducibility if properly employed. Poor technique, a hostile environment (e.g., high atmospheric humidity) or faulty peripheral equipment (e.g., ion-chamber cables or electrometer) may nevertheless cause poor reproducibility. A statement about the accuracy of a dosimeter refers to the freedom from error of its calibration, or of the parameters (such as the ion-chamber volume) that are relevant to its operation as an absolute instrument.
Accuracy depends on the type of radiation being measured, and dosimeter calibrations are more or less specific in that respect. A dosimeter that is accurately calibrated to measure the exposure at one x-ray quality may be significantly in error at another.
The quantity that a dosimeter is inherently the most capable of measuring accurately, and that is the least influenced by changing the type or quality of the radiation, is the absorbed dose deposited in the dosimeter’s own sensitive volume.
1.10.3 Dose Range
1.10.3.1 Dose Sensitivity
To be funcitonal, a dosimeter must have suitable dose sensitivity (𝑑𝑟 𝑑𝐷⁄ ̅̅̅̅𝑔) the dose range to be measured. A constant dose sensitivity throughout the range offers a linear response (i.e., reading vs. dose, r vs. (𝐷̅̅̅̅), that is desirable for ease of calibration and interpretation. However, 𝑔
21 single-valuedness of the function (𝐷̅̅̅̅), even if nonlinear, may be acceptable, though it requires 𝑔 that the calibration be carried out at a multiplicity of doses to provide a calibration curve.
1.10.3.2 Background Readings and Lower Range Limit
The lower limit of the useful dose interval can be imposed by the instrumental background or zero-dose reading. This is the value of r = r0 detected when 𝐷̅̅̅̅ = 0; every so often it is 𝑔 denoted as ‘‘spurious response”, since it is not caused by radiation. Examples of r0 include charge readings due to ion-chamber insulator leakage, and thermoluminescence dosimeter readings resulting from response of the reader to infrared light emission by the dosimeter heater.
Obviously the instrumental background should be deducted from any dosimeter reading. The typical procedure for defining this correction is to do measurements with the same dosimeter treated in the same way (including duration of the time) excluding the absence of the applied radiation field. In this maner the quantity one measures is 𝑟0, plus the radiation background reading 𝑟𝑏. Therefore, if the radiation field to be measured is turned of during the background measurement, the ambient radiation field contributed by cosmic rays and by natural and man-made terrestrial sources will still affect the dosimeter, so the observed reading will be 𝑟0 + 𝑟𝑏. In some applications, such as personnel dosimetry in radiation protection, this is the correct amount to be subtracted from a dose reading, since background radiation is not supposed to be included in personnel dose limits.
Nevertheless, if for another reason the total dose is to be measured, including radiation background, then 𝑟0 should be determined either after a minimal time delay or after an suitable storage period in a low-background (or known-background) environment such as a whole-body counter facility. The unshielded natural radiation-background tissue dose rate of about 0.3 mrad per day at sea level could previously be low enough to be irrelevant in comparison with the value of 𝑟0, that is observed with short exposure times. A photographic film badge, for example, typically displays an instrumental background optical density approximating that of a 100-mrad reading, and even a 30-day exposure to natural background adds less than 10% to that reading.
If a background reading is very reproducible from run to run, deducting it from a dosimeter reading might have little effect on the precision of the measurement. In most of the cases, nevertheless, the background reading displays significant nonreproducibility. As a rule of thumb, the lower limit of the practical dose range of a dosimeter is usually estimated to be the
22 dose necessary to double the instrumental background reading. Estimation of the precision of the measurements from recurrent readings of both the radiation and the background will of course provide more quantitative information: If σ’ is the standard deviation of the average of a group of radiation readings 𝑟̅, and 𝜎̅̅̅ is the S.D. of the average of the background readings 0 𝑟̅ , then the S.D. of the net radiation reading r – r0 0 is given by
𝜎𝑛𝑒𝑡′ = √(𝜎′)2+ (𝜎
0′)2 (1.15) (Note that these are not percentage standard deviations.)
If the background reading is insignificantly small, then the lower dose limit is imposed by the capability of the dosimeter readout instrument to provide a readable value of r for the dose to be measured, 𝐷̅̅̅̅. If r is less than 10% of full scale on analogue instruments, or contains less 𝑔 than three significant figures on digital readouts, the precision and accuracy may both become unacceptable. A more sensitive scale should then be used. Some dosimeter readout devices, particularly electrometers, are designed to switch to the optimum-sensitivity range automatically.
If neither the background reading nor constraints on instrumental sensitivity provide a lower limit to the usable dose range, the stochastic nature of the radiation field itself will finally limit the precision of a small dose measurement.
1.10.3.3Upper Limit of Dose Range
The upper limit of the suitable dose range of a dosimeter can be imposed simply by external instrumental limitations, such as reading off scale on the least sensitive range of an electrometer. Otherwise some kind of inherent limit can be imposed by the dosimeter itself. Causes of this type include:
i. Exhaustion of the supply of atoms, molecules, or solid-state entities (“traps”) being acted upon by the radiation to produce the reading.
ii. Competing reactions by radiation products, for example in chemical dosimeters. iii. Radiation damage to the dosimeter (e.g., discoloration of light-emitting dosimeters, or
damage to electrical insulators).
Generally the upper limit of the dose range is demonstrated by a decrease in the dose sensitivity (dr/d𝐷̅̅̅̅) to an unacceptable value. It can be reduced to zero, or to a negative value, as in Fig. 𝑔
23 2, which causes the dose-response function to become double-valued. In such a case other information is needed to decide which dose is represented by a large r-value, as shown in the figure. It is of course possible in principle to make use of the negative-slope part of a dose-response curve such as that in Fig. 2 for dosimetry purposes if it is sufficiently reproducible.
Figure 2: Illustrating a double-valued dose-response function resulting from a decrease in the dosimeter sensitivity at high doses.
1.10.4 Stability
1.10.4.1 Before Irradiation
The features of a dosimeter should be stable with time until it is used. That comprises “shelf life” and time spent in situ until irradiated (e.g. worn by personnel if a health-physics monitoring dosimeter.) Effects of temperature, atmospheric oxygen or humidity, light, and so on can cause a gradual change in the dose sensitivity or the instrumental background. Photographic, chemical, or solid-state dosimeters are usually more vulnerable to these influences than ion chambers or counters.
Protection from harmful influences can frequently be designed into a dosimeter’s envelope if the environmental cause of the problem is recognized. Film badges for example necessitate sealing in a plastic bag to eliminate humidity for use as personnel dosimeters in tropical climates. Some thermoluminescent dosimeters (TLDs, notably LiF) display a gradual sensitivity change during storage at room temperature due to a migration and rearrangement of the trapping centers in the crystalline phosphor, that can be controlled by special annealing.
24 1.10.4.2 After Irradiation
For TLDs, preparing (i.e., annealing) the dosimeters at various times tp and reading out all groups in one session at the end of the experiment. This is preferable for TLDs and because it is especially difficult to obtain long-term constancy of TLD reading instruments, while it is straightforward to “prepare” TLDs that are made from a common batch of phosphor by annealing them identically at different times tp.
1.10.5 Energy Dependence
Normally the energy dependence of a dosimeter is the dependence of its reading r, per unit of the quantity it is supposed to measure, upon the quantum or kinetic energy of the radiation. a. Energy Dependence ≡ Dependence of the Dosimeter Reading, per Unit of X- or γ-ray Exposure, on the Mean Quantum Energy or Quality of the Beam, r/X vs. E̅
This practice is usually found in health-physics personnel monitoring or any application in which exposure is usually referred to. 60Co γ-rays are regularly used as the reference energy for normalization, creating energy dependence curves looking usually like Fig. 3 for dosimeters made of materials higher than, equal to, and lower than air in atomic number (the medium to which exposure refers). The ordinate of such a curve is often found to be labeled “relative sensitivity,” “relative response,” or some other such nondescript term, while what is actually meant is shown in Fig. 3.
The rise in the top curve below about 0.1 MeV is caused by the onset of photoelectric effect in the sensitive volume of the dosimeter. The flat maximum usually occurs at about 30-50 keV, below which the curve can slowly descend due to attenuation in the dosimeter, onset of photoelectric effect in the reference material (air), and LET dependence of the dosimeter. The shape of the curves in Fig. 3 can be estimated by:
(𝒓 𝑿)𝑬̅ (𝒓 𝑿)𝟏.𝟐𝟓
≅
[(𝝁𝒆𝒏 𝝆⁄ )𝒈 (𝝁𝒆𝒏 𝝆⁄ )𝒂𝒊𝒓]𝑬̅ [(𝝁𝒆𝒏 𝝆⁄ )𝒈 (𝝁𝒆𝒏 𝝆⁄ )𝒂𝒊𝒓]𝟏.𝟐𝟓 (1.16)where the subscript g refers to the material in the dosimeter’s sensitive volume. This equation is based on the assumptions that:
25 i. The dosimeter’s sensitive volume is in charged-particle equilibrium, and the wall
medium w = g.
ii. Attenuation is negligible in the dosimeter, both for incident photons and for fluorescence photons generated in the dosimeter.
iii. A given absorbed dose to the sensitive volume produces the same reading, irrespective of photon energy (i.e., the dosimeter is LET-independent).
Figure 3: Typical energy-dependence curves in terms of the response per unit exposure of x- or 𝛾-rays
26
1.11 Integrating Dosimeters
1.11.1 Thermoluminescence Dosimetry
1.11.1.1 The Thermoluminescence Process
i. Phosphors
The sensitive volume of a thermoluminescent dosimeter (TLD) comprises a small mass (~ 1 - 100 mg) of crystalline dielectric material containing appropriate activators to make it perform as a thermoluminescent phosphor. The activators, that might be present only in trace amounts, provide two kinds of centers, or crystal-lattice imperfections:
a. Traps for the electrons and “holes” (i.e., carriers analogous to positive ions in gases), which can capture and hold the charge carriers in an electrical potential well for usefully long periods of time.
b. Luminescence centers, located at either the electron traps or the hole traps, which emit light when the electrons and holes are allowed to recombine at such a center.
Fig. 4 is an energy-level diagram showing the thermoluminescence process. At left it shows an ionization event elevating an electron into the conduction band, where it migrates to an electron trap (e.g. a site in the crystal lattice where a negative ion is missing). The hole left behind migrates to a hole trap. At the temperature existing during irradiation, for example room temperature, these traps must be deep enough in terms of potential energy to prevent the escape of the electron or hole for extended periods of time, until slow heating releases either or both of them.
At right in Fig. 4 the effect of such heating is shown. We will assume that the electron is released first, that is, that the electron trap in this phosphor is “shallower” than the hole trap. (The reverse might instead be true, so that the holes would be liberated first.) The electron again enters the conduction band and migrates to a hole trap, which can be assumed either to act as a luminescence center or to be closely coupled to one. In this case recombination is accompanied by the release of a light photon.
27 Figure 4: Energy-level diagram of the thermoluminescence process: (A) ionization by radiation, and trapping of electrons and holes; (B) heating to release electrons, allowing
luminescence production.
ii. Randall-Wilkins Theory
The simple first-order kinetics for the escape of such trapped charge carriers at a temperature T(K) were first described for trapped electrons by Randall and Wilkins (1945) using the equation
p =
1𝜏
= α𝑒
−𝐸 𝑘𝑇⁄(1.17)
where p is the probability of escape per unit time (s-1), τ is the mean lifetime in the trap, 𝜶 is called the frequency factor, E is the energy depth of the trap (eV), and k is Boltzmann’s constant (k = 1.381 × 10-23 J K-1 = 8.62 × 10-5 eV K-1).
It is evident from Eq. (1.16) that, on the assumption of constant values for k, E, and α, increasing T causes p to increase and τ to decrease. Therefore, if the temperature T is examined upward linearly vs. time, starting at room temperature, an increase in the rate of escape of
28 trapped electrons will occur, reaching a maximum at some temperature Tm, followed by a decrease as the source of trapped electrons is gradually exhausted.
Supposing that the intensity of light emission is proportional to the rate of electron escape, an equivalent peak in thermoluminescence (TL) brightness will also be observed at Tm. This is called a glow peak, as shown in Fig. 4. The presence of more than one trap depth E gives rise to plural glow peaks, which may be unresolved or only partially resolved from one another in the glow curve.
The value of Tm is related to the linear heating rate q (K/s) by the following relation from Randall-Wilkins theory: 𝐸 𝑘𝑇𝑚2
=
𝛼 𝑞𝑒
−𝐸 𝑘𝑇⁄ 𝑚 (1.18)which simplifies to the following approximate relationship on the assumption of α = 109/s and q = 1 K/s:
Tm = (489 K/eV) E (1.19)
Hence Tm = 216 ℃ for E = 1 eV.
Even though it is not obvious from Eq. (1.18), Tm increases progressively with q, so that Tm = 248 ℃ at q = 5 K/s, and 263 ℃ at 10 K/s for the same values of α and E. The light-emission efficiency can be found to decrease with increasing temperature by a process called thermal quenching. Therefore, at higher heating rates some loss of total light output may be noticed. Apart from this effect, changing the heating rate leaves total light output constant, conserving the area of glow curves in terms of brightness vs. time (but not brightness vs. temperature), given the same dose to the phosphor.
This is demonstrated very clearly in the remarkable results of Gorbics et al., shown in Fig. 5. They repeatedly irradiated a CaF2: Mn (manganese-activated calcium fluoride) TL dosimeter and read it out at eight linear heating rates ranging from q = 4 to 640 ℃/min. The TL brightness was concurrently recorded vs. time and vs. temperature. As an alternative to giving identical doses to the phosphor, the doses were adjusted to be inversely proportional to the heating rate used in reading out the dosimeter. Therefore, the maximum TL brightness, which is directly proportional to the heating rate for a constant dose, should hold nearly constant, since CaF2: Mn responds linearly vs. dose over a wide range. This constancy is evident in Fig. 5 for heating
29 rates up to 40 ℃/min, above which the influence of thermal quenching is seen to diminish the peak brightness down to about one-half at 640 ℃/min. Several other features of these curves should also be noticed:
a. The time to reach the glow peak is seen in Fig. 5 to be approximately inversely proportional to the heating rate.
b. For q ≤ 40 ℃/min the glow curve areas are roughly constant in the TL brightness vs.temperature plot (Fig. 6). Nevertheless, the dose was 10 times larger for q = 4°C/min than for 40 ℃/min. In Fig.5 it can be seen that the glow curve areas are roughly proportional to the dose in the absenteeism of thermal quenching, as anticipated. c. The temperature at which the glow peak occurs moves increasingly higher with the
heating rate; the onset of thermal quenching is around Tm = 290°C in this phosphor.
It can be seen that employing the light sum rather than the height of a glow peak as a measure of the absorbed dose is less subject to errors caused by oscillations in the heating rate. Nevertheless, the peak height may be used if the heating rate is very stable, and this may be advantageous in measuring small doses for which the upper limb of the glow curve rises due to IR and spurious effects, as shown in Fig. 5 and discussed in the next subsection.
Figure 5: (a) Glow curves vs. time obtained with a CaF2: Mn TL dosimeter at eight linear heating rates. The dose to the phosphor was adjusted to be inversely proportional to the heating rate in each case.
30 Figure 6: (b) Glow curves vs. temperature recorded simultaneously with the curves in a.
iii.
Trap StabilityThe practicality of a certain phosphor trap (and its associated TL glow peak) for dosimetry applications depends on its independence of time and ambient conditions.
If the traps are not stable at room temperature before irradiation, but migrate through the crystal and combine with other traps to form different configurations, changes in radiation sensitivity and glow-curve shape will be observed. LiF (TLD- 100) is such a phosphor, necessitating special annealing (e.g. 400 ℃ for 1 h, quick cooling, then 80 ℃ for 24 h) to minimize sensitivity drift. In general TL phosphors give best performance as dosimeters if they receive uniform, reproducible, and optimal (depending on the phosphor) heat treatment before and after use.
The incapability of traps to hold charge carriers at ambient temperature after irradiation is called trap leakage, and of course it becomes greater if the ambient temperature is increased. As a rule of thumb, in typical TLD phosphors a glow peak at ≅ 200-225 ℃ is ordinarily found to have small enough leakage for practical room temperature dosimetry, having a half-life of trapped charge carriers measured in months or years. A glow peak at 150 ℃ usually has a half-life only of the order of a few days, while a 100 ℃ peak decays in a matter of hours. Even
31 though short-term dosimetry can still be possible with rapidly leaking traps, careful timing control is required.
Higher-temperature traps than 200-225 ℃ are generally even more stable, and would be advantageous for dosimetry apart from for the existence of two competing effects mentioned earlier:
a. Heat (Infrared) Signal. As the phosphor and its heating tray rise in temperature, the short-wavelength tail of the blackbody radiation begins to extend into the visible region and produce a non-dose-related response in the photomultiplier tube used for measuring the TL light output. A bandpass light filter in the TL spectral region (usually 400-500 nm) minimizes this effect, but above 300 ℃ it still becomes a serious handicap in trying to measure small doses.
b. Spurious Thermoluminescence signal. The combined effects of adsorbed gases, humidity, dirt, and mechanical abrasion of the phosphor surface tend to produce a spurious (i.e., not dose-related) TL emission, sometimes loosely called “triboluminescence.” This light is believed to originate at the phosphor surface and in the adjacent gas. It tends to have wavelengths in the 500-600 nm range and is emitted mainly in the 300-400 ℃ temperature region.
Flowing an oxygen-free inert gas such as N2 or Ar through the space above the heater pan, thus surrounding the phosphor during the TL readout process, allows the stored energy due to these surface effects to be released without light emission.
Thus, N2 flow is often used to reduce spurious background TL readings, especially when small doses (mrad) are to be measured.
iv. Intrinsic Efficiency of TLD Phosphors
Only a small part of the energy deposited as absorbed dose in a TLD phosphor is emitted as light when the substance is heated, providing the dosimetric parameter to be measured. The ratio (TL light energy emitted per unit mass)/(absorbed dose) is called the intrinsic thermoluminescence efficiency. This has been measured as 0.039% in LiF (TLD-100), 0.44% in CaF2:Mn, and 1.2% in CaSO4 : Mn. The energy budget in LiF (TLD-100) has been projected to account for the loss of the missing 99.96% of the energy deposited by ionizing radiation that eventually goes into heat production. It should not be surprising that TLDs must be used under reproducible conditions to obtain steady results, considering that such a small fraction of the absorbed dose energy is count on upon as a measure of the entire dose.
32 1.11.1.2 TLD Readers
The instrument used to heat a TLD phosphor, and to measure the resulting thermoluminescence light emitted, is simply called a “TLD reader”. Its design principle is shown schematically in Fig.7. The TLD phosphor to be measured is placed in the heater pan at room temperature, and heated while the emitted light is measured with a photomultiplier.
33 Figure 8: TLD reader at the Nuclear Measurements Laboratory at University of Pisa
34 Heating of the sample can be done by of an ohmically heated pan as shown, or by preheated N2 gas, or by an intense light spot from a projector lamp or a laser, or other suitable means. Habitually the heating program can be more complex than simply linear vs. time. One representative scheme used in commercial TLD readers is to heat the phosphor rapidly through the unstable-trap region, ignoring light emission until some preset temperature is reached. Then the phosphor is either heated linearly or abruptly raised to a temperature sufficient to exhaust the glow peak of dosimetric interest, while measuring the emitted-light sum, which is displayed as a charge or dose reading. Lastly, the phosphor can be heated further to (say) 400 ℃ to release any remaining charges from deeper traps, while ignoring any additional light emitted, as it usually includes a noteworthy contribution from spurious effects. Figure 9 illustrates such a heating program.
As mentioned before, heating-program reproducibility is important in achieving reproducible TL dosimetry. Furthermore, light sensitivity must be provided constantly so that a given TLD light output always gives the same reading. This necessitates constant PM-tube sensitivity (including a stable power supply and no PM-tube fatigue), and a clean optical system (filters, mirrors, lenses, light pipes, and heater-pan surface). Periodic cleaning may be required. A constant light source with an appropriate spectrum (e.g. a phosphor “button” excited by a small internal radioactive 𝜶- or β- source) can be built into the reader to substitute for a TLD as a check on the constancy of light sensitivity. Nevertheless, this says nothing about heating constancy. TLD readers for large-scale personnel monitoring can be equipped with magazine feed for automatic readout of large numbers of dosimeters, automatic identification of dosimeters from digital codes, and computer processing and storage of identity and dose information.
35 Figure 10: Typical programmed readout cycle in a modern TLD reader, consisting of a “preheat” period without light integration to discriminate against unstable low-temperature
traps, a “read” period spanning the emission of the part of the glow curve to be used a “preheat” period without light integration to discriminate against unstable low-temperature
traps, a “read” period spanning the emission of the part of the glow curve to be used as a measure of the dose, an “anneal” period during which the remainder of the stored energy is “dumped” without light integration, and the cooling-down period after the heater-pan power
is turned off
1.11.1.3
TLD Phosphors
TLD phosphors is made up of of a host crystalline material containing one or more activators that may be linked with the traps, luminescence centers, or both.
Quantities of activators vary from a few parts per million up to several percent in different phosphors. The host crystal almost entirely determines the radiation interactions, since the activators are usually present in such small amounts.
36 Numerous different TLD phosphors have been studied and reported in the literature. A few typical ones are listed in Table 2. Fig.10 shows their glow curves at a heating rate of 40°C/min. Figure 11 gives their approximate light output vs. 60Co γ-ray exposure. The dashed lines indicate strictly linear TL response vs. exposure. All the phosphors show some degree of “supralinearity” of response, this effect being most pronounced in lithium borate. In CaF2: Mn the rise is only ≅ 4 % in the neighborhood of 104 R, which is too small to be seen on this figure. Supralinearity is shown to some extent by most TL phosphors, and may be due to the increased availability of luminescence centers when the charged-particle tracks become closer together, or to radiation-induced trap formation, or to other causes. At big enough doses all TL phosphors either saturate in their output as all available traps become filled, or maximize and then decrease due to radiation damage of the phosphor.
Lithium fluoride (Harshaw) has been by far the most commonly used, partly because of its low effective atomic number, only slightly greater than that of tissue and air. It is also available in a variety of forms (described in the next section) and with three levels of 6Li/Li ratio: ≅ 0 for LiF (TLD-700), 7% for LiF (TLD-100), and =96% for LiF (TLD-600). 6Li has a high (n, α) capture cross section for thermal neutrons, while 7Li is low in this respect. Thus, in a mixed field of neutrons and γ-rays a LiF (TLD-700) dosimeter primarily measures the γ-ray dose, while a TLD- 100 or TLD-600 dosimeter responds strongly to any thermal neutrons present as well. Such pairs of LiF dosimeters are widely used in personnel neutron-dose monitoring.
1.11.1.4 TLD Forms
The most common forms of TLDs are:
i. Bulk granulated, sieved to 75-150-μm grain size. Typically dispensed volumetrically into an irradiation capsule (e.g., pharmaceutical gel capsule). After irradiation, the powder is poured onto the reader heating pan.
ii. Compressed pellets or “chips”, usually 3.2 mm square by 0.9 mm (or 0.4 mm) thick. For best accuracy, individual chips may be calibrated with 60Co γ-rays. Or else the batch sensitivity statistics (typically ≅ 5 % S.D.) must be relied upon. Groups of three or four chips are often packaged and irradiated together to improve precision.
iii. A Teflon matrix containing 5% or 30% by weight of <40 – μm grain-size TLD powder (from Isotopes, Inc.). Typically made in the shape of discs, 6 or 12 mm diam. by 0.1 or 0.3 mm thick. Film-badge-sized pieces are manufactured for personnel monitoring, to be used with filters to provide an estimate of the x-ray quality, as is typically done with
37 photographic film badges. Ultrathin microtomed slices (6-mm-diam. discs) down to 25 pm thick are also available for approximating a B-G cavity.
iv. A TLD pellet fastened on an ohmic heating element in an inert-gas-filled glass bulb, which plugs into a special reader. These are particularly good for personnel monitoring in aggressive environments (e.g., factories, shipyards, etc.), and for environmental γ-ray monitoring. Very small doses (~ 1 mrad) can be measured reproducibly.
v. Single-crystal plates, sliced from a larger grown crystal boule. These are used only experimentally because of inconvenience, expense, and lack of reproducibility from one piece to another.
vi. Powder enclosed in plastic tubing that can be heated, and through the wall of which the TL light passes to reach the PM tube (e.g., in the Scanditronix reader). This form is used mostly in clinical applications.
38 Figure 11: Glow curves vs. temperature (upper scale) and time (lower scale) for four thermolnminescent dosimetry phosphors. Heating rate: 40 ℃/min. The amplitudes are arbitrary. (Gorbics et al., 1969. Reproduced with permission from Pergamon Press, Ltd.)
1.11.1.5 Calibration of Thermoluminescent Dosimeters i. Form
Solid TLD chips or Teflon-TLD discs are the favored forms of the phosphor for furthermost applications. They can be independently identified and calibrated, they do not require containment (which would attenuate low-energy radiation), and they are flat, which means they can be oriented perpendicularly to a monodirectional radiation beam, therefore presenting a known cross-sectional area.
39 Figure 12: Glow-peak-area response vs. 60Co 𝛾-ray exposure for several TL phosphors. The
relative TL output of the phosphors is arbitrary (see Table 2)- The LiF: Mg, Ti curve was taken from Cameron et a1. (1967); Li2B4 : Mn, from Wilson and Cameron (1968); CaSO2:
Mn, from Bjarngard (1967); CaF2:Mn, from Gorbics et al. (1973).
ii. Basis for Calibration
Furthermost TL phosphors have some threshold dose level below which the TL light output per unit mass is proportionate to the absorbed dose in the phosphor, given that:
(a) the LET of the radiation remains low or almost constant, and (b) the phosphor sensitivity is kept constant by using reproducible annealing procedures.
Assuming TL-reader constancy, and negligible attenuation of light in escaping from the phosphor during heating, one can then say that the same TL reading will result from a given average phosphor dose in a TL dosimeter, regardless of the spatial distribution of absorbed dose within it, as long as the dose throughout remains in the linear range.
The practical significance of this is that a 60Co γ-ray calibration in terms of average phosphor dose in the TL dosimeter can then be used as an estimated calibration for all low-LET
40 radiations, including x- and γ-rays, and electron beams of all energies above ~ 10 keV, even if they deposit dose nonuniformly in the dosimeter.
Connecting the phosphor dose measured to the dose in a comparable mass of tissue theoretically substituted for the TLD necessitates a separate step based on cavity theory. For the simplest (B-G) case of a thin TLD and very penetrating electrons, the dose ratio 𝐷𝑡𝑖𝑠𝑠⁄𝐷𝑇𝐿𝐷is proportional to the mass collision stopping-power ratio, (dT/ρdx)c,tiss /(dT/ρdx)c, TLD evaluated at the average electron kinetic energy.
If the incident radiation beam is totally stopped by the TLD, then the incident energy fluence can be consequent (correcting for backscattering losses if necessary). The 60Co calibration (under TCPE conditions) gives the TL reading per unit of average phosphor dose. Multiplying that dose by the mass of the TLD chip permits relating the TL reading to a specified integral dose, or energy spent in the chip. If the chip area offered to the beam is A (m2), its mass is m (kg), and the 60Co γ-ray calibration factor is k
Co = (𝐷̅𝑇𝐿𝐷/r)Co [Gy/(scale division)], where r is the TLD reading, then the energy fluence of a stopped beam is given by
Ψ = 𝑘𝐶𝑜 𝑟𝑚
𝐴 (J/m
2) (1.20)
iii. 60Co γ - Calibration
For a free-space 60Co γ-ray exposure X (C/kg) at the point to be engaged by the center of the TLD in its capsule, the average absorbed dose in the TLD, in grays, under TCPE conditions is given by
𝐷̅𝑇𝐿𝐷 = 33.97aβX
[
(𝜇𝑒𝑛⁄ )𝜌 𝑇𝐿𝐷(𝜇𝑒𝑛⁄ )𝜌 𝑎𝑖𝑟
]
𝐶𝑜(1.21)
where n is a correction for broad-beam γ-ray attenuation in the capsule wall plus the half thickness of the TLD. For a LiF TLD chip in a Teflon capsule 2.8 mm in thickness, (for TCPE) the mean absorbed dose calculated from Eq. (1.20) is approximately
𝐷̅𝑇𝐿𝐷 = 31.1X (Gy) (1.22)
If the resulting TLD reading is r scale divisions, then the calibration factor is kCo =(D̅TLD/r)Co, which applies at the dose value used in calibration and throughout the linear response vs. dose
41 range. For all low-LET radiations, the average absorbed dose in the TLD can then be found from the observed TLD reading r by
𝐷̅𝑇𝐿𝐷 = kCor (1.23)
For higher-LET radiations than 60Co γ-rays, TLDs usually show some difference in efficiency, and therefore a mutual change in the low-LET calibration factor kCo. Figure 12 gives the results of measurements by Tochilin et al. (1968) for lithium fluoride, lithium borate, and another phosphor, beryllium oxide. Their LET dependence is seen to be different, with lithium borate being the most constant.
All three, however, tend to rise somewhat in TL efficiency as the LET augments from about 0.25 keV/μm for 60Co to about 1 keV/μm.
Figures 12 and 13 show the photon energy dependence of lithium fluoride and lithium borate. Curves A were attained from the right side of Eq. (1.15), showing the CPE dose in the phosphors per unit of exposure, normalized to 1.25 MeV (60Co). Curves B show the TL response per unit exposure, and curves C the TL response per unit of absorbed dose in the phosphors. Therefore, curves C represent the LET-dependence of the TL efficiency relative to 60Co, or k
Co/kLET. Equation (1.22) can be improved by using kLET in place of kCo where curve c diverges meaningfully from unity.
In the case of CaF2 : Mn, the results of Ehrlich and Placious (1968) indicate that roughly the same amount of TL light is emitted for a given energy imparted by 60Co γ-rays or electrons over the full range studied, that is, 20 to 400 keV incident on, and stopping in, the phosphor powder spread in Teflon.
42 Figure 13: LET response of BeO, Li2B4O7:Mn, and LiF. The curves give values of kCo/kLET as
a function of LET in water, in keV/𝜇m. The inset indicates the types of radiation sources and particles used. (Tochilin et d., 1968. Reproduced with permission from E. Tochilin)
43 Figure 14: Thermoluminescent response of LiF per roentgen and per rad for photon energies
from 6 to 2800 keV. (Tochilin et al., 1968. Reproduced with permission from E. Tochilin.)
Figure 15: Thermoluminescent response of Li2B4O7:Mn per roentgen and per rad for photon energies from 6 to 2800 keV. Tochilin et al., 1968. Reproduced with permission from E.
