Calibration of Mg2SiO4(Tb) thermoluminescent dosimeters for use in determining diagnostic x-ray doses to adult health study participants

Characteristics of Mg2SiO4(Tb) thermoluminescent dosimeters (TLD) were ascertained preparatory to measuring doses from diagnostic x-ray examinations received by Adult Health Study participants. These detectors are small, relatively sensitive to low-dose x-rays, and are appropriate for precise dosimetry. Extensive calibration is necessary for precisely determining doses according to their thermoluminescent intensities. Their sensitivities were investigated by dose, according to x-ray tube voltage, and by exposure direction, to obtain directional dependence. Dosimeter sensitivity lessened due to the fading effect and diminution of the planchet. However, these adverse effects can be avoided by storing the dosimeters at least 1.5 h and by using fresh silver-plated planchets. Thus the TLDs, for which sensitivities were determined in this study, will be useful in subsequent diagnostic x-ray dosimetry.     

Automated data collection and analysis system for MOSFET radiation detectors

Metal oxide semiconductor field effect transistors (MOSFET) have been used as radiation dosimeters. Because of their small detector size, minimal power requirements, and signal integration characteristics, they offer unique possibilities as real-time dose monitors in radiotherapy. An automated data collection and analysis system for use with MOSFET radiation dosimeters has been designed and built. The objective was to design a system which can acquire and process the MOSFET signals in real time, in any radiation field encountered in radiotherapy. In particular, major problems have been solved arising from the intrinsic drifts of the MOSFET signal during low dose rate measurements. These signal drifts are significant when the MOSFET detector is used in applications such as on-line monitoring of radiation dose delivery in brachytherapy or radioimmunotherapy. The data collection and analysis system includes a portable IBM-compatible personal computer fitted with digital-to-analog and analog-to-digital converter boards. A single-chip programmable current supply is used to power the MOSFET dosimeters. Intrinsic and extrinsic drifts in signal due to ion diffusion and electron tunneling are corrected by deconvolution of the collected data in real time or after data collection. The data acquisition system and signal-processing methodologies are described.     

Dosimetry tools and techniques for IMRT

Intensity modulated radiation therapy (IMRT) poses a number of challenges for properly measuring commissioning data and quality assurance (QA) radiation dose distributions. This report provides a comprehensive overview of how dosimeters, phantoms, and dose distribution analysis techniques should be used to support the commissioning and quality assurance requirements of an IMRT program. The proper applications of each dosimeter are described along with the limitations of each system. Point detectors, arrays, film, and electronic portal imagers are discussed with respect to their proper use, along with potential applications of 3D dosimetry. Regardless of the IMRT technique utilized, some situations require the use of multiple detectors for the acquisition of accurate commissioning data. The overall goal of this task group report is to provide a document that aids the physicist in the proper selection and use of the dosimetry tools available for IMRT QA and to provide a resource for physicists that describes dosimetry measurement techniques for purposes of IMRT commissioning and measurement-based characterization or verification of IMRT treatment plans. This report is not intended to provide a comprehensive review of commissioning and QA procedures for IMRT. Instead, this report focuses on the aspects of metrology, particularly the practical aspects of measurements that are unique to IMRT. The metrology of IMRT concerns the application of measurement instruments and their suitability, calibration, and quality control of measurements. Each of the dosimetry measurement tools has limitations that need to be considered when incorporating them into a commissioning process or a comprehensive QA program. For example, routine quality assurance procedures require the use of robust field dosimetry systems. These often exhibit limitations with respect to spatial resolution or energy response and need to themselves be commissioned against more established dosimeters. A chain of dosimeters, from secondary standards to field instruments, is established to assure the quantitative nature of the tests. This report is intended to describe the characteristics of the components of these systems; dosimeters, phantoms, and dose evaluation algorithms. This work is the report of AAPM Task Group 120.     

The influence of cooling rate on the accuracy of normoxic polymer gel dosimeters

Polymer gel dosimeters offer a wide range of applications in the three-dimensional verification of complex radiation dose distributions such as in intensity-modulated radiotherapy (IMRT). With the release of polymer gel dosimeters that can be fabricated in normal atmospheric ('normoxic') conditions, the gel manufacturing process has been significantly simplified. Gel dosimeters are calibrated by use of a series of calibration vials irradiated with known doses or by use of a calibration phantom with a known dose distribution. The overall accuracy of the polymer gel dosimeters is determined by different dosimetric properties. In this study, we show the influence of the temperature history during storage of the gel dosimeter on the dose response curve for two gel dosimeters using the monomers acrylamide/N,N'-methylene-bis-acrylamide (nPAG) and methacrylic acid (nMAG) respectively and bis[tetrakis(hydroxymethyl)phosphonium]sulphate (THP) as antioxidant in both gel dosimeters. This study reveals that differences in temperature history after fabrication of normoxic polymer gel dosimeters may compromise the dosimetric accuracy. It was found that the acrylamide based gel dosimeter (nPAG) is less dependent on the post-manufacture temperature history than the methacrylic acid based gel dosimeter (nMAG). The importance of an equal temperature history for the gel dosimeter and calibration vials is emphasized by this study. A reproducibility study has also been performed on the nPAG gel dosimeter when additional efforts are made to control the temperature changes upon cooling.     

Comparison study of MOSFET detectors and diodes for entrance in vivo dosimetry in 18 MV x-ray beams

The feasibility of dual bias dual metal oxide semiconductor field effect transistors (MOSFETs) for entrance in vivo dose measurements in high energy x-rays beams (18 MV) was investigated. A comparison with commercially available diodes for in vivo dosimetry for the same energy range was performed. As MOSFETs are sold without an integrated build-up cap, different caps were tested: 3 cm bolus, 2 cm bolus, 2 cm hemispherical cap of a water equivalent material (Plastic Water) and a metallic hemispherical cap. This metallic build-up cap is the same as the one that is mounted on the in vivo diode used in this study. Intrinsic precision and response linearity with dose were determined for MOSFETs and diodes. They were then calibrated for entrance in vivo dosimetry in an 18 MV x-ray beam. Calibration included determination of the calibration factor in standard reference conditions and of the correction factors (CF) when irradiation conditions differed from those of reference. Correction factors for field size, source surface distance, wedge, and temperature were determined. Sensitivity variation with accumulated dose and the lifetime of both types of detectors were also studied. Finally, the uncertainties of entrance in vivo measurements using MOSFET and diodes were discussed. Intrinsic precision for MOSFETs for the high sensitivity mode was 0.7% (1 s.d.) as compared to the 0.05% (1 s.d.) for the studied diodes. The linearity of the response with dose was excellent (R2 = 1.000) for both in vivo dosimetry systems. The absolute values of the studied correction factors for the MOSFETs when covered by the different build-up caps were of the same order of those determined for the diodes. However, the uncertainties of the correction factors for MOSFETs were significantly higher than for diodes. Although the intrinsic precision and the uncertainty on the CF was higher for MOSFET detectors than for the studied diodes, the total uncertainty in entrance dose determination, once they were calibrated, was of 2.9% (1 s.d.) while for diodes it was 2.0% (1 s.d.). MOSFETs showed no sensitivity variation with accumulated dose or temperature. When used in the high sensitivity mode, after approximately 50 Gy of accumulated dose MOSFETs could no longer be used as radiation dosimeters. In conclusion, MOSFETs can be used for entrance in vivo dosimetry in high energy x-rays beams if covered by an appropriate build-up cap. Metallic build-up caps, such as those used for in vivo diodes, have the advantage of greater patient comfort and less perturbation of the treatment field than the other build-up caps tested, while keeping the correction factors of the same order.     

An assessment of GafChromic film for measuring 50 kV and 100 kV percentage depth dose curves

Percentage depth dose (PDD) curves were obtained for 50 kV and 100 kV x-rays on a Gulmay Medical D3000 DXR unit. Different dosimetry systems were compared including a Scanditronix Wellhofer small volume cylindrical ion chamber, a Wellhofer photon PFD diode, a PTW soft x-ray parallel plate chamber (N23342) and two types of radiochromic film: GafChromic EBT and GafChromic MD55. The PDD curves were also compared to BEAMnrc Monte Carlo predictions. GafChromic film was found to be a valid choice of dosimeter for measuring percentage depth dose curves at 100 kV and 50 kV. All the dosimeters showed agreement with predictions at depths greater than 10 mm, while near the surface GafChromic film and PFD diodes give the best agreement to Monte Carlo values.     

Dosimetry of ultrasoft x-rays (1.5 keV Al(Kalpha)) using radiochromatic films and colour scanners

This work explores the possibility of measuring the absorbed dose of ultrasoft x-rays (USX, 1.5 keV Al(Kalpha)) with GAFCHROMIC HD-810 radiochromatic dosimetry films (HD-810 films) and colour scanners. HD-810 films were exposed to USX, soft x-rays (14.8 keV) and gamma-rays (60Co) for various times. The response of HD-810 films to absorbed doses of gamma-rays in water was calibrated with Fricke dosimetry and used for the calibration of USX. The optical density of the HD-810 films was quantified with an HP ScanJet 6100C scanner and Corel Picture Paint 7. The choice of the reading channel and colour adjustment settings were optimized to either improve sensitivity or expand the measurable dose range. The response of the HD-810 films to the absorbed dose in water decreased by 50% when the effective photon energy decreased from 1.25 MeV to 14.8 keV. The ratio of the mass energy absorption coefficient of the active layer of HD-810 films to that of water was found to play a major role in this decrease. The mean absorbed doses of the active layer of the HD-810 films exposed to USX were derived. The calculation of the initial photon fluence rate and the mean absorbed doses of USX to biological samples such as plasmid DNA is discussed. This study suggests that radiochromatic dosimetry films are promising secondary dosimeters for measuring the absorbed dose of USX.     

Preliminary evaluation of implantable MOSFET radiation dosimeters

In this paper, we report on measurements performed on a new prototype implantable radiation detector that uses metal-oxide semiconductor field effect transistors (MOSFETs) designed for in vivo dosimetry. The dosimeters, which are encapsulated in hermetically sealed glass cylinders, are used in an unbiased mode during irradiation, unlike other MOSFET detectors previously used in radiotherapy applications. They are powered by radio frequency telemetry for dose measurements, obviating the need for a power supply within each capsule. We have studied the dosimetric characteristics of these MOSFET detectors in vitro under irradiation from a 60Co source. The detectors show a dose reproducibility generally within 5% or better, with the main sources of error being temperature fluctuations occurring between the pre- and post-irradiation measurements as well as detector orientation. A better temperature-controlled environment leads to a reproducibility within 2%. Our preliminary in vitro results show clearly that true non-invasive in vivo dosimetry measurements are feasible and can be performed remotely using telemetric technology.     

The fundamental radiation properties of normoxic polymer gel dosimeters: a comparison between a methacrylic acid based gel and acrylamide based gels

Polymer gel dosimeters offer a wide range of applications in the three-dimensional verification of complex dose distributions such as in intensity-modulated radiotherapy. One of the major difficulties with polymer gel dosimeters is their sensitivity to oxygen, as oxygen inhibits the radiation-induced polymerization reaction. For several years, oxygen was removed from the gels by bubbling the sol with inert gases for several hours during the gel fabrication. Also, the gel had to be poured in containers with low oxygen permeability and solubility. Recently, it was found that these technical difficulties can easily be solved by adding an antioxidant to the gel. These gels are called 'normoxic' gels as they can be produced under normal atmospheric conditions. In this study several properties of polymer gel dosimeters have been investigated: the dose sensitivity, the temporal and spatial stability of the gel, the sensitivity of the dose response to temperature during irradiation and during MR imaging, the energy dependence and the dose-rate dependence. This study reveals that the normoxic polymer gel dosimeter based on methacrylic acid (nMAG) studied in this work has inferior radiation properties as compared to the polyacrylamide gelatine (PAG) gel dosimeters. It is shown that from the three different gel dosimeters investigated in this study, the nPAG gel dosimeter results in a less sensitive gel dosimeter but with superior radiation properties as compared to the nMAG gel dosimeter. The importance of investigating relevant radiation properties of gel dosimeters apart from the radiation sensitivity-prior to their use for dosimetric validation experiments-is illustrated and emphasized throughout this study. Other combinations of monomer and gelling agent may result in more reliable normoxic polymer gel dosimeters.     

Polymer gel dosimeters with reduced toxicity: a preliminary investigation of the NMR and optical dose-response using different monomers

In this work, three new polymer gel dosimeter recipes were investigated that may be more suitable for widespread applications than polyacrylamide gel dosimeters, since the extremely toxic acrylamide has been replaced with the less harmful monomers N-isopropylacrylamide (NIPAM), diacetone acrylamide and N-vinylformamide. The new gel dosimeters studied contained gelatin (5 wt%), monomer (3 wt%), N,N'-methylene-bis-acrylamide crosslinker (3 wt%) and tetrakis (hydroxymethyl) phosphonium chloride antioxidant (10 mM). The NMR response (R2) of the dosimeters was analysed for conditions of varying dose, dose rate, time post-irradiation, and temperature during irradiation and scanning. It was shown that the dose-response behaviour of the NIPAM/Bis gel dosimeter is comparable to that of normoxic polyacrylamide gel (PAGAT) in terms of high dose-sensitivity and low dependence on dose rate and irradiation temperature, within the ranges considered. The dose-response (R2) of NIPAM/Bis appears to be linear over a greater dose range than the PAGAT gel dosimeter. The effects of time post-irradiation (temporal instability) and temperature during NMR scanning on the R2 response were more significant for NIPAM/Bis dosimeters. Diacetone acrylamide and N-vinylformamide gel dosimeters possessed considerably lower dose-sensitivities. The optical dose-response, measured in terms of the attenuation coefficient for each polymer gel dosimeter, showed potential for the use of optical imaging techniques in future studies.     

MOSFET dosimeter depth-dose measurements in heterogeneous tissue-equivalent phantoms at diagnostic x-ray energies

The objective of the present study was to explore the use of the TN-1002RD metal-oxide-semiconductor field effect transistor (MOSFET) dosimeter for measuring tissue depth dose at diagnostic photon energies in both homogeneous and heterogeneous tissue-equivalent materials. Three cylindrical phantoms were constructed and utilized as a prelude to more complex measurements within tomographic physical phantoms of pediatric patients. Each cylindrical phantom was constructed as a stack of seven 5-cm-diameter and 1-cm-thick discs of materials radiographically representative of either soft tissue (S), bone (B), or lung tissue (L) at diagnostic photon energies. In addition to a homogeneous phantom of soft tissue (SSSSSSS), two heterogeneous phantoms were constructed: SSBBSSS and SBLLBSS. MOSFET dosimeters were then positioned at the interface of each disc, and the phantoms were then irradiated at 66 kVp and 200 mAs. Measured values of absorbed dose at depth were then compared to predicated values of point tissue dose as determined via Monte Carlo radiation transport modeling. At depths exceeding 2 cm, experimental results matched the computed values of dose with high accuracy regardless of the dosimeter orientation (epoxy bubble facing toward or away from the x-ray beam). Discrepancies were noted, however, between measured and calculated point doses near the surface of the phantom (surface to 2 cm depth) when the dosimeters were oriented with the epoxy bubble facing the x-ray beam. These discrepancies were largely eliminated when the dosimeters were placed with the flat side facing the x-ray beam. It is therefore recommended that the MOSFET dosimeters be oriented with their flat sides facing the beam when they are used at shallow depths or on the surface of either phantoms or patients.     

Initial evaluation of a commercial EPID modified to a novel direct-detection configuration for radiotherapy dosimetry

Electronic portal imaging devices (EPIDs) integrated with medical linear accelerators utilize an indirect-detection EPID configuration (ID-EPID). Amorphous silicon ID-EPIDs provide high quality low dose images for verification of radiotherapy treatments but they have limitations as dosimeters. The standard ID-EPID configuration includes a high atomic number phosphor scintillator screen, a 1 mm copper layer, and other nonwater equivalent materials covering the detector. This configuration leads to marked differences in the response of an ID-EPID compared to standard radiotherapy dosimeters such as ion chambers in water. In this study the phosphor and copper were removed from a standard commercial EPID to modify the configuration to a direct-detection EPID (DD-EPID). Using solid water as the buildup and backscatter for the detector, dosimetric measurements were performed on the DD-EPID and compared to standard dose-in-water data for 6 and 18 MV photons. The sensitivity of the DD-EPID was approximately eight times less than the ID-EPID but the signal was sufficient to produce accurate and reproducible beam profile measurements for open beams and an intensity-modulated beam. Due to the lower signal levels it was found necessary to ensure that the dark field correction (no radiation) DD-EPID signal was stable or updated frequently. The linearity of dose response was comparable to the ID-EPID but with a greater under-response at low doses. DD-EPID measurements of field size output factors and beam profiles at the depth of maximum dose (dmax), and tissue-maximum ratios between the depths of 0.5 and 10 cm, were in close agreement with dose in water measurements. At depths beyond dmax the DD-EPID showed a greater change in response to field size than ionisation chamber measurements and the beam penumbrae were broader compared to diode scans. The modified DD-EPID configuration studied here has the potential to improve the performance of EPIDs for dose verification of radiotherapy treatments.     

Dose-response stability and integrity of the dose distribution of various polymer gel dosimeters

In this study the stability of different polymer gel dosimeters is investigated. Further to a previous chemical stability study on a (6%T, 50%C) PAG gel, the change in slope and intercept of the linear part of the R2-dose plot is recorded with time for different gel formulations. In addition to this R2-dose-response stability study, the dose edge of a half-blocked field was recorded with time. Three different PAG type polymer gels, a hydroxyethyl acrylate (HEA) gel and two different normoxic polymer gels were investigated. In the PAG type polymer gels, the relative concentration of gelatin and comonomers was varied in order to study the influence of the different components, that constitute the dosimeter, on the stability. It is shown that the R2-dose-response stability is largely determined by the chemical composition of the gel dosimeters. All the PAG gel dosimeters and the normoxic gel dosimeters are found to preserve the integrity of the dose distribution up to 22 days after irradiation. The half-life of the change in dose sensitivity of a MAGIC gel is found to be 18 h compared to 5.7 h for a (6%T, 50%C) PAG gel. A maximum relative decrease in dose sensitivity of 21% was noted for the MAGIC gel compared to an increase of 50% for a (6%T, 50%C) PAG gel. A loss of integrity of the dose distribution was found in the HEA gel.     

Dosimetric characterization of a bi-directional micromultileaf collimator for stereotactic applications

A 6 MV photon beam from Linac SL75-5 has been collimated with a new micromultileaf device that is able to shape the field in the two orthogonal directions with four banks of leaves. This is the first clinical installation of the collimator and in this paper the dosimetric characterization of the system is reported. The dosimetric parameters required by the treatment planning system used for the dose calculation in the patient are: tissue maximum ratios, output factors, transmission and leakage of the leaves, penumbra values. Ionization chambers, silicon diode, radiographic films, and LiF thermoluminescent dosimeters have been employed for measurements of absolute dose and beam dosimetric data. Measurements with different dosimeters supply results in reasonable agreement among them and consistent with data available in literature for other models of micromultileaf collimator; that permits the use of the measured parameters for clinical applications. The discrepancies between results obtained with the different detectors (around 2%) for the analyzed parameters can be considered an indication of the accuracy that can be reached by current stereotactic dosimetry.     

Radiation-induced statistical uncertainty in the threshold voltage measurement of MOSFET dosimeters

The results of a recent study on the limiting uncertainties in the measurement of photon radiation dose with MOSFET dosimeters are reported. The statistical uncertainty in dose measurement from a single device has been measured before and after irradiation. The resulting increase in 1/f noise with radiation dose has been investigated via various analytical models. The limit of uncertainty in the ubiquitous linear trend of threshold voltage with dose has been measured and compared to two nonlinear models. Inter-device uncertainty has been investigated in a group of 40 devices, and preliminary evidence for kurtosis and skewness in the distributions for devices without external bias has been observed.     

Dosimetric parameters for small field sizes using Fricke xylenol gel, thermoluminescent and film dosimeters, and an ionization chamber

Dosimetric measurements in small therapeutic x-ray beam field sizes, such as those used in radiosurgery, that have dimensions comparable to or smaller than the build-up depth, require special care to avoid incorrect interpretation of measurements in regions of high gradients and electronic disequilibrium. These regions occur at the edges of any collimated field, and can extend to the centre of small fields. An inappropriate dosimeter can result in an underestimation, which would lead to an overdose to the patient. We have performed a study of square and circular small field sizes of 6 MV photons using a thermoluminescent dosimeter (TLD), Fricke xylenol gel (FXG) and film dosimeters. PMMA phantoms were employed to measure lateral beam profiles (1 x 1, 3 x 3 and 5 x 5 cm2 for square fields and 1, 2 and 4 cm diameter circular fields), the percentage depth dose, the tissue maximum ratio and the output factor. An ionization chamber (IC) was used for calibration and comparison. Our results demonstrate that high resolution FXG, TLD and film dosimeters agree with each other, and that an ionization chamber, with low lateral resolution, underestimates the absorbed dose. Our results show that, when planning small field radiotherapy, dosimeters with adequate lateral spatial resolution and tissue equivalence are required to provide an accurate basic beam data set to correctly calculate the absorbed dose in regions of electronic disequilibrium.     

An NMR relaxometry and gravimetric study of gelatin-free aqueous polyacrylamide dosimeters

In conformal radiation therapy, a high dose of radiation is given to a target volume to increase the probability of cure, and care is taken to minimize the dose to surrounding healthy tissue. The techniques used to achieve this are very complicated and the precise verification of the resulting three-dimensional (3D) dose distribution is required. Polyacrylamide gelatin (PAG) dosimeters with magnetic resonance imaging and optical computed tomography scanning provide the required 3D dosimetry with high spatial resolution. Many basic studies have characterized these chemical dosimeters that polymerize under irradiation. However, the investigation of the fundamental properties of the radiation-induced polymerization in PAG dosimeters is complicated by the presence of the background gelatin matrix. In this work, a gelatin-free model system for the study of the basic radiation-induced polymerization in PAG dosimeters has been developed. Experiments were performed on gelatin-free dosimeters, named aqueous polyacrylamide (APA) dosimeters, containing equal amounts of acrylamide and N,N'-methylene-bisacrylamide. The APA dosimeters were prepared with four different total monomer concentrations (2, 4, 6 and 8% by weight). Nuclear magnetic resonance (NMR) spin-spin and spin-lattice proton relaxation measurements at 20 MHz, and gravimetric analyses performed on all four dosimeters, show a continuous degree of polymerization over the dose range of 0-25 Gy. The developed NMR model explains the relationship observed between the relaxation data and the amount of crosslinked polymer formed at each dose. This model can be extended with gelatin relaxation data to provide a fundamental understanding of radiation-induced polymerization in the conventional PAG dosimeters.     

Calculation of radiation dose enhancement factors for dose enhancement therapy of brain tumours.

When brain tumours are loaded with iodinated contrast media (CM) and exposed to x-rays, the photoelectrons, Auger electrons and fluorescent x-rays from the iodine enhance the radiation dose absorbed by the tumour. A modified CT scanner, the CTX, can be used to localize the tumour and to deliver the dose enhancement therapy. Monte Carlo calculations are presented here of the central-axis radiation depth dose in a brain containing a tumour loaded with an iodine concentration of 5 mg ml-1 and irradiated with the CTX operated at various kV settings. The dose enhancement factor (DEF) is also calculated for various field sizes and for 5 mg ml-1 of gadolinium in the tumour when the CTX is operated at 140 kV. The calculated values of the DEF are close to published experimental results.     

Measurement of radiotherapy x-ray skin dose on a chest wall phantom

Sufficient skin dose needs to be delivered by a radiotherapy chest wall treatment regimen to ensure the probability of a near surface tumor recurrence is minimized. To simulate a chest wall treatment a hemicylindrical solid water phantom of 7.5 cm radius was irradiated with 6 MV x-rays using 20x20 cm2 and 10x20 cm2 fields at 100 cm source surface distance (SSD) to the base of the phantom. A surface dose profile was obtained from 0 to 180 degrees, in 10 degrees increments around the circumference of the phantom. Dosimetry results obtained from radiochromic film (effective depth of 0.17 mm) were used in the investigation, the superficial doses were found to be 28% (of Dmax) at the 0 degrees beam entry position and 58% at the 90 degrees oblique beam position. Superficial dose results were also obtained using extra thin thermoluminescent dosimeters (TLD) (effective depth 0.14 mm) of 30% at 0 degrees, 57% at 90 degrees, and a metal oxide semiconductor field effect transistor (MOSFET) detector (effective depth 0.5 mm) of 43% at 0 degrees, 62% at 90 degrees. Because the differences in measured superficial doses were significant and beyond those related to experimental error, these differences are assumed to be mostly attributable to the effective depth of measurement of each detector. We numerically simulated a bolus on/bolus off technique and found we could increase the coverage to the skin. Using an alternate "bolus on," "bolus off" regimen, the skin would receive 36.8 Gy at 0 degrees incidence and 46.4 Gy at 90 degrees incidence for a prescribed midpoint dose of 50 Gy. From this work it is evident that, as the circumference of the phantom is traversed the SSD increases and hence there is an inverse square fluence fall-off, this is more than offset by the increase in skin dose due to surface curvature to a plateau at about 90 degrees. Beyond this angle it is assumed that beam attenuation through the phantom and inverse square fall-off is causing the surface dose to reduce.