The effects of revised operational dose quantities on the response characteristics of a beta/gamma personal dosemeter

According to the proposal (Endo 2016, 2017) the personal dose H_p(θ, ε) at a given energy and angle will be set equal to the maximum of the corresponding effective doses at either +θ or −θ, i.e. MAX[E(θ, ε), E(−θ, ε)], where for plane parallel exposures θ is constrained to lie in a horizontal plane, i.e. perpendicular to the presumed head-to-feet 'axis' of the body. For rotational or isotropic exposures, H_p(θ, ε) ≡ E(θ, ε) by definition. The units of H_p(θ, ε) will therefore be sieverts, Sv. The fluence to personal dose conversion coefficient at a given energy and angle, H_p(θ, ε)/Φ, is hence obtainable from the maximum of the fluence to effective dose conversion coefficients at angles +θ and −θ, such as those derivable using the ICRP Reference Man and Woman voxel phantoms (ICRP 2009) and tabulated at selected angles in ICRP Publication 116 (ICRP 2010).

According to the proposed definition (Endo 2016, 2017) the personal absorbed dose in local skin, D_p skin(θ, ε), at a given energy and angle will be defined in terms of the absorbed dose deposited in a region located at a mean depth of ∼75 μm in a specified phantom, inside of which is a 2 mm thick outer layer of material representing skin of reference composition (ICRP 2002) and density 1.09 g cm⁻³ (ICRP 2010); the units of D_p skin(θ, ε) will therefore be grays, Gy. The choice of phantom, and shape and size of this region, will differ according to the intended location of wear of the dosemeter calibrated in terms of D_p skin(θ, ε), and hence according to what the phantom is intended to represent: the rod phantom for the finger; the pillar phantom for the extremities; and the slab phantom for the trunk of the body. For the PHE two-element whole-body TLD it is the trunk that is relevant, and D_p skin(θ, ε) is defined within a slab with outer dimensions 30 × 30 × 15 cm³ of ICRU 4-element tissue (density: 1.0 g cm⁻³), within a 2 mm layer of skin, in which the dose is averaged over the volume of a right circular cylinder with its axis perpendicular to the surface between the depths of 50 μm and 100 μm and a cross-sectional area of 10 mm² below the centre of the front surface.

A comparison of H_p(10, θ, ε)/Φ and H_p(θ, ε)/Φ as a function of photon energy and angle of incidence is shown in figure 1, where the ratio r_body = H_p(θ, ε)/H_p(10, θ, ε) is plotted for a series of monoenergetic (15 keV to 10 MeV) and ¹³⁷Cs (662 keV) and ⁶⁰Co (mean energy: 1253 keV) sources, for plane-parallel exposures at 0° (i.e. anterior-posterior, AP), 30° and 60°. The data for H_p(10, θ, ε)/Φ are taken from ICRU Publication 57 (ICRU 1998).

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It is clear from the figure that H_p(10, θ, ε)/Φ always provides a reasonable estimate of effective dose within the energy and angle range plotted, though this is unlikely to be true for angles >90°. This aligns with the intended use of H_p(10, θ, ε) as a measurable surrogate for the protection quantity (ICRU 1985), though it is seen that at the lowest energy the effective dose is over-estimated by a factor of ∼5×. The observation is also as expected: in general, most radio-sensitive organs are located deeper than 10 mm in the body, and because the depth-dose profile is not uniform due to attenuation of the photons, differences between doses at 10 mm and doses to deep organs will be always be exhibited; moreover, because the gradient of the depth-dose profile varies inversely with photon energy, those differences will typically be greatest for low-energy exposures. Whilst it might be argued that it is better to over-estimate than under-estimate risk, it is clearly still an undesirable feature in the dose quantity, especially over this energy range that is typical of the workplace fields in which personal dosemeters are usually worn. On balance, therefore, the proposed quantity H_p(θ, ε) represents a more reliable assessment of potential risk to individuals than H_p(10, θ, ε), with the advantages particularly apparent in workplace fields featuring low-energy photons.

A comparison of H_p(0.07, θ, ε)/Φ and D_p skin(θ, ε)/Φ as a function of photon energy and angle of incidence is shown in figure 2, where the ratio r_skin = D_p skin(θ, ε)/H_p(0.07, θ, ε) is plotted for a series of monoenergetic (15 keV to 1 MeV) and ¹³⁷Cs (662 keV) sources, for plane-parallel exposures at 0° (i.e. anterior-posterior, AP), 30° and 60°. The data for H_p(0.07, θ, ε)/Φ were taken from ICRU Publication 57 (ICRU 1998), with 1 MeV the maximum energy provided therein.

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It is clear from the figure that D_p skin(θ, ε) and H_p(0.07, θ, ε) are essentially equivalent at low energies: they differ by no more than ∼3% across the energy range from 15 to 200 keV, for all three angles considered. At higher energies, however, larger divergences are observed between the current and proposed quantities, with D_p skin(θ, ε) becoming significantly lower than H_p(0.07, θ, ε). This deviation arises because the numerical values of the conversion coefficients given in ICRU 57 were calculated using the kerma approximation under the assumption of secondary charged particle equilibrium (CPE); they therefore begin to over-estimate absorbed dose to the skin at energies for which the range of the generated electrons is >0.07 mm, i.e. at energies above ∼70 keV at normal incidence, though the impact of this is only really observed above ∼200 keV. On the other hand, the data used for D_p skin(θ, ε) in figure 2 were not calculated using the kerma approximation, so discrepancies arise with H_p(0.07, θ, ε). The 50 to 100 μm depth range used for D_p skin(θ, ε), rather than 70 μm for H_p(0.07, θ, ε), also contributes to the form of figure 2. However, conversion coefficients for the new skin quantity have also been calculated under CPE conditions using the kerma approximation (Endo 2016, 2017), which might conveniently be labelled ${{D}_{{\rm{p}}{\rm{skin}}}}^{K}$(θ, ε)/Φ. If those data are instead compared against personal dose equivalent (figure 2), much better consistency is found: at 1 MeV, for example, ${{D}_{{\rm{p}}{\rm{skin}}}}^{K}$(θ, ε) and H_p(0.07, θ, ε) can be shown to agree to better than 1% at each of 0°, 30° and 60°.

Whether or not CPE is assumed, it may be concluded that adoption of the proposed quantity would impact the photon response of the uncovered element of dosemeters only negligibly from 15 to 200 keV (figure 2), which is the energy range of primary interest in assessing skin doses from soft x-rays and low-energy gammas. Moreover, if calibrated in terms of personal absorbed dose in local skin under the kerma conditions of secondary charged particle equilibrium, the response of the uncovered element is unlikely to be affected by the proposed changes across the entire 15 keV to 1 MeV energy range considered. Indeed, it might be argued that assuming CPE is preferable anyhow, being a more realistic representation of the likely conditions existing in most workplace photon fields (and calibrations); this strongly mitigates in favour of employing ${{D}_{{\rm{p}}{\rm{skin}}}}^{K}$(θ, ε)/Φ data rather than D_p skin(θ, ε)/Φ. But, if calibrated without build-up to ensure secondary charged particle equilibrium, the uncovered element could over-respond significantly at high energies. This could pose additional challenges in laboratory type-testing and routine calibration of dosemeters: in particular, routine calibration to ¹³⁷Cs may require additional complications, such as precise specification and correction for source encapsulation and source-dosemeter separation, so calibration using a lower energy source or multiplication by a scaling factor may potentially prove preferable. It is anticipated that the International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC) would have to resolve these issues before the new quantities were used in practice.

Personal dose equivalent conversion coefficients for d = 0.07 mm are not provided in ICRU 57 for electrons. However, directional dose equivalent data, H'(0.07, θ, ε), are included at that depth, and these may be assumed to be numerically similar to H_p(0.07, θ, ε) for exposures from the front, i.e. θ = 0°. A comparison of H'(0.07, 0°, ε)/Φ and D_p skin(0°, ε)/Φ for electrons is therefore insightful and shown in figure 3, where the ratio r_skin' = D_p skin(0°, ε)/H'(0.07, 0°, ε) is plotted for a series of monoenergetic electron sources from 70 keV to 2 MeV. It is clear from the figure that D_p skin(0°, ε) and H_p(0.07, 0°, ε) (≈ H'(0.07, 0°, ε)) are essentially equivalent at all but the lowest energies: they differ by no more than 5% across the energy range from 150 to 2000 keV. At low energies however, i.e. from ∼80 to ∼150 keV, large divergences are observed, which is likely caused by the impact of differing electron ranges on dose depositions with regards to the 70 μm depth at which H_p(0.07, 0°, ε) is defined and the 50 to 100 μm depth over which D_p skin(θ, ε) is defined. The volume of the scoring region for D_p skin(θ, ε) is also large compared to the ranges of those lowest energy electrons: effectively, the D_p skin(θ, ε) dose calculation may be 'diluting' their localised energy deposition over a large mass, relative to the H'(0.07, θ, ε) dose calculated at 70 μm. Analogous discrepancies between D_p skin(θ, ε) and H_p(0.07, θ, ε) would be expected at angles other than θ = 0°, albeit over slightly different energy ranges due to the energy-dependence of the electrons' Bragg peaks. Nevertheless, personnel monitoring in such low-energy, short-ranged beta radiation fields tends not to be a major application of two-element whole-body dosemeters, such as the PHE TLD. So, it may tentatively be inferred that the ICRU proposal would not impact the electron response of the TLD too deleteriously overall if its uncovered element were calibrated in terms of D_p skin(θ, ε). However, greater impact might be expected for dosemeters designed and worn to assess localised skin exposures from low energy beta-emitters, such as ring or fingerstall dosemeters.

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In summary, the conclusion is that two-element body personal dosemeters such as the PHE TLD would in general likely still be adequate for measuring skin absorbed doses from beta particles. Consequently, the construction of the PHE TLD would not need to be altered from the current design if its uncovered element were required to respond in terms of D_p skin(θ, ε) rather than H_p(0.07, θ, ε), which might otherwise have been necessary to 'correct' for any changes to its response characteristics.

The covered element of the current PHE dosemeter is intended to be effectively insensitive to beta particles. This is because most beta sources encountered in the workplace are relatively low in energy, and electrons with energies below ∼2 MeV are unable to penetrate to a depth of 10 mm in tissue (ICRU 1984) so do not contribute directly to H_p(10). Accordingly, range-energy tables were employed during the design stage of the PHE TLD to ensure that its PTFE + PP filter effectively stops electrons below this energy (Eakins et al 2007). However, the proposed quantity personal dose is not zero for electrons with energies below 2 MeV, because low-energy electrons will always deposit skin doses and will hence always contribute to effective dose (and therefore H_p(θ, ε)), albeit reduced by a tissue weighting factor of 0.01. As a consequence, rather than being null, the H_p(θ, ε)/Φ conversion coefficients for low-energy electrons instead very approximately match those for low-energy photons, as shown in figure 4 for 0°, which is the limiting exposure geometry for H_p(θ, ε)/Φ for electrons (Endo 2016, 2017). Any dosemeter that is intended to monitor H_p(θ, ε) for β/γ exposures ought therefore to be able to respond both to low-energy electrons and photons. The current design of PHE TLD would clearly fail to meet this criterion for common beta sources, such as ¹⁴⁷Pm, ⁸⁵Kr and ⁹⁰Sr/⁹⁰Y, for which it would respond negligibly as required for H_p(10).

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Designing a single element H_p(θ, ε) dosemeter that responded equally well to both β and γ exposures across a wide energy range would be difficult: essentially, measurement of electrons would demand very little filtration, but a thick filter (e.g. ∼10 mm tissue-equivalence) is required to simulate the attenuation of more penetrating photons that deposit doses to organs located deep within the body. However, a two-element dosemeter need not necessarily exhibit this limitation if considered in combination: skin doses, which are the main contributor to effective dose from beta exposures, could potentially be monitored by the uncovered element. A non-negligible filter could therefore be retained in front of the covered element, because information on the contribution to H_p(θ, ε) from low-energy betas could conceivably be accounted for implicitly by the TLD's other element. In such a case, careful calibration and subtraction could be required to avoid-double counting of the photon component to dose that could concurrently be deposited in that second element.

Also shown in figure 4 are the fluence to personal absorbed dose in local skin conversion coefficients for electrons; of course D_p skin(θ, ε) and H_p(θ, ε) have different units, Gy and Sv, respectively, and are intended to quantify different risks, tissue reactions and stochastic risks, respectively, but for photons and electrons they may be assumed numerically equivalent. The values for D_p skin(θ, ε)/Φ and H_p(θ, ε)/Φ were also determined differently (Endo 2016, 2017), with electron doses in the latter calculated by dividing the energy deposited in the ∼2 mm thick voxels that represent the skin by their combined mass. This explains why the ratio D_p skin(θ, ε)/Φ: H_p(θ, ε)/Φ varies by amounts different from simply 100:1, which might naively be assumed from considering just the 0.01× tissue weighting factor. Electrons with energies below ∼60 keV are unable to reach the 50 to 100 μm deep region used to determine D_p skin(θ, ε), but are still able to deposit doses in the voxels; indeed, electrons will always deposit more energy in the voxel than in the 50 to 100 μm deep region, because of the energy deposited in the first 50 μm. Moreover, the position of the electron's Bragg peak, and specifically whether it lies at a depth between 50 and 100 μm or well beyond that range, as well as the different masses of the two regions over which the two doses are averaged, both lead to the D_p skin(θ, ε)/Φ: H_p(θ, ε)/Φ ratio varying either above or below 100: 1.

Figure 4 shows that H_p(θ, ε)/Φ for electrons is never the largest quantity in this energy range, compared to H_p(θ, ε)/Φ for photons and D_p skin(θ, ε)/Φ for electrons. However, the skin dose limit is 500 mSv and the whole body dose limit only 20 mSv, so there is a factor of 25× in the way in which the quantities are applied. In practice, this means that the skin dose will be limiting for electrons when it is more than a factor of 25× larger than personal dose for electrons, which is the case for electrons with energies between 60 keV and 1.5 MeV (figure 4). Although D_p skin(θ, ε)/Φ is less than H_p(θ, ε)/Φ for electrons with energies below ∼60 keV, these have a range in air of <6 cm (ICRU 1984), so are essentially irrelevant for whole body dosimetry, and in any case would be unlikely to be detected by the body dosemeter unless it happened to be located ideally. Moreover, the actual H_p(θ, ε) doses deposited by electrons are small at those energies, being ∼2 orders of magnitude lower than at 1 MeV, for instance (figure 4). At energies above ∼2 MeV, H_p(θ, ε)/Φ for electrons is greater than that for photons, but these energies are not directly relevant for common beta sources.

The difference between D_p skin(θ, ε) and H_p(θ, ε) raises an important question: what should the 'skin element' (i.e. the uncovered element) of the TLD measure if the proposed quantities were accepted? The region from 50 to 100 μm in skin was adopted because it approximates the location of the basal cells of the epidermis, which are the skin tissue at radiogenic risk (ICRP 2010). It might therefore be argued that averaging doses over an entire ∼2 mm thick voxel is not an optimal means of assessing stochastic risks from low-energy electrons. So, whilst H_p(θ, ε) might be considered preferable to H_p(d, θ, ε) for neutral particles and for very high-energy, very highly penetrating charged particles that can deposit doses deep within the body (such as might be encountered in cosmic ray or accelerator dosimetry for instance), it may prove to be a less appropriate quantity for assessing stochastic risks from low-energy electrons, such as beta particles. Indeed from this argument, H_p(θ, ε) might also be viewed as less appropriate for electrons than D_p skin(θ, ε), even though personal absorbed dose in local skin (in Gy) is intended to assess risks from tissue reactions. On the other hand, it might naturally be assumed that the 'body' element of a personal dosemeter would be expected to respond in terms of H_p(θ, ε) if the proposed quantities were adopted; if electrons are contributing to that quantity, a whole body β/γ dosemeter ought therefore to respond adequately to beta sources in terms of personal dose, rather than just dose to local skin. But, that would be difficult to achieve in practice using a single covered element, without concurrently degrading its photon H_p(θ, ε) response.

It might be argued that whole-body exposures to plane-parallel beta sources are unlikely in most practical workplace fields. Low-energy electrons straggle considerably, and also have very short ranges: a 100 keV electron has a range of only ∼0.14 m in air, for instance, though this increases to ∼4 m and ∼9 m for 1 MeV and 2 MeV electrons respectively (ICRU 1984). Further, the beta-emitting radionuclide itself is likely to be spatially confined, leading to a highly divergent field unless located a large distance from the individual. The lack of an H_p(θ, ε) response for betas by the covered element might therefore be a somewhat artificial limitation, which may only be a problem in principle, but would not lead to significant under-estimates of overall risks in realistic workplace fields. In that regard, the precise position where the dosemeter is worn may be a more significant contribution to uncertainty than the lack of a β response in the covered element, with the inverse-square dose variations that are caused by the divergence of a beta point-source perhaps more likely to lead to under- or over-estimations of overall skin doses. Likewise, using a whole body dosemeter to monitor D_p skin(θ, ε), which is a quantity that is intended just to quantify localised tissue reactions in skin, could greatly misassess risk; since those exposures are mainly encountered just in extremity dosimetry, it could again be argued that the two-element PHE TLD ought not be used to estimate the personal absorbed dose in local skin.

The above supports the suggestion that if the proposed dose quantities were accepted, such that H_p(10, θ, ε) and H_p(0.07, θ, ε) became superseded, the use of a two-element whole body dosemeter could become redundant unless the uncovered element were instead somehow repurposed for assessments of the electron component to H_p(θ, ε). However, this suggestion is complicated by the observations discussed earlier regarding the definition of H_p(θ, ε), specifically that it is calculated by averaging doses over an entire voxel rather than just at the depths of radiosensitive regions within the skin. Moreover, the ∼2 order-of-magnitude variation in H_p(θ, ε) across the energy range relevant to beta dosimetry (figure 4) may make its assessment by a single, unfiltered LiF: Mg, Cu, P element somewhat challenging.

Overall, it is unclear at present what the preferred use or intended function of the uncovered element of the two-element TLD should be optimally if H_p(θ, ε) and D_p skin(θ, ε) were both adopted. Further clarification from ICRU on this issue might therefore be required, along with guidance on the recommended approach for electron and beta dosimetry in the context of the proposed local and whole body dose quantities.

The performances of photon/electron personal dosemeters are typically judged against criteria stipulated in international standards, such as those recommended by the IEC; the current standard (IEC 2012) supersedes the previous version (IEC 2006), which the PHE TLD was originally designed to meet, though their differences in requirements for H_p(10, θ, ε) response characteristics are relatively minor. Amongst other criteria, the IEC standard recommends that the TLD be type-tested using the ISO Narrow Series fields (ISO 1996), as well as ¹³⁷Cs and ⁶⁰Co radionuclide sources, and that in the angle range −60° ≤ θ ≤ +60° its relative responses should lie: between 0.67 and 2.00 for 12 ≤ ε_m < 33 keV; between 0.69 and 1.82 for 33 ≤ ε_m < 65 keV; and between 0.71 and 1.67 for ε_m ≥ 65 keV, where ε_m denotes the mean energy of the photon field. These recommended limits have been superimposed onto figures 6(a) and (b) for illustration, though it is reiterated that they do not apply for the ROT and ISO exposures. Clearly, the recommendations are met for the H_p(10, θ, ε) relative response of the PHE TLD at all energies above ∼20 keV, with the responses at 15 keV only just overstepping the criterion, notwithstanding that the calculated response data are for monoenergetic sources rather than a distribution. However, in general the criteria are not met for the H_p(θ, ε) relative response at energies below ∼50 keV.

Several comments may be made regarding the above observation for the H_p(θ, ε) relative response. Firstly, the energy range considered 'mandatory' in the standard is only from 80 keV to 1.25 MeV, and the H_p(θ, ε) relative response is not in violation of the recommendations within these limits. Nevertheless, the rated energy range of the PHE TLD is currently broader than this restricted range, so not complying over that whole span is undesirable: when used in workplaces with significant components of the field below 80 keV, the dosemeter would be expected to respond across the full intended energy range.

Secondly, the overall asymmetry in the over- versus under-response across the entire energy range may be improved a little by recalibrating using a source other than ¹³⁷Cs, or by applying a constant scaling factor, to 'shift' the whole response downwards. For example, calibrating instead to the H_p(0°, 60 keV) response, or multiplying the H_p(0°, Cs) result by ∼1.15× prior to normalizing the other responses to it, would both serve to reduce the over-response at low energies whilst maintaining compliance with the minimum relative response requirements at all other energies. However, these two options are just compromises: whilst recalibration may improve relative responses overall, and in turn lower the energy range of compliance from ∼50 keV to ∼40 keV, it would be insufficient to address the large over-response peaked at 20 keV, so cannot alone solve all of the limitations that would be introduced for the current design of TLD upon adopting the new dose quantity. In addition, use of H_p(0°, 60 keV) as a routine calibration source, or even the N80 field that has a mean energy of ∼60 keV (ISO 1996), would be less convenient than a readily available radionuclide such as ¹³⁷Cs.

Thirdly, however, and conversely to all of the above, it is noted that because the IEC criteria are given in terms of the H_p(10, θ, ε) response, it may be argued that they would not be an appropriate test for dosemeters calibrated to H_p(θ, ε). This leads naturally to the suggestion that changing the dose quantity from H_p(10, θ, ε) to H_p(θ, ε) would inevitably require corresponding amendments to those standards against which personal dosemeters are judged. Of course, guidance on assessing the under-responses of the TLD to ROT and ISO fields, which is common in both H_p(10, θ, ε) and H_p(θ, ε) responses but worse for the latter, would also ideally be addressed in any revised standard; the current practice of calibration on a slab phantom presents geometric difficulties for exposures for angles >85° in terms of personal dose equivalent, but these are not problems with personal dose, so the IEC might choose to add performance requirements for specific reverse angles if personal dose were adopted.

It is not possible to predict what the performance limits might be for personal dosemeters if the new operational quantities were introduced, but the current requirements for performance of whole body dosemeters in terms of H_p(0.07) only specify a range from 0.71–1.67 for exposure to ⁹⁰Sr/⁹⁰Y at normal incidence (IEC 2012). Extremity dosemeters have more onerous performance requirements for energy and angle dependence of response, but the relatively large distances between the source and the torso make lower energy betas less relevant for whole body dosimetry.

A simple redesign procedure was performed for the PHE TLD using the Monte Carlo code MCNP6, with the dosemeter again located on an ISO water-filled slab phantom. The aim was to converge upon an adapted filter that could be used within the current PP holder, which was presumed to be the most cost-effective solution. Moreover, by choosing this constraint that any redesign should be externally identical to the current TLD, it can be assumed that doses to the uncovered element of the dosemeter would be relatively unaffected by any modification; if a much thicker overall design were instead proposed, for instance, some 'shadowing' could potentially arise. Thus, hybrid filters were considered as the simplest first step, consisting of x mm of metal plus (4.3-x) mm of PTFE: it was speculated that incorporating a material with a greater effective-Z and/or density than PTFE would supress the over-response in the low-energy (i.e. photoelectric) range (figure 6(b)).

The general methodology for the redesign process was iterative, varying the material, thickness and relative locations of the filter components, and calculating and comparing the H_p(θ, ε) relative response characteristics for θ = 0°, 30°, 60°, ROT and ISO exposures to a series of monoenergetic (15 to 300 keV) and ¹³⁷Cs and ⁶⁰Co sources; for a given configuration, normalisation to its calculated H_p(0°, Cs) response was applied. Aluminium, copper and tin filters were considered, with thicknesses from 0.2 to 1.5 mm, as these provided a range of different atomic numbers (Z = 13, 29 and 50, respectively), are higher in density (∼2.68, 8.96 and 7.31 g cm⁻³ respectively) than PTFE, and are each readily and cheaply available.

The full details and results from all of these trials are not included here for brevity. Out of the variants considered, the optimum design featured a 1.5 mm thick, 18 mm diameter aluminium cylinder located between the 2 mm thick PP wall of the holder and the PTFE cylinder, the thickness of which had been reduced accordingly to 2.8 mm. The relative responses of this redesigned dosemeter are shown in figure 7. For the ¹³⁷Cs exposure, the absorbed dose to the LiF: Mg, Cu, P per applied air kerma in the redesigned model was found to be 0.99 Gy Gy⁻¹, which is the same as the value for the current design of TLD, indicating that the modification would not cause any significant loss of sensitivity. By consulting range-energy tables (ICRU 1984), it was also shown that the currently required insensitivity of the covered element to most β-particle sources would also not be compromised by the modification. For completeness, the H_p(10, 0°, ε)/H_p(10, 0°, Cs) performance of this new design is also shown in figure 7, which displays a significant under-response at low-energies as expected.

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Superimposed on figure 7 are the performance limits recommended by IEC for personal dosemeters (IEC 2012). Notwithstanding that these are defined in terms of personal dose equivalent rather than personal dose, so would likely be revised if the proposed dose quantity were accepted, it is encouraging to note that the redesigned dosemeter complies with the current standard across the entire energy range apart from at 15 keV, where it still under-responds by a large degree. Although technically these limits do not apply for ROT or ISO exposures, it is also interesting to note that the responses to these fields would also comply with the standard apart from at 15 keV and for ROT at 100 keV. Moreover, if a constant scaling factor of 1.1× were applied during calibration, this latter ROT response would then meet the 0.71 minimum without causing the other responses to non-comply: the worst-case relative over-responses, i.e. H_p(0°, 30 keV) and H_p(30°, 30 keV), would still be less than the recommended limit of 2.00.

The uncovered element of the TLD was unchanged in the above redesign process, so should generally respond well to D_p skin(θ, ε) (and H_p(0.07, θ, ε)) for both photons and betas. As discussed earlier, however, designing a dosemeter with a single covered element that responds equally well to H_p(θ, ε) for both electron and photon exposures across a wide energy range would be problematic; indeed, designing a single element dosemeter with an adequate H_p(θ, ε) response for just electrons would be challenging. To illustrate the difficulty, the H_p(0°, ε) responses of the redesigned TLD to monoenergetic electrons from 1 to 20 MeV have been calculated using MCNP6 for both the covered and uncovered elements. The results are shown in figure 8 given relative to their respective H_p(0°, Cs) responses, though in fact those calibrations only differ by <3%. It is seen that whilst the covered element greatly under-responds below ∼2 MeV, it greatly over-responds between ∼3 MeV and ∼10 MeV. Conversely, the uncovered element always over-responds. In both cases, only above 15 MeV is the relative response within ∼50% of unity. Thus, it is clear from figure 8 that the covered element in the redesigned TLD, with its aluminium insert, does not resolve the issue for electrons like it did for photons. In fact, neither element of the redesigned dosemeter could be used to directly assess H_p(θ, ε) for electrons for the entire range of energies for which conversion coefficient data are provided in the ICRU proposal.

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It might be remarked that plane-parallel exposures of individuals to a wide range of monoenergetic electron sources are an unlikely scenario for practical radiation protection in the workplace. Instead, responses to β or mixed β/γ fields are perhaps more relevant, in which electrons typically exhibit a distribution of energies with a relatively low mean. With this refocus, it might be speculated that the proposed redesign of two-element TLD could still potentially be capable of assessing both D_p skin(θ, ε) and H_p(θ, ε) in mixed β/γ fields if some changes were made to its dose algorithm. No electrons with energies below ∼2 MeV would be detected by the covered element of the redesigned dosemeter; but, those electrons could be measured effectively by the uncovered element of the dosemeter. The solution might therefore be to reclassify the two-element dosemeter as capable of assessing 'skin' doses and the beta component of H_p(θ, ε) with one of its elements, and the γ component of H_p(θ, ε) using the second element. Indeed, in workplace fields known to contain beta sources, potentially two calibration factors could be applied to the readout from the uncovered element: one to convert the measured TL to an assessment of D_p skin(θ, ε), and one to convert it to an assessment of H_p(θ, ε) for betas. Of course, these conversion factors would have different magnitudes and units, Gy⁻¹ and Sv⁻¹ respectively, and careful calibration and subtraction may also be required to avoid double-counting of the photon component to H_p(θ, ε) that would concurrently be deposited in the uncovered element. Careful sensitivity analyses would also need to be performed on the algorithm to avoid incorrect dose assessments caused by any improper weighting of the different components across the energy range. Furthermore, if this option were pursued, dosemeter performance requirements, such as those recommended by the IEC, might need to be amended to clarify the reclassification.

To explore the above considerations, the responses of the elements of the dosemeter have also been calculated using MCNP for exposures to ¹⁴⁷Pm, ⁸⁵Kr and ⁹⁰Sr/⁹⁰Y beta sources at 0°, notwithstanding the earlier comments that plane-parallel beta fields are somewhat artificial, especially at low energies, and that exposures in a vacuum neglect the inevitable attenuation of the field by air in a real workplace. The energy-distribution spectra of the radionuclides were obtained from the RADAR resource (RADAR 2018). Conversion coefficient data were derived by convolving the beta spectra with the available monoenergetic D_p skin(0°, ε)/Φ and H_p(0°, ε)/Φ data (Endo 2016, 2017), and are provided in table 1 along with the TLD response results for the uncovered element. For completeness, the relative H_p(0°, ε) response results of both elements are also plotted in figure 8 at the mean energies of the fields (∼0.05 MeV for ¹⁴⁷Pm, ∼0.2 MeV for ⁸⁵Kr, and ∼0.3 MeV for ⁹⁰Sr/⁹⁰Y), noting that this is for convenience but is also somewhat misleading: for ⁹⁰Sr/⁹⁰Y, for instance, most of the dose is deposited by its high energy components, which extend significantly beyond 0.3 MeV up to ∼2.2 MeV.

It is seen in table 1 that for D_p skin(0°, ε) the uncovered element of the TLD responds poorly for ¹⁴⁷Pm, likely because the very low energy electrons from that source are absorbed by the thin wrappings surrounding the sensitive LiF: Mg, Cu, P element. However, the mean energy of electrons in the ¹⁴⁷Pm distribution is ∼50 keV and their maximum is ∼200 keV, which will have ranges in air of ∼4 cm and ∼40 cm respectively (ICRU 1984), so ¹⁴⁷Pm is unlikely to be particularly relevant to realistic whole body exposures in the workplace.

For ⁸⁵Kr and ⁹⁰Sr/⁹⁰Y the uncovered element of the TLD also under-responds to D_p skin(0°, ε), but by less than 50% in both cases; moreover, if recalibrated in terms of ⁹⁰Sr/⁹⁰Y the relative response for ⁸⁵Kr would be ∼0.98. The uncovered element of the TLD over-responds greatly to H_p(0°, ε) for ¹⁴⁷Pm, ⁸⁵Kr and ⁹⁰Sr/⁹⁰Y, but again if recalibrated in terms of ⁹⁰Sr/⁹⁰Y, the relative responses for ¹⁴⁷Pm and ⁸⁵Kr would 'only' under- and over-respond, respectively, by a factor ∼3×. Though ultimately still unsatisfactory, and well outside of the limits specified in the current performance requirements for H_p(0.07, θ, ε) (IEC 2012), these exceptions might be the best that could be achieved, so might potentially have to be considered acceptable for pragmatism with the caveat that whole body beta exposures in the workplace are perhaps unlikely to be a very large component to an individual's overall dose. Again, guidance and considerations on this would be required from IEC before the TLD could be employed in this way.

Of course, changing the calibration source for the uncovered element from the current ¹³⁷Cs to ⁹⁰Sr/⁹⁰Y would have consequences for its concurrent measurement of photons. The D_p skin(0°, ⁹⁰Sr/⁹⁰Y) response of the uncovered element of the TLD can be shown to be ∼0.19× lower than its D_p skin(0°, ¹³⁷Cs) response; conversely, its H_p(0°, ⁹⁰Sr/⁹⁰Y) response is ∼140× higher than its H_p(0°, ¹³⁷Cs) response. Whichever dose quantity the uncovered element were calibrated in terms of, its responses to betas and X-rays would therefore be very different, drastically so for personal dose and easily explainable from a consideration of the penetrating nature of 662 keV photons compared to the much shorter ranged electrons.

Overall, then, the very different measurement and dosimetric requirements for electrons and photons, and their different calibration requirements, may mean that the uncovered element of the redesigned dosemeter could only be used in mixed photon/electron environments when the field was sufficiently well-characterised such that the anticipated dose contributions from the two components may be estimated in advance and the presence of higher-energy electrons can be ruled out; this might permit the use of appropriate weighting factors to deconvolve their respective contributions from the single TL signal that is read-out. This might lead to a scenario in which workplace field-specific correction factors need to be applied. Though clearly a disadvantage relative to the 'universal' calibration presently adopted for routine-issue TLDs, such a practice can be relatively common in neutron workplace fields (Hager et al 2017) so would not necessarily represent a complete departure from currently accepted practice in personal dosimetry.