Report of AAPM Therapy Physics Committee Task Group 74 : ln-air output ratio , S " , for megavoltage photon beams

The concept of in-air output ratio (S.) was introduced to characterize how the incident photon fluence per monitor unit (or unit time for a Co-60 unit) varies with collimator settings. However, there has been much confusion regarding the measurement technique to be used that has prevented the accurate and consistent determination of S.. The main thrust of the report is to devise a theoretical and measurement formalism that ensures interinstitutional consistency of S.. The in-air output ratio, ,S., is defined as the ratio of primary collision water kerma in free-space, Ko, per monitor unit between an arbitrary collimator setting and the reference collimator setting at the same location. Miniphantoms with sufficient lateral and longitudinal thicknesses to eliminate electron contamination and maintain transient electron equilibrium are recommended for the measurement of S.. The authors present a comection formalism to extrapolate the correct S. from the measured values using high-Z miniphantom. Miniphantoms made of high-Z material are used to measure S. for small fields (e.9., IMRT or stereotactic radiosurgery). This report presents a review of the components of S., including headscatter, source-obscuring, and monitor-backscattering effects. A review of calculation methods (Monte Carlo and empirical) used to calculate S. for arbitrary shaped fields is presented. The authors discussed the use of S. in photon dose calculation algorithms, in particular, monitor unit calculation. Finally, a summary of S. data (from RPC and other institutions) is included fbr QA purposes. O 2009 American Association of Physicists in Medicine. [DOI: 10. I I lSl t .322]36t1


LIST OF SYMBOLS
The symbols used for all physical quantities in the report are listed here.Arguments to the dosimetry quantities are grouped such that those dependent on the radiation field geometry ͑e.g., c or A͒, the position relative to the radiation source ͑x , y , z͒, and the phantom geometry specifications ͑e.g., d, and SSD͒ are placed together where the groups are separated by a semicolon.The group always follow the same order, e.g., D͑c , s ; x , y , z ; d , SSD͒.Whenever we emphasize selected variables, we will ignore the other variables, e.g., D͑x , y , z͒.When the energy fluence ⌿ is required as an explicit variable, it will be placed as the last group, e.g., D͑x , y , z ; ⌿͑A ; x , y , z ref ͒͒.
1͔ z SCD ϭ Distance from the source to the backscattering collimator surface ͑unit: cm͒ z ref ϭ Reference ͑or normalization͒ distance from the source to the point of interest ͑unit: cm͒ ͓see Eq. ͑2͔͒

I. INTRODUCTION AND SCOPE
2][3] This quantity is also called the in-air output factor, 4 collimator-scatter factor, 5 headscatter factor, 6,7 and in common usage, the field size factor.The names, collimatorscatter factor and headscatter factor, are somewhat misleading since they emphasize a single component of the output ratio, while the last is unspecific as to which quantity that varies with the field size.We retained the symbol S c because it has been widely used in North America. 5The development of three-dimensional conformal radiotherapy ͑3D CRT͒ in the 1990s motivated investigation of models and experimental procedures to quantify different components of the accelerator output to provide more accurate dose computation.
There are multiple factors 8 shown to influence the in-air output ratio; in particular, photons are scattered by structures in the accelerator head ͑headscatter͒, photons and electrons are backscattered into the monitor chamber ͑monitor backscat-ter͒, and at very small field sizes, a portion of the x-ray source is obscured by the collimators ͑source-obscuring ef-fect͒.Various sources of headscatter, which include the primary collimator, the flattening filter, the secondary collimators, the monitor chamber ͑and a wedge, if used͒, have been characterized.0][11] The availability of Monte Carlo simulation has provided a methodology to study various components of the headscatter to interpret the measurement results or validate analytical models.Without a commonly agreed formal definition, an in-air output ratio has been widely applied in various approaches for calculation of absorbed dose per MU.These approaches include derivation of parameters for explicit modeling of headscatter components as well as for direct use in factorbased monitor unit calculation schemes.Use of asymmetric jaws has compelled the need to characterize S c on and off the central axis.The introduction of intensity-modulated radiotherapy ͑IMRT͒ has further required S c inside and outside beam collimation.Accurate determination of in-air output ratios for IMRT is much more challenging, where extremely small and/or severe irregularly shaped fields are being more commonly used.
The main thrust of the report is about devising a theoretical and measurement formalism that ensures interinstitutional consistency of S c .Historically, S c is often measured at depth of maximum dose with a build-up cap.This experimental definition of S c , while popular for TMR-based MU calculation formalism, is fundamentally different from the in-air output ratio ͑S c ͒ as defined in this report.For clarity, we will refer to the old definition of S c as collimator-scatter factor.Detailed discussion on the use of the collimatorscatter factor is beyond the scope of TG74 because of the large interinstitutional variations, lack of published theoretical investigations of the behavior of contaminating electrons, and other potential complications ͑e.g., detector response difference for electrons and photons͒ caused by the contaminating electrons.
There has been much confusion regarding the measurement technique to be used that has prevented the accurate and consistent determination of S c .Ideally, the build-up cap/ miniphantom should provide full electron equilibrium as in full water medium, with negligible photon scattering, and be small enough to be fully covered by a homogeneous part of the radiation beam.In this report, "full water phantom" will be referred to simply as "in water."The shape, dimension, and material of the build-up cap/miniphantom, and the type and size of the detector are all design considerations.Earlier designs of build-up caps were thin shells, meant for use in cobalt beams, with a water-equivalent thickness of approximately 0.5 cm.The build-up cap surrounded the chamber, which was oriented perpendicularly to the beam axis.Such caps are generally not suitable for measurement of S c at higher photon energies due to the presence of electron contamination. 12A discussion on measurement techniques of S c comes later in this report.
The purpose of this task group is to address the issues related to the determination, validation, and use of in-air output ratios for megavoltage photon beams from clinical linear accelerators.This task group report provides a comprehensive review of the current status including the clinical significance of the output ratio and the findings of the existing theoretical and experimental investigations.The report consist of self-contained sections: Section II focuses on the definition of essential dosimetry quantities; Sec.III and IV focus on the overall framework for the use of in-air output ratio in dose and monitor unit calculations and the various processes that contribute to S c ; Sec.V focuses on how to measure in-air output ratio; and Sec.VI and VII focus on practical methods for parametrization of S c and quality assurance ͑QA͒ issues, respectively.Readers who are interested in the practical aspect of S c measurement can jump to Sec.V since it contains the main recommendations of this report on how to determine S c .Section VIII summarizes the main recommendations and clarifications of the report.Readers who are interested in how to parametrize S c can jump to Sec.VI, although Sec.IV is essential for understanding various factors that affect S c .

II.A. Photon beam and absorbed dose components
It is important to distinguish the terminology for photon beam components ͑e.g., primary or scattered photons͒, the quantities used to quantify the radiation ͑e.g., fluence͒, and the quantities used to describe the radiation impact ͑e.g., absorbed dose or ionization͒.It is often useful to separate the radiation incident on the patient into different components with distinguishable different dose deposition properties.The radiation is commonly separated based on the origin of radiation.Direct radiation is that photon radiation generated at the source that reaches the patient without any intermediate interactions.Indirect radiation is that photon radiation with a history of interaction/scattering with the flattening filter, collimators or other structures in the treatment unit head ͑see Fig. 1͒.Indirect radiation is commonly called headscattered radiation ͑or simply headscatter͒.Electrons and positrons released from interactions with either the treatment head or the air column constitute charged particle contamination, or in short, electron contamination.Together, the direct radiation, indirect radiation, and electron contamination comprise the output radiation, which from the patient point of view equals the incident radiation.The output ͑or incident͒ radiation is independent of the irradiated subject ͑i.e., patient; throughout this report, any reference to "patient" in a treatment situation will be understood to apply to a "phantom" in a measurement condition.Usually the terms simply imply a volume scattering medium.͒ In the patient, charged particles released from the first interaction of the incident photons in the patient give rise to the primary component of the absorbed dose, also called the primary dose for short.For hypothetical points experiencing both lateral and longitudinal charged particle equilibrium ͑CPE͒, the primary dose is directly proportional to the primary collision kerma to within a constant ͑D p = ␤K p ͒ and it depends on the depth ͑or the attenuation of materials intersecting the beam along the ray line between the x-ray source and point of interest͒.Note that there can be a primary dose component from both the direct and indirect photons.The contribution to the absorbed dose from electrons released by photons scattered from elsewhere in the patient is called the phantom scatter component of the absorbed dose, in short the scatter dose.The scatter dose depends on the field size in the patient as defined by the collimation and the depth ͑these variables describe the scattering volume͒ and the incident fluence.The ratio of the scatter dose to the primary dose is called scatter-to-primary ratio ͑SPR͒ and is also expressed by the scatter factor, SF͑s;d͒ = 1 + SPR͑s,d͒ = D͑s;d͒ D p ͑s;d͒ , ͑1͒ which denotes the ratio of the total absorbed dose to the primary dose.The SPR depends on the field size in the patient and the depth and is almost independent of the sourceto-skin distance ͑SSD͒ and other beam geometry parameters that affect the incident radiation.The absorbed dose from contaminant electrons is considered separately as charged particle contamination dose or electron contamination dose for short.This dose component cannot be further separated into primary and scatter parts since it stems from charged particles directly entering the patient.Table I summarizes the general terminology described in this section.
The definitions of the geometrical parameters characterizing a treatment head and a phantom are shown in Fig. 2. The collimator setting c is always specified at the isocenter at the source-to-axial distance ͑SAD͒ ͑usually 100 cm from the source͒.The field size, s, is always specified at depth d of measurement at the source-to-detector distance z ͑or SDD͒.

II.B. Output ratios
The in-water output ratio, S cp , for a field of size s is defined as the ratio of the absorbed dose for the used collimator setting to the absorbed dose for the reference ͑or nor-malization͒ field size ͑s ref ͒, for the same MU, in a large water phantom at the same reference depth, d ref , and the same reference source-to-detector distance, z ref , on the central axis ͑commonly at the isocenter͒, where D is the absorbed dose in the phantom, c = s indicates that the field size of the phantom at depth d ref , s, is that defined by the collimator setting, c, at the isocenter, usually 100 cm from the radiation source.The meaning of the water phantom being large is that it should enable full lateral and back scattering conditions for the field in question.The phantom should extend at least 9 cm in depth beyond the point of interest to ensure effectively full backscatter conditions for photon energy as low as cobalt-60. 13he in-air output ratio, S c is now defined as the ratio of primary collision water kerma in free-space, K p , per monitor unit between an arbitrary collimator setting, c, and the reference collimator setting, c ref , at the same location on the central axis, where z ref is the reference source-to-detector distance ͑usually z ref = 100 cm͒.Normally, the reference collimator setting is 10ϫ 10 cm 2 , i.e., c = 10 cm, for SAD ϭ 100 cm.Notice that the primary collision kerma excludes the scattered collision kerma induced by scatter from any surrounding phantom but includes all scattering that has occurred in the treatment head.The main need for S c is to quantify fluence variations with collimator settings for use in beam modeling and dose calculations.The idea behind the definition in Eq. ͑3͒ is to have a well defined quantity that is independent of experimental conditions yet closely related to energy fluence and primary dose.The collision kerma from photons is defined as the energy fluence for each energy times its mass energy absorption coefficient, The formal definition in Eq. ͑3͒ lends itself to the derivation of correction factors to compensate for any systematic deviations introduced by particular experimental methods used to estimate S c , e.g., for differences in cap attenuation and filtration resulting from spectral differences between the arbitrary collimator setting and the reference setting ͑see Sec.V B͒.
For fields centered at points ͑x , y͒ off the axis of the collimator rotation ͑x ref =0, y ref =0͒, Eq. ͑3͒ becomes Experimentally, S c can be estimated by the ionization ratio measured in a miniphantom that has sufficient thickness to eliminate electron contamination.The lateral dimensions of the miniphantom shall, besides eliminating contaminant electrons from the side, provide lateral electronic equilibrium at the detector.The material composition of the miniphantom must be carefully chosen as to minimize medium-induced deviations from water kerma ratios due to spectral differences between the beams c and c ref or compensated by correction procedures ͑see Sec.V B͒.Measurement details are discussed later in Sec.V. When using a miniphantom and a detector, the ratio of primary collision kerma at the detector, K p , can be expressed as 14 where en ͑E͒ / is the mass energy absorption coefficient for the miniphantom medium at the photon energy the total collision kerma to the primary collision kerma, or the kerma scatter factor, for the entire miniphantom.If the primary spectrum is independent of the collimation setting, then it follows that the signal ratio measures the energy fluence output ratio, ͐⌿ E ͑c ; z ref ͒dE / ͐⌿ E ͑c ref ; z ref ͒dE.However, in situations where the beam quality is different from reference conditions ͑e.g., while using physical wedges͒, it must be noticed that the signal ratio is only an estimator of the energy fluence ratio, biased by the miniphantom and spectrum specific variations of collision kerma and attenuation.
A quantity more inclusive for different beam geometries is the in-air output function for the incident photon beam, O air , defined as the ratio of primary collision water kerma in free-space per monitor unit for an arbitrary collimator setting ͑possibly with a beam modifier in place͒ and position, to the primary collision water kerma in free-space per monitor unit for the reference open beam under reference conditions ͑usually c ref =10 In the numerator, B represents all of the physical modifiers that may be in the beam, such as wedges, compensators, or trays.The use of O air to map the lateral energy fluence variation for primary dose calculations will directly include the effects of off-axis variations in the energy absorption coefficient en .Notice that in the absence of beam modifiers, O air at the reference distance, z ref is identical to the in-air output ratio, S c .If it is desired to do in-air quantity based dosimetry with modifiers, K p in the denominator of Eq. ͑7͒ refers to the reference open field without wedge at the reference conditions, thus O air includes the transmission of the wedge filter while S c does not.Similarly, the tray factor can be included in O air .However, a common practice and the recommendation of AAPM TG71 makes the wedge factor and tray factor a ratio of doses in full phantom. 15Either approach gives the same result but the corresponding MU formulation must be used.
The phantom scatter factor, S p , is defined as the ratio of the scatter factors between the actual field size, s, in the phantom and that of the reference field size, s ref , both at the reference depth, d ref , where SF is the ratio of the total dose in water ͑D͒ to the primary dose ͑D p ͒ for the same field setting and depth at the same location.Assuming that a particular collimator setting c equals the field size s at the isocenter, i.e., z is z ref , the phantom scatter factor can, by using Eqs.͑2͒ and ͑3͒, be determined using K p ͑s͒ = D p ͑s͒ / ␤ p ͑s͒, by Equation ͑9͒ shows that the requirement for the approximation S p ͑s͒ϷS cp ͑s͒ / S c ͑s͒ is that ␤ p ͑s͒ / ␤ p ͑s ref ͒ is close to unity.This condition is fulfilled for all fields large enough to provide lateral electronic equilibrium.The intention of the phantom scatter factor is to describe the effects of photon scattering in the phantom only, and it follows that identical value of phantom scatter factors could be achieved for different collimator settings that result in equal amounts of phantom scatter at the point of interest.However, two fields that yield identical phantom scatter contributions from their respective direct component of the beams may give different scatter contributions in the phantom from the headscatter components since headscatter varies differently with collimation than the direct parts.This effect can be considered as small due to a rather large correlation between the shapes of the effective portals for the direct and indirect components of the beam, respectively.

III. THE ROLE OF S c FOR MU CALCULATION
Dose calculation formalisms specify the parameters and their relationship to calculate monitor units from the prescribed dose.Given a particular formalism, its parameters may be estimated using very different methods, e.g., measurements, kernel-based convolution/superposition models, or Monte Carlo ͑MC͒ simulations, as long as the parameters are well defined in terms of the underlying physical interaction processes.Hence, a monitor unit formalism can be viewed as a framework, or "top level" model, within which different computation models can be implemented.We will here review two groups of formalisms, a factor-based formalism tailored for "hand" calculations and a model-based energy fluence formalism typical for modern treatment planning systems.Both calculation paths may use data, directly or indirectly, based on measurements of S c .

III.A. Factor-based dose-to-dose ratio formalisms
Factor-based methods determine absorbed dose per monitor unit by using the product of standardized dose ratio measurements.Successive dose ratio factors are multiplied for a chain of geometries, and thus the dose ratio factors are varied one by one until the geometry of interest is linked back to the reference geometry,

͑10͒
This equation is an identity equation.where ␤ = D͑c , s ; z ; d͒ / K͑c , s ; z ; d͒ is the dose-to-collision kerma ratio, SF K = K͑c , s ; z ; d͒ / K p ͑c , s ; z ; d͒ =1+SPR K is the kerma scatter factor due to photon phantom scattering, and K p is the primary collision kerma.SF K = SF under electron equilibrium.͑One could use the dose-to-energy fluence ratio directly if a method to measure energy fluence could be developed.͒The principle of the separation of primary and scatter components states that SF is only a function of phantom ͑depth and irradiated field size͒ and is independent of the source-to-detector distance, z, to the first order and collima-tor setting c; and ␤ is a constant at sufficient depths, under transient charged particle equilibrium.K p can be separated into components that are only correlated with the incident energy fluence K inc ͑c ; z͒ and the transmission function T͑d͒ due to attenuation in the medium 16 K p ͑c;z;d͒ = K inc ͑c;z͒ • T͑d͒.͑12͒ The tissue-phantom ratio TPR and S cp can be expressed as where ͑s ; d ref ͒ = ␤͑s ; z ; d͒ / ␤͑s ; z ; d ref ͒ is the electron disequilibrium factor ͑ ϭ 1 for adequate depths and positions adequately far from the edges of the field͒.We assumed that d ref is sufficiently large to establish electron equilibrium and shield from contamination electrons.The accuracy of the factor-based dose calculation algorithms is determined by the accuracy of SF and S c calculation under electron equilibrium conditions.S c is very important in this formalism since it directly characterizes the variation in the incident collision kerma.The basic equation for dose calculation on the central axis at an arbitrary distance z can be derived using Eqs.͑11͒-͑14͒ as

͑15͒
where is the dose per monitor unit under the reference conditions ͑usually collimator settings of 10ϫ 10 cm 2 , 100 cm SAD, 10 cm depth͒, and using Eqs.͑7͒ and ͑12͒ we can obtain O air in Eq. ͑16͒ can be further separated into two factors as where z eff indicates the source-to-detector distance and the subscript "eff" means the source-to-point distance ͑SPD͒ fit to an inverse-square relationship.
The in-air output function, O air , can be used for MU calculation for more general cases, e.g., for points off the axis and at an arbitrary distance from the source, where the dose can be expressed as In this equation, c ref is the reference field ͑10ϫ 10 cm 2 ͒ that is centered on the collimator axis.d ¯and d are the average depth and the depth along the ray line ͑x , y͒ from the x-ray source, respectively.The equivalent square, sЈ, for the off-axis point ͑x , y͒ is chosen so that SF͑sЈ ; x ref , y ref ; d͒ =SF͑s ; x , y ; d͒, where s is the square field centered on the central axis.The equivalent square for an arbitrary point in the field, sЈ, can be determined using the measured SF for circular fields on the central-axis and the scatter integration. 17The definition of the TPR has been expanded for application to rays off the collimator axis, but keeping the numerator and denominator on the same ray.Off-axis beam-softening renders TPR͑s ; x , y ; d ¯, d͒ different from TPR͑sЈ ; x ref , y ref ; d ¯͒. 18Further details are beyond the scope of this report.
In Eq. ͑18͒, O air can be separated as For off-axis points, S c was defined by Eq. ͑5͒ in Sec.II B. Notice that the definition of S c includes the variation of the incident radiation with the point off the axis.For points within 4 cm of the collimator axis, the value for S c at off-axis point is very close to that on the central axis for points well within beam collimation. 19or a wedged beam, S c defined in Eq. ͑19͒ is now denoted as S c,w , i.e., where WF air ͑c ref ͒ is the in-air wedge factor for the reference condition, DIST w is the inverse-square distance factor, and S p,w ͑sЈ͒ is the phantom scatter factor for the wedged beam.S c,w as defined in this report for a wedged beam is often not used in conventional MU calculation algorithms.The formalism from more conventional equation has the form, where S c for open beam alone is used, and the headscatters from wedge fields are lumped into a field size dependent wedge factor, WF͑c ; x ; d͒, where the wedge gradient is in the x direction.Users are cautioned to avoid double counting the in-air output ratio if a field size dependent wedge factor is used.The POAR is the primary off-axis ratio measured at depth d ref in a miniphantom for the largest collimator setting.Detailed derivation can be found in Appendix B.

III.B. Model-based dose-to-energy fluence formalisms
The absorbed dose resulting from an irradiation is directly proportional to the energy fluence incident onto the patient.This makes normalization of the calculated dose per energy fluence appealing.Energy fluence is more practical than particle fluence since the kerma per energy fluence is only weakly dependent on photon energy.Thus, this application of the formalism is robust for small shifts in beam quality.Both kernel-based convolution/superposition models and Monte Carlo-based calculations can be implemented using such a formalism since the absorbed dose can be calculated per monitor unit following a "global" energy fluence to monitor units calibration.Details of such a formalism have been outlined by Ahnesjö and co-workers [19][20][21] and Mackie et al. 22 The core of the dose calculation engine is supposed to deliver the quantity, dose to energy fluence ratio, , ͑x,y,z͒ = D͑x,y,z;⌿͑A;x,y, where D͑x , y , z ; ⌿͑A ; x , y , z ref ͒͒ is the absorbed dose at point ͑x , y , z͒, given that the lateral energy fluence distribution for the applicator setting A , ⌿͑A ; x , y , z ref ͒ is defined free in-air at a reference distance z ref from the source, and ⌿ 0 is the energy fluence of direct photons free in-air at the isocenter.Following Ahnesjö et al., 23 the MU registered for a given beam can be separated into two parts, MU= MU 0 +MU b where MU 0 is the signal proportional to the forward fluence through the monitor chamber and MU b = b͑A͒ • MU 0 is proportional to the fluence of particles backscattered into the monitor from the upper sides of the adjustable collimators.The total energy fluence delivered free in-air per monitor unit can thus be written as The ratio ⌿ 0 / MU 0 provides the key link between the absorbed dose per energy fluence as calculated by the dose calculation engine and the absorbed dose per monitor unit as needed for monitor unit settings.This ratio is directly derived from the monitor backscatter corrected ratio of dose calculated and measured for the reference geometry according to where MU= MU 0 ͑1+b͑A͒͒ have been used.
Modeling of the energy fluence is commonly done separately for the direct and indirect photons, respectively.The direct photons are simply given by blocking collimated parts in a relative distribution of the direct photons for an uncollimated beam to yield the relative distribution f͑A ; x , y , z ref ͒.Adding indirect photons, ⌿ ind , from irradiated parts of the treatment head then yields the total photon energy fluence of the beam, where f is the relative energy fluence of direct particles.
Equations ͑23͒-͑26͒ specify a framework for model-based dose calculations.To calculate the absorbed dose, fluence must be modeled such that the energy fluence distributions of both direct and indirect particles are provided relative to the reference fluence of direct particles ⌿ 0 as well as the collimator backscatter to the monitors through b͑A͒.
Writing the in-air output ratio on the central axis as an energy fluence ratio ͑assuming the mass energy absorption coefficient does not change with aperture setting A͒ shows the role for the measured data, where S h is the headscatter factor and S b is the monitor backscatter factor.We have used Eqs.͑3͒, ͑24͒, and ͑26͒ in the derivation.The most direct way of determining parameters for headscatter models is through matching the model results to measured S c data since it directly depends on the variation in headscatter and monitor backscatter.In Sec.IV, we will review the physical processes leading to the variation in ⌿ ind / ⌿ 0 , with varying field settings, and the main approaches used for its modeling.

IV. PHOTON BEAM CHARACTERISTICS
Different approaches have been investigated to derive the beam characterization data for dose calculations.The Monte Carlo method has proven useful in analyzing the various components of the output ratio, an approach pioneered by Nilsson and Brahme 24 and later systematically implemented in the BEAM package, 25 which has been used extensively in photon beam modeling.A practical approach that avoids handling of extensive phase space data sets is to use comprehensive "multisource" models, and then to derive the model parameters from measured S c .7][28][29][30] At best, such models are developed based on the analysis of Monte Carlo simulated beam data, and the model parameters can have clear physical interpretation.Multiple source models assume that particles in a radiotherapy beam are from different subsources representing major contributing components of a clinical accelera-tor.2][33] A source model might have slightly different subsource geometries for different linac models but the model parametrization is basically generic for commonly used clinical accelerators.A detailed model would provide the time independent energy fluence ⌿ E,⍀ , differential in energy and direction at all points ͑x , y , z ref ͒ in a beam at the reference plane, z ref , all normalized per monitor unit signal.In practice, the fluence monitoring is nontrivial since scattered photons from the treatment head add an "unmonitored" contribution to the fluence, and backscatter into the monitor yields a "false" contribution to the total signal It is therefore common to describe the direct beam ⌿ 0 and the indirect components ⌿ ind of the beam separately as we will do in the following sections.We will briefly review photon beam characteristics based on experimental investigations, Monte Carlo simulations, and analytical studies and modeling.Related reviews exist on multisource modeling, 34 on dose calculations, 35 and on Monte Carlo linac simulation methods. 36,37

IV.A. Photon spectra and direct beam fluence distribution
Given an energy fluence spectrum of direct photons, many dosimetric quantities such as attenuation, kerma, etc., are trivial to calculate directly using generally available tabulations of interaction data.Hence there has been a great interest to determine the beam spectra.Monte Carlo simulations and several reconstructive techniques from attenuation or depth dose measurements have been explored.
In a much cited study, Mohan et al. 38 used Monte Carlo to determine spectra for 4-24 MV photon beams from Varian accelerators.Recent comparisons with more sophisticated MC simulations 39,40 showed that the spectra of Mohan et al. still represent a fair approximation.For accurate results, Monte Carlo simulations require tuning of the electron beam properties based on the measured beam data. 39,41Sheikh-Bagheri and Rogers 39 performed a thorough MC study of nine photon beams in the energy range of 4-25 MV from Varian, Siemens, and Elekta linacs.An important result was to point out that in-air dose profiles measured with an ion chamber and a proper build-up cap is the most effective experimental data to match simulation results while varying the energy and spatial characteristics of the primary electron beam.
Reconstructive techniques based on depth dose or attenuation is an appealing alternative to full Monte Carlo simulations since the reconstruction process in itself implies consistency with end result verification data such as depth doses.The main difficulty in reconstructive techniques is the poor numerical conditioning of photon spectrum unfolding, which makes the use of spectral shape constraints necessary.Also, the absorbed dose from charged particle contamination in the build-up region must be considered while including the data from the build-up region.Ahnesjö and Andreo 42 combined a parametrized model for charged particle contamination with a semianalytical spectrum model whose parameters were varied to minimize the difference between the measured depth doses and the depth doses reconstructed from the sum of the absorbed dose for a pure photon beam and the charged particle dose.In a similar dose reconstructive approach, Sauer and Neumann 43 used general shape properties of realistic spectra imposing positivity and monotony requirements.5][46][47][48][49][50] Most of these studies also used constraints on the spectral shape to handle numerical conditioning problems.
The spectra at off-axis positions are "softer," i.e., have a lower mean or effective energy, than those at the central axis.In a broad experimental survey involving 15 different linac beams, Tailor et al. 18 showed that the relative change, with off-axis angle, of the narrow beam half value thickness had a similar shape for all investigated machines, also confirmed by earlier data from Yu et al. 51 and Bjärngard and Shackford. 16Although these general parametrizations exist, off-axis beam quality variations depend on the material of the flattening filter 52 and should therefore be at least checked as part of the machine commissioning procedure.The check can be easily performed by comparing calculation and measurement of D / MU at an off-axis point at depths larger or equal to 20 cm in a large enough field.
Off-axis variations in the energy fluence depend on the design of the flattening filter and the energy of the electron beam hitting the target.The in-air output function ͓Eq.͑7͔͒ is an obvious option based on direct measurements using build-up cap that directly includes the kerma bias ͑i.e., multiplication of en / to the energy fluence͒ needed for correct primary dose calculation.Treuer et al. 53 and Ahnesjö and Trepp 54 worked out procedures to allow for full lateral mappings of general, nonrotational symmetrical beams based on deconvolution of a dose distribution measured in a lateral plane with respect to the beam axis.
Physical wedges and compensating filters, if present, change the beam spectrum.van der Zee and Welleweerd 55 simulated the Elekta internal wedge.They found that the presence of the wedge altered the primary and scattered photon components from the linac significantly: Beam hardening shifted the mean photon energy by 0.3 and 0.7 MeV for the two components, respectively, for a 10 MV photon beam.58]27 The consequences from spectral changes in terms of change in primary and scatter dose deposition pattern with depth have been further analyzed and modeled. 20

IV.B. Photon scatter from the flattening filter and primary collimator
The scatter from the flattening filter acts as an extended source, a concept in beam modeling that has been explored and refined over the years.Measurements, 4,6,[8][9][10][59][60][61][62][63][64] Monte Carlo simulations, 38,65,66 and analytic approximations 19 have all established the role of the flattening filter and the primary collimator as a distributed source which may contribute up to 12% of the output photons. Distr67,68 Most variation in the in-air output ratio with field size and position can be explained through modeling the number of scattered photons by an extended source integration over the part of the linac head visible from the calculation's point of view 4,8,10,19,23,63,65,69 ͑see Fig. 3͒.These characteristics of photon beams stem from a partial eclipsing of the extrafocal source by the field defining collimators.Different intensity distributions of the extended source have been used in the simulation, such as triangular, constant, or Gaussian functions, yielding similar results indicating that the actual area of the filter being exposed to the primary beam is more important than the particular intensity distribution used to model it.Beam models that employ extrafocal source distributions and the geometry of the treatment head can predict the change of headscatter and beam penumbra with field size.Since the flattening filter is located downstream from the target and introduces an extended photon source, which will reach outside of the beam collimation where it will dominate since the collimator leakage contribution is even less.Experimental data confirm these findings.70 Several studies also show up to 2% variation in S c values at off-axis locations inside beam collimation.62,[70][71][72] It must be emphasized that because the dose contribution from headscattered photons usually dominates the dose distribution outside the beam, accounting for indirect radiation is very important for the prediction of absorbed dose in such locations.An off-axis headscatter model is thus very important to accurately predict the absorbed dose at off-axis points.70  normalized scatter-to-primary ratio, SPR air ͑c ; x͒ / SPR air ͑c ;0͒, for headscatter and direct components of a 6 MV photon beam from a Varian accelerator for two different collimator settings c = 20 and 40 cm.The curves are obtained by fitting two Gaussian-source models for SPR air ͑c ; x͒ to S c ͑c ; x͒ / POAR͑x͒, where S c ͑c ; x͒ is the in air output ratio as defined by Eq. ͑5͒ and POAR͑x͒ is the primary off-axis ratio.70 Since the flattening filter scatter may constitute up to 12% of the output photon radiation, its location downstream of target will influence the variation in incident radiation as a function of patient distance to the x-ray source, a phenomenon that can be modeled through the use of a virtual source position.It has been shown that the virtual source position was about 1 cm downstream of the target for an open field and about 2-3 cm for a wedged field from Elekta, which has an internal physical wedge.7 A more detailed study to examine the correlation between S c and SDD showed that the change in S c for open beam at different SDD is indeed very small ͑Ͻ1%͒ for SDD up to 300 cm. 73 A similar stud for wedged beams estimated that the change in S c at different SDD is about 2% for wedged beams.74

IV.C. Wedge and compensator scatter
The presence of a wedge or a compensating filter increases the fraction of headscattered photons, and hence the variation in S c with changes in collimation. 8In principle, one should account for the headscatter source from the wedge and the flattening filter separately. 20,75Due to the difference in geometry, one can anticipate different field size dependence of S c between an internal wedge and an external wedge. 75The former is mounted inside the accelerator head and always completely irradiated but not always completely seen through the collimator opening, while the latter is irradiated only by the collimated beam, always completely seen from the point of interest and also closer to the patient compared to the former.
Analytical calculation models based on first scatter integration over the scattering device 20,76 and an "extended phantom concept" using precalculated modulator kernels superimposed over the modulator within the calculation point of view 77 have all shown good agreement.Monte Carlo simulations confirm and bring further details to these results.Schach von Wittenau et al. 78 investigated to which degree Monte Carlo simulations can be approximated without changing the result.

IV.D. Collimator scatter and leakage
Detailed jaw and MLC geometries have been studied for different accelerators using Monte Carlo simulations 79,80,26,81 and analytical models. 82Collimators play an important role in defining scatter contributions from the treatment head through partial obscuring of structures such as target, primary collimator, and flattening filter.The scatter contributions from the movable collimators themselves are less than 1% of the total dose 123 ͑about one-tenth that of the total headscatter͒, but rounded MLC edges might add more scat-ter.The photon leakage through the bulk of the jaws is generally less than 0.5% although the interleaf leakage in between MLC leaves can be 1%-2%. 83van de Walle et al. 84 simulated the 80-leaf Elekta SLiplus MLC.They showed that the interleaf leakage hardens the transmitted radiation by about 0.15 MeV for a 6 MV photon beam and noted significant differences for photon spectra under the leaf body compared to under the leaf gap.Deng et al. 85 studied the MLC tongue-and-groove effect on IMRT dose distributions.Based on the actual leaf sequence and MLC leaf geometry, they derived a fluence map using a ray-tracing approach for an IMRT plan.Their results suggest that the effect of the tongue-and-groove geometry is probably insignificant in IMRT with multiple gantry angles, especially when organ/ patient movement is considered.
For blocks, Thatcher and Bjärngard 86 pointed out that they should in most cases have a negligible effect on S c ͑at most a 1% change for most clinic cases including extreme blocks͒ because the collimator jaws are located closer to the location of the flattening filter than the blocks, thus it is the collimator jaws rather than the blocks that influence the amount of headscatter from the flattening filter.Jursinic, however, noticed a headscatter effect of up to 2% due to photon scattering from the tray and the block. 87van Dam et al. 88 examined the effect of the block on a large number of accelerators and quantified its variation to be Ͻ 1%.Higgins et al. 89 performed an exhaustive study and quantified the effect of the block on S c to be 1%.

IV.E. Monitor backscattering
Photon backscatter from the collimator jaws into the monitor chamber may, for collimators located close to the monitor, have a significant effect on output for some accelerators.As pointed out through Eq. ͑24͒, the total output from a machine may be less than monitored due to a perturbation signal MU b caused by backscattered particles.The monitor backscatter has been studied by a variety of experimental methods.Techniques for measuring b =MU b / MU 0 include activation of metal foils, 60 using a pinhole telescope aimed at the target, [90][91][92][93] comparing output differences with and without an acrylic filter between the chamber and the jaws, 61 counting beam pulses, 10,93,94 measuring beam current, 95 and measuring beam charge. 92Kubo 90 used a telescopic technique to exclude the scattered components from the readout of an external detector and measured the variation in monitor units delivered per unit external signal.For a Clinac 1800, he found small variations ͑1%-2%͒ between small and very large collimator settings.For a Therac 20 machine, however, the backscatter variation was as high as 7.5% ͑cf.Fig. 5͒.Hounsell 96 also used a telescopic technique and found small variations of the order of less than 1% for an Elekta-Philips SL15 with a protection sheet ͑3 mm Al͒ in place between the collimators and the monitor chamber.The variation was considerably higher when the protection sheet was removed, approximately 5% between the 4ϫ4 and 40 ϫ 40 cm 2 field.Several investigators 10,93,97 used the number of linac pulses as an independent measure of the primary fluence and found that the monitor backscatter signal varied from 2% to 5% for the largest to the smallest fields with a kapton window monitor chamber.When a protection sheet of aluminium was set in place to stop low energy charged particles, the variation reduced to 0.5%-1.0%.Yu et al. 93 applied this technique to a Varian Clinac 600C and 2100C and found a variation of approximately 2% for the inner jaws and 1% for the outer jaws at energies above 15 MV, and about half of those values for 6 MV.Lam et al. 92 measured the target charge needed to deliver a given number of monitor units as a function of collimator setting, as it was considered more reliable than the number of linac pulses.On a Varian Clinac 2100C, they found a 2.4% variation for the upper jaws and 1.0% variation for the lower pair of jaws.More recent measurements have shown that the monitor backscatter factors for a flattening filter free accelerator have the same magnitude as that for the same accelerator with the flattening filter. 98In general, all methods to explicitly measure S b are rather cumbersome, and to various degrees invasive to the accelerator structure or controls and cannot be recommended for routine use.
Using Monte Carlo, Verhaegen et al. 99 and Ding 66 modeled the photon beams in a Varian Clinac 2100C linac.By tagging particles and selectively transporting photons and electrons, they found that low energy electrons cause most of the backscatter effect.
An analytical model for the backscatter signal fraction b =MU b / MU 0 has been proposed by Ahnesjö et al. 23 assuming that it can be determined by a proportionality factor k b times a geometry factor for backscatter radiation, where z SMD is the source to monitor distance, z SCD is the distance from the source to the backscattering collimator surface, z MCD is the monitor to backscattering surface distance, A is the angle between the normal of the backscattering element dA ˆand its view vector of the monitor, and A ˆis the irradiated backscattering area.͑In the original paper sourceto-isocenter distance was erroneously used instead of z SMD and the reflected radiation stated to be isotropic rather than diffuse.͒A comparison of data from the work of Lam et al. 92 versus Eq. ͑29͒ yields k b values of the order of 0.3-0.4 for Kapton windowed chambers and approximately zero for chambers with metal sheet windows.
Since b =MU b / MU 0 decreases with increasing field size ͑less backscattering area͒, S b = ͑1+b͑A ref ͒͒ / ͑1+b͑A͒͒ will increase with collimator settings.Hence, the net effect of monitor backscatter is to increase the output per monitor unit with increasing field size, as the scatter fluence from extended sources does.

IV.F. Direct source obscuring effect
For very small collimator settings ͑usually less than 2 ϫ 2 cm 2 ͒, the target, i.e., the effective x-ray source, is partially obscured by the collimator jaws resulting in a substantial reduction in the output. 100Due to the finite source size, S c is expected to reduce to zero when the collimator jaws are completely closed.The source-obscuring effect dominates the output ratio for very small fields at low energies. 101For higher energies, the loss of lateral electron equilibrium becomes more important.For all energies, it is important that during measurement the open part of the beam covers both the detector and the entire build-up phantom.
Not only the size but also the shape of the source, as affected by the beam transport system, are of importance for small fields.Figure 6 shows the measured S c values for several different accelerators. 100The greatest effect is shown for the Clinac-6/100, which has no bending magnet.The next largest effect shown is from the SL75-5 with a 90°permanent bending magnet.The SL25 has a 90°bending magnet as well, but it is preceded by a "slalom" magnet arrangement.The Clinac-1800 with a 270°bending magnet and an electron slit shows the smallest effect and has the smallest x-ray source size among the accelerators examined.Zhu et al. 11 demonstrated that one can reconstruct the shape of the x-ray source with S c , measured for a series of slit collimator settings at different collimator angles.Jaffray et al. 9   detailed measurements of the x-ray source distribution of a linear accelerator.The cumulative source distribution of a linear accelerator was measured in terms of focal and extrafocal components using secondary collimation techniques, as depicted schematically in Fig. 3.
In practice, information about the source size is often inferred from the penumbra width and shape.Studies also correlate the value of S c at small field sizes with the penumbra width produced by an accelerator. 102

V. MEASUREMENT OF IN-AIR OUTPUT RATIO
This section deals with the experimental methods used to measure in-air output ratio and the correction formalism one can use to correct for artifacts caused by miniphantoms made of different materials.

V.A.1. Measurement of the effect of miniphantom on S c
V.A.1.a.Conventional build-up cap measurements.The original in-air measurements to determine S c used build-up caps ͓Fig.7͑a͔͒ to bring the thickness of detector walls to provide equilibrium.While 60 Co gamma rays require build-up caps of approximately 0.5 g cm −2 in mass thickness, when extended to higher energies the diameter of the cap may became impractically large.While full build-up thick-ness is commonly interpreted to equate with d max for the photon component of the beam, the thickness required to eliminate electron contamination is often larger than d max . 104hus, the use of build-up caps with a thickness just equal to d max may allow charged particle contamination radiation to reach the detection volume, erroneously increasing the reading particularly for the larger field sizes.Frye et al. 104 and Venselarr et al. 105 showed that the field size dependence of S c is affected by electron contamination if the cap thickness is not sufficient.
For the measurement signal to scale with the kerma of incident radiation, lateral electron equilibrium conditions must be established, and the full cap must be exposed to the radiation beam, limiting the minimum beam size to the cap diameter plus a margin to account for penumbra.To enable the use for smaller fields, higher Z materials have been used, such as lead. 100However, it has been argued that the high-Z materials may alter beam spectra and thus introduce errors. 12,106Several investigators studied the influence of build-up cap material on the measurement of S c . 104,107,108rye et al. 104 reported significant differences ͑up to 4.8% for a 24 MV beam͒ between the measurements with conventional build-up caps made of Solid Water and those with graphite.Using a magnetic field to sweep the contaminant electrons in the 24 MV beam, they concluded that a significant portion of the difference was indeed from the charged particle contamination.With build-up caps made of low-and high-Z materials, Jursinic and Thomadsen 107 found large difference ͑up to 4%͒ for an 18 MV beam, especially for large field sizes.These increased differences are most likely due to the contributions from contaminating electrons, as the longitudinal thicknesses of their caps were no more than the maximum dose build-up depths.Thomadsen et al. 103 reported that electron contamination penetrates considerably farther than the depth of maximum dose, and for the 24 MV beam, some contamination reaches as much as 10 cm depth.This report does not provide a solution for situation when the historically used "collimator-scatter factor" measured at d max is used for TMR-based MU calculation algorithm.In this case, we recommend using S c ͑in air output ratio͒ defined at 10 cm ͑see below for van Gasteren miniphantom͒ so long as S p = S cp / S c is determined using S cp measured at d max .A brief description of the rationale why this approach will improve MU calculation accuracy, which is an expansion of the argument made by Ten Haken, 109 is included as follows: We will consider the common situation where the dose to be determined is for a point at the isocenter at a depth d ͑d is much deeper than the range of contamination electrons͒ with field size s and collimator setting c.The collimator setting c is, in general, greater than or equal to the field size s.If we reduce the collimator setting for the moment to a new value cЈ such that cЈ = s, then the dose can be determined by multiplying the dose at the reference configuration by S cp for the change in the field size and then multiplying by TMR for the change in depth.When cЈ = s, S cp and TMR are measured under the same conditions ͑d max ͒ as that of the calculation so that the calculation is as accurate as the measured data.When the collimator setting is increased back to c from cЈ, the increase in dose is represented by a factor S c ͑c͒ / S c ͑cЈ͒.Since the calculation point is at the depth d without contaminating electrons, the S c measured with miniphantom should be used for this factor instead of the S c measured at d max .Thus, as long as the depth of calculation is beyond the range of contaminating electrons, the S c measured with the miniphantom should be used whether one uses TMR or TPR.When the depth of calculation is shallow, the contribution from electron contamination is included in S p ͑s͒ and S c ͑c͒ for the TMR-based formalism, depending on whether S c is measured at depth beyond electron contamination or d max .The equivalent square dependence for photon phantom scatter, s, and that for the headscatter, c, do not strictly apply in either cases for S p ͑s͒ and S c ͑c͒ due to the additional field size dependence caused by electron contamination.In this case, neither method provides a satisfactory solution when c and s is very different.

V.A.1.b. van Gasteren miniphantom measurements.
It can be concluded, based on the studies above, that one of the most important factors in the measurement of S c is to ensure that the cap's longitudinal dimension is sufficient to prevent contaminating electrons from reaching the detector.van Gasteren et al. 12 showed that once the water-equivalent cap, or "miniphantom," is thick enough, S c can be measured reliably.They proposed the use of a columnar, cylindrical miniphantom, 20 cm longϫ 4 -5 g cm −2 in diameter, oriented coaxially with the chamber and beam ͓see Fig. 7͑b͔͒. 12The minimum lateral dimension ͑or diameter͒ must exceed 4 g cm −2 ͑for up to 24 MV photons͒ to reach lateral electron equilibrium. 110The radiation field edges must exceed the miniphantom lateral dimension to maintain the cap in the uniform part of the radiation field ͑keeping the penumbra from impinging on the miniphantom͒.This requirement ensures that the phantom-scatter contribution generated by the miniphantom for the actual and the reference collimator settings would mutually cancel ͑see Sec.II B͒.We endorse this cylindrical columnar miniphantom for the range of fields it can accommodate; however, for output ratio measurements for small fields common in IMRT treatment, we instead recommend using higher mass density material with medium Z ͑see Figs. 9 and 10͒.10.Schematics of a brass miniphantom recommended for measurements of S c for square fields larger than 1.5ϫ 1.5 cm 2 and photon energy less than 25 MV.The longitudinal thickness ͑h l ͒ of the miniphantom facing the radiation should equal to or be larger than 1.2 cm ͑or 10 g / cm 2 , = 8.4-8.7 g / cm 3 ͒.The inner diameter of the miniphantom, 1 equals to the outer diameter of the detector, e.g., 0.6 cm.The height, h, should be sufficient long to cover the detector sensitive volume, e.g., 2 cm.The outer diameter of the miniphantom, 2 , can be such that the wall is thinner ͓but minimum 1.2 mm brass for up to 18 MV ͑Refs.107 and 115͔͒ than the thickness required for CPE given that the total lateral dimension above the chamber well ensures lateral CPE for the photon energy, and the effect on S c measurement falls within required accuracy demands.
Choices of phantom materials affect the results with the van Gasteren-style miniphantoms.Miniphantoms made of low-Z materials are generally recommended.To extend the range of S c to smaller field sizes, one approach has been to use higher density, higher atomic number miniphantoms.Li et al. 110 compared the measurements using cylindrical miniphantoms made of polystyrene and brass.Their data show that as long as the longitudinal dimension of miniphantom is sufficient to prevent contaminating electrons from reaching the detector, the measurements with polystyrene and brass miniphantoms agree within 0.5% for both 6 and 18 MV beams.However, even if the thicknesses of a miniphantom is sufficient to stop contaminating electrons, the use of a lead phantom may result in errors in the values of S c of up to Ϯ1%.By comparing measurements with build-up caps made of low-and high-Z materials ͑carbon for low Z, brass and lead for high Z͒, Weber et al. 108 observed deviations of up to Ϯ1% in the S c values for high-energy beams ͑see Fig. 8͒.They reported that the thicknesses of their build-up caps were sufficient to stop contaminating electrons.The magnitude of errors caused by high-Z material increases with collimator setting, being small for collimator settings less than 6 ϫ 6 cm 2 , but rising to the 1% level for a 40ϫ 40 cm 2 field for lead.For lead and acrylic miniphantoms, no differences were found for small collimator settings. 100When using miniphantoms of a high-Z material, the methodology in Sec.V C of this report is recommended.

V.A.2. Monte Carlo simulation of the effect of miniphantom on S c
At the time of this report, the task group is not aware of any literature that addresses the Monte Carlo simulation of miniphantom for investigation of S c .Johnsson and Ceberg performed a Monte Carlo study on the effect of waterequivalent miniphantom's longitudinal thickness on the accuracy of transmission measurement. 111They defined a measurable quantity as the "collision kerma in-water" at a point in free space, similar to the definition of the in-air output function, O air .When the ionization ratio measured in a miniphantom equals the collision water kerma ratio in the free space, the condition is called in-air equivalent. 111They reported a range of miniphantom depths for specific photon energy in order to obtain accurate measurement of transmission to within 1% ͑or in-air equivalent͒ in a water-equivalent miniphantom.However, the limit of phantom thickness on S c is likely to be much relaxed because the photon energy spectra do not change as much as that for the transmission measurements.Experimental studies have shown no effect of phantom's longitudinal thickness on S c as long as the thickness is sufficient for CPE. 12 Tonkopi et al. 112 performed MC simulation for OAR measurement and showed that using a plastic miniphantom gives more accurate air-kerma profile measurement than using high-Z material build-up caps.

V.A.3. Influence of detectors on measurement of S c
Various detectors ͑e.g., ionization chamber and diode͒ have been used to measure S c .Values of S c measured with diode detectors, shielded or unshielded, are identical to those from ionization chamber measurements. 113It is also reported that the ionization chamber orientation ͑whether its axis is perpendicular or parallel to incident radiation͒ does not affect the measured results. 70,107However, for very small field size, the detector sensitive volume will have a drastic effect on measured value of S c . 114Thus it is important to choose detectors with small sensitive volume for collimator setting less than 1 ϫ 1 cm 2 .

V.B. Development of correction factors for high accuracy applications
An important aspect of the unambiguous formal definition of S c given by Eq. ͑3͒ is that build-up cap and detector combinations of practical interest can be Monte Carlo simulated or modeled by means of cavity theory to fully quantify correction factors for high accuracy applications. 14,115The ratio of readings for an S c measurement can, by assuming equilibrium conditions and a detector fulfilling the Bragg-Gray cavity criteria, be expressed with a more general formulation than used in Eq. ͑6͒ to yield where S c is defined in Eq. ͑3͒, ⌿ is the energy fluence free in air, ͑ ¯en / ͒ is the mean ͑energy fluence weighted͒ mass energy transfer coefficient for the miniphantom material, SF K = K / K p is the total-to-primary kerma ratio ͑or kerma scatter factor͒ that accounts for miniphantom scatter, S det,med S-A is the mean ͑secondary electron fluence weighted͒ Spencer-Attix stopping power ratio of electrons between the detector and the miniphantom medium for the detectors sensitive volume, 116 d is the effective depth of the detector, ¯is the mean attenuation coefficient ͑energy fluence weighted͒, ␤ is the dose-to-collision kerma ratio, ͑ ¯en / ͒ wat med is the mass energy transfer coefficient ratio for the miniphantom material and water, and the variables with a subscript "ref" denotes the corresponding variables for the reference geometry.Correction factors can be used to mitigate eventual spectral/ material induced shifts caused by measurement technique as to convert the reading from the measurement geometry to the "water kerma in free-space" conditions of definition for S c .For example, from Eq. ͑30͒ we can derive where CF en = ͑ ¯en / ͒ wat,ref med / ͑ ¯en / ͒ wat med corrects for energy transfer shifts, CF SF =SF K,ref / SF K corrects for miniphantom scatter factor differences, CF S = ͓S det,med S-A ͔ ref / S det,med S-A corrects for stopping power differences, 117 CF ␤ = ␤ ref / ␤ corrects for electron equilibrium, and CF att =e ͑ ¯− ¯ref ͒d is to cancel out attenuation differences.All these correction factors can be a function of collimator setting, energy, and miniphantom geometry and material.For miniphantoms made with sufficient thickness, CF ␤ = 1.The shift of stopping power ratio at different depth d and collimator setting c is usually negligible for an open beam: CF S =1. 117The values of various correction factors for S c determination have been evaluated in several recent publications. 14,115For example, for a waterequivalent miniphantom the total correction factor remains indistinguishable from unity, while for a miniphantom made of lead, the total correction factor with thickness of 21.6 g cm −2 is up to Ϯ1%. 14,115

V.C. Recommendation of miniphantom dimension for S c
For most field sizes, S c measurements should be made with the detector in a miniphantom, as shown in Fig. 9.The miniphantom should be made from water-equivalent materials, such as solid water, acrylic ͑PMMA͒, or graphite, with 4 g/ cm 2 diameter and with the detector at 10 g / cm 2 depth, as described by van Gasteren et al. 12 and the ESTRO protocol. 1For small collimator settings ͑c Ͻ 5 cm͒, a miniphantom made of high-Z material ͑e.g., brass or lead͒ must be used to ensure CPE and contaminant electron filtering, and the procedure for their use is given below.Measurement at extended SSD for small fields may result in different S c because of the different projections of the x-ray source from the detector point of view.Such measurements should be avoided as discussed in the next section.The lateral dimension ͑diameter͒ of the miniphantom should be sufficiently large to maintain lateral CPE. 110Thinner lateral wall thickness 107 may be used if experimental verification show that the effect on S c measurement falls within the user's desired accuracy.The height above the detector should be sufficient ͑10 g / cm 2 ͒ to not only maintain longitudinal CPE but also to eliminate contaminant electrons.The detector and miniphantom should be supported on a low density stand ͑e.g., Styrofoam͒ to minimize additional scatter into the detector volume.
To provide lateral CPE for the small segment fields that are common in IMRT, a high-density miniphantom shall be used to enable full beam coverage of a phantom providing enough filtering and buildup.Jursinic et al. 107,115 showed that a water-equivalent wall thickness of 1 g cm −2 ͑about half of MC predicted lateral CPE range͒ is sufficient to measure changes in S c data to within an uncertainty of 0.3% for open beams.Brass ͑approximately 63% Cu, 37% Zn͒ is an acceptable alloy compromising high density ͑8.4 g cm −3 ͒ with moderate atomic numbers ͑29 and 30͒, good machinability and well known dosimetric properties. 108,110,118Figure 10 shows the schematics of a brass miniphantom suitable for measurement of small field sizes.However, the introduction of high-Z material changes the response and the use of correction factors calculated by Eqs.͑30͒ and ͑31͒ is preferred, when available.
A recommended method to determine S c is as follows: For field sizes larger than 5 ϫ 5 cm 2 , use a water-equivalent miniphantom; for field sizes below 5 ϫ 5 cm 2 , use a highdensity ͑and thus high-Z͒ miniphantom, allowing extension to field sizes for which the diameter of the high-density miniphantom is completely within the field, including the penumbral margins.The ratio obtained with the high-density miniphantom does not give the correct values for S c but normalizing the results obtained with the high-density miniphantom to a 5 ϫ 5 cm 2 field and multiplying the resultant values by the S c measured for a 5 ϫ 5 cm 2 field with a waterequivalent miniphantom gives values with very little error.

V.D. Measurement of S c for small field sizes
For IMRT and stereotactic radiotherapy, it is often desirable to measure S c for small field sizes ͑c less than 3 ϫ 3 cm 2 ͒.For these field sizes, the primary cause of variations in S c is the direct source-obscuring effect, as discussed in Sec.IV F. We recommend measuring S c at the distance of interest, usually at the isocenter plane ͑SAD ϭ 100 cm͒ following the procedure in Sec.V C. To ensure that the miniphantom is completely covered within the small field, a high-Z material miniphantom such as the one described in Fig. 10 can be used.This one is suitable for measurement of field sizes down to 1.2 cm.Several studies has found that there is no Z dependence of phantom materials for small field sizes. 14,100,119A recent study suggested one can obtain reliable data using a miniphantom of zero side wall thickness for photon energy up to 6 MV. 114However, for source size less than 1 cm diameter ͑e.g., 0.5 cm stereotactic cone͒, the averaging effect of the active volume of the detector becomes more important than the miniphantom lateral dimension. 114hus it is recommended that measurement for field size less than 1 ϫ 1 cm 2 be avoided unless cares are taken to account for the detector convolution effect. 114easurement at large extended SSD ͑e.g., SSD ϳ400 cm͒ is not recommended for use at the isocenter because of the different projections of the x-ray source from the detector point of view.Further studies are necessary to convert the S c measured at different SSDs for small field sizes.Several groups have made measurements of S c at extended SSD to study the x-ray source size distribution because the radiation beam becomes almost parallel. 11,64,100

VI.A. Empirical modeling of multiple photon sources and monitor backscattering
The collimator exchange effect described the fact that the in-air output ratio differs for a rectangular radiation field depending on which side of the rectangle delineates the inner and outer collimator jaws ͑i.e., c x ϫ c y or c y ϫ c x ͒. 120 It can be explained by the varying view of the flattening filter at the point of detector ͑Fig.3͒.An equivalent square formula can be used to characterize this effect, 121

͑32͒
Here c x and c y denote the settings of the outer and inner collimators, respectively, and k ͑Ͼ1͒ is the collimator exchange coefficient.If only the headscattered photons are considered, then k can be determined from the head geometry as. 122 where z x and z y are the source-to-collimator distances for outer and inner collimators and SDD is the source-todetector distance ͑see Fig. 1͒.The value of k has been determined experimentally for the Elekta 121 and Varian 122 accelerators ͑k = 1.8͒.However, k for a particular make/model of accelerator may be different from this value and varies between 1.2 and 1.8 for the major accelerator types. 123Table V in Appendix A gives examples of S c for rectangular fields to illustrate the collimator exchange effect.Other formalisms ͑k = z x / z y ͒ have also been proposed to calculate S c for rectangular fields. 124The source-obscuration effect is only relevant for very small collimator settings ͑usually less than 2 ϫ 2 cm 2 ͒, then it becomes the dominating effect and reduces the in-air output ratio to zero when the collimators are closed.It has been described by Zhu et al. 100,102 The monitor-backscatter effect differs for different accelerator models and can be measured by operating the accelerator without the dose-rate servo control, 94 by using a "telescope" method, 91,93,90 by target-current pulse counting, 93 by using the target charge method, 93 or by photoactivation of copper placed above the flattening filter. 60The first two methods do not require opening up the accelerator head or special electronic instruments and can achieve a reproducibility of 0.3%, but are still very time consuming.For some Varian accelerators, the maximum contribution from the monitor backscatter can be large ͑3%-5%͒. 91In principle, the monitor backscatter factor could be defined as

͑34͒
where we have neglected the cosine factor in the integrand of Eq. ͑29͒ and have made further assumption that the maximum irradiated area is 40ϫ 40 cm 2 , projected at the isocenter.The distances ͑z x , z y , and z SMD ͒ are shown in Fig. 1,  and c x = c x1 + c x2 and c y = c y1 + c y2 are the collimator settings of the independent jaws.͑Y jaws are always defined as the inner collimator jaws and X jaws are always the outer collimator jaws.͒Clearly, the monitor backscatter factor increases with increasing collimator settings and Y-jaw setting is dominant since z y Ͻ z x .The backscatter can also be characterized by separating the in-air output ratio S c into a multiplication of S b and S h ͓see Eq. ͑27͔͒, where

͑35͒
We have used expression Eq. ͑34͒ for b and assume that b Ӷ 1. Several headscatter models have been successfully used to predict S c on the central axis.These models use a set of measurements from square collimator settings to extract the necessary parameter.One example of such model uses three parameters ͑a 1 , a 2 , and ͒ to calculate S c . a 1 is the monitorbackscatter coefficient, a 2 is the maximum scatter-to-primary ratio, i.e., if a 2 = 0.10, 10% of the incident fluence is indirect radiation, and is the width of the indirect radiation distribution at the isocenter plane.The in-air output ratio on the central axis is 123 where H 0 is a normalization constant that sets S c = 1 at the collimator setting 10ϫ 10 cm 2 and SPR air ͑c͒ = a 2 erf͑c / ͒ 2 is the scatter-to-primary ratio for the headscatter component compared to the primary component, and erf͑x͒ = ͐ 0 x e −t 2 dt is the error function.c is the equivalent square calculated from the collimator jaws using Eq.͑32͒ for rectangular fields.The incident kerma measured in the miniphantom is separated into the direct K d and the indirect ͑or headscatter͒ K h components such that K air = K d + K h = K d • ͑1 + SPR air ͒.Details of the derivation can be found elsewhere. 123Typical parameters for a range of linear accelerators can be found in Table II.
Equation ͑36͒ can also be used to model S c,w for a wedged beam. 123͑Some representative data are shown in Table IV.͒However, it is better to separate the headscatter components from the wedge and the flattening filter.Zhu et al. 75 provided some empirical expressions to model the headscatter from internal and external wedges appropriately ͑see Fig. 11͒.SPR air,w is the ratio of headscatter-to-direct radiation for the wedge, SPR air,w ͑c͒ = ͭ ␥ w erf͑c/ w ͒ 2 ͑internal wedge͒ ␣ w • ͑c/40͒ 2 ͑external wedge͒, ͮ ͑37͒ where ␥ w , ␣ w , and w are constant parameters.The parameter ␥ w ͑or ␣ w ͒ determines the maximum SPR for the largest field ͑40ϫ 40 cm 2 ͒ and can be obtained by least squares fitting to the square field S c data for wedged beams. 75

VI.B. S c for MLC shaped fields
The use of an MLC for field shaping does not change the way the phantom scatter is computed.The in-phantom scatter depends on the final field size projected on the patient and the methods for calculating scatter dose in the patient are well established.However, the in-air output ratio for MLC shaped fields is dependent on the design and the geometry of the MLC system.The amount of scatter radiation reaching a point downstream from a MLC system depends on the area of the extrafocal radiation source as seen by the point through different levels of collimators.If the MLC is located at the position of the inner jaws in the secondary collimator, as in the Elekta MLC design, the irregular field shape determines both the headscatter and the phantom scatter.In the Elekta design, there is a pair of backup jaws situated under the MLC leaves and motorized to travel in the same direction as the leaves.These backup jaws serve to minimize the interleaf transmission outside the radiation field.These jaws are normally set at the same position as the outermost leaves and make only a small contribution to the headscatter.Palta et al. 125 showed that the in-air output ratio for shaped fields with Elekta MLC can be accurately calculated using an equivalent square 126 of the MLC shaped field.The equivalent square for the MLC shaped field can be readily calculated using Clarkson sector integration method 127 if it is assumed that the source of extrafocal radiation is radially symmetric.It is important to note that the integration method is valid only when the field dimensions in both the measurements and the calculations are projected from the calculation point back through the collimation system to the effective source plane of extrafocal radiation. 129If the MLC replaces the outer jaws in the secondary collimator, as in the MLC design of Siemens, both the MLC leaf positions and the upper jaw positions determine the in-air output ratio.Since the jaws are closer to the effective collimator-scatter source, they define the field aperture in the dimension perpendicular to the direction of leaf travel in both the BEV and in the projection of the calculation points.When the MLC is used as a tertiary collimator along with the inner and the outer collimator, as in the design of Varian, the field shape defined by the MLC is closer to the plane of any given calculation point than the inner or outer jaws.Unless the MLC shaped field is substantially smaller than the rectangular field formed by the inner and outer collimator jaws, the tertiary blocking boundary will not affect the projection of the field size from the calculation point back to the effective source of extrafocal radiation.In this case, the jaw openings determine the in-air output ratio. 128However, Kim et al. 4 showed that the scatter radiation contribution from the tertiary MLC to the in-air output ratio for small MLC shaped fields may not be negligible.This is often the case in small beam apertures used for intensity modulation.
Zhu et al. developed an algorithm to calculate S c based on an empirical model 123 by projecting each leaf position to the isocenter plane, 68

͑38͒
where / 2 is the effective radius of the extended source of photons scattered from the flattening filter projected on the isocenter plane and H 0 is an normalization factor to make S c =1 for a 10ϫ 10 cm 2 field.The integral extend to infinite on the isocenter plane.This formula does not require the exact knowledge of the head geometry., a 1 , and a 2 can be determined from least squares fitting the measured S c to Eq. ͑36͒ for square field sizes on the central axis.The integral can be calculated analytically for a known MLC leaf pattern.
The calculation agrees with measurement to within 1.2% for points both on and off the central axis and is better than the equivalent square method.The fitting parameters used in the algorithm are derived from measurements for square field sizes on the central axis.Zhu et al. 68 compared the results for the three types of MLC mentioned above and found that for the same MLC shaped irregular field, the value of S c increases from the Elekta, to the Siemens, to the Varian accelerators, with differences up to 4%.When the MLC leaf positions are substantially different from the secondary collimators ͑or the rectangular field encompassing the irregular field͒, one observes differences up to 5% in the value of headscatter correction factor ͑HCF͒ defined as the ratio of in air output ratio between the MLC shaped irregular field and that of the rectangular field encompassing the irregular field.

VI.C.1. Dynamic wedge
The dynamic wedge ͑DW͒ makes use of movement of one pair of independent linac collimators closing ͑or open-ing͒ during the treatment delivery to produce a wedgeshaped profile.This offers flexibility in creating wedgeshaped dose distributions.As an example, the Varian DW is implemented using so-called "segmented treatment tables" ͑STTs͒ that control the dose rate and collimator movement for producing the dynamic wedges.Each STT contains information on the moving collimator position versus cumulative weighting of the monitor units.There are a total of 132 STT for four wedge angles ͑15°, 30°, 45°, and 60°͒.
The second generation of dynamic wedge, called the enhanced dynamic wedge ͑EDW͒, became available later on Varian linacs.EDW uses a single STT to generate all the other STTs for all field sizes and wedge angles.
It has been reported that the S c,w values for the dynamic wedge are significantly different from that for the open 129,130 or physically wedged 58 field.This difference is primarily because of the change in scattering conditions as the dynamic collimator jaw moves.In order to characterize this difference, Liu et al. 129,130 proposed that the S c for dynamic wedge may be expressed as: S c,w = S c,n • N͑c y ͒, where N͑c y ͒ is the ratio of the STT weights on the central axis between the field of interest ͑c y ͒ and the reference field ͑c y =10 cm͒, Here, c y is the field width in the wedge direction and y i is the distance between the central axis and the moving jaw edge, so y i = 0 represents the position of the moving jaw at the collimator axis.The S c,n values were found to be approximately the same as the S c values for the open fields. 129,130he introduction of S c,n and N͑c y ͒ simplifies the determination of S c for dynamic wedge.The quantity N͑c y ͒ characterizes the impact of dynamic wedge on S c and varies between 0.4 and 1 for c y varying between 10 and Ϫ10 cm.As noted previously, S c,w for wedged beam is often not used in conventional MU calculation algorithms, where S c for open beam alone is used, and the headscatters from wedge fields are lumped into the field size dependent wedge factors.Users are cautioned to avoid double counting the in-air output ratio if a field size dependent wedge factor is used.

VI.C.2. IMRT
There is, in principle, no difference between calculation of S c for an IMRT field and calculation of S c for an open field since the former is simply an MU-weighted summation of the latter, particularly, a summation of a series of MLC shaped fields.However, it is more demanding in terms of the accuracy required to determine S c for each segment of an IMRT field.One has to determine S c for points not only inside of the beam collimation but also outside the beam collimation ͑under the blocks͒.2][133][134] Hounsell and Wilkinson 135 proposed a simple method, a first-order Compton scatter approximation from the flattening filter, which only considers scatter from the flattening filter.The calculation of S c using this method was found to agree with the measurements only at small field sizes ͑between 2 ϫ 2 and 10ϫ 10 cm 2 ͒. 135 Naqvi et al. 134 used a two-source model combined with raytracing algorithm to calculate the headscatters for IMRT fields.Their data indicated that the potential accumulative errors in S c on the order of a few percent could be avoided with the use of this model.Yang et al. 133 proposed a three-source model to calculate the headscatter distribution for irregular segments shaped by MLC.In this model, the values of S c for each beamet in a segment at the point of calculation are considered to be contributed from three sources: Primary photons and scattered photons from primary collimators or flattening filter.S c predicted by this model agreed with the measurement within Ϯ3% at an any calculation point. 133Recently, Zhu et al. 68 calculated S c for an MLC field using an empirical algorithm that projects each leaf position to the isocenter plane.Their calculation showed that S c for an irregular MLC field can be different by as much as 5% from the S c for the rectangular field encompassing the irregular field.

VII. QUALITY ASSURANCE
As outlined in AAPM Task Group Report 40, 136 QA, in general, has a critical role in all aspects of radiation oncology.The quality of S c data is important for accuracy of dose calculations in both treatment planning systems and MU calculations.QA of S c is needed ͑i͒ at the time of beam commissioning, ͑ii͒ for periodic ͑yearly͒ checks, ͑iii͒ after any major repair of the linac, and ͑iv͒ at the time of upgrade of treatment planning software.This section will discuss various QA methods existing in literature for S c data.That includes, primarily four categories of methods: ͑a͒ Use of linac specific published data, ͑b͒ use of published parameterized values, ͑c͒ use of the in-water output ratios divided by published phantom scatter factors, and ͑d͒ remeasurement.
A database of measured values, for open and wedged fields of major linac models and cobalt units, exists in literature. 123Tables III and IV provide open and wedgedfield data measured by some of the authors of this report on select linacs.To emphasize the impact of linac head design, the data include linacs from three major vendors: Varian, Siemens, and Eleckta.For convenience, the tabulated data are also presented in a graphical form ͑Fig. 12͒.The shaded region simply emphasizes the behavior with field size.Interestingly, the limited data, irrespective of the beam energy and the linac model, show remarkable agreement ͑maximum-to-minimum spread of ϳ2%͒.However, for field sizes smaller than 2 ϫ 2 cm 2 , the differences in S c with respect to the model of the linac become significant ͑see Fig. 6͒.The dashed curve represents the RPC average of user submitted data, without any QA of the measured data.Strikingly, at photon energies exceeding 15 MV, the dashed curve exhibits a significant departure from the plotted data points.Most build-up caps in current use are near depth of d max instead of 10 cm.Therefore, it is important that electron contamination be avoided by use of build-up cap of adequate dimensions and proper material.͑Note that this difference does not necessarily reflect an error in dose calculation provided that the beam data are normalized at the same depth.Since the electron contamination can be strongly depth dependent for depths less than the range of highest electron energies, these data show potential large errors for photon energies larger than 15 MV if the depth of normalization is not chosen to be beyond the range of electron contamination.͒One may fit the measured values to a model such as shown by Eq. ͑36͒ by determining the three parameters ͑a 1 , a 2 , and ͒.Table II provides a cross-check of the published parameters for known linear accelerators.
It has been proposed that one can measure the in-water phantom scatter factor ͑S cp ͒ to determine S c using a known phantom scatter factor ͑S p ͒ and the relationship S c = S cp / S p . 137The phantom scatter factor S p at 10 cm has been shown to be a function of quality index and field size and is not sensitive to the make/model of the linear accelerators. 12,138Using these published data, the user can even determine S c for square fields directly.However, this method is dependent on the correct value of S p and thus needs to be further refined to determine S c at off-axis locations.
The importance of the materials and dimensions of the miniphantom used should not be underestimated.This implies acquiring proper miniphantoms for both large ͑ജ4 cm͒ and small ͑Ͻ 4 cm͒ fields is important.The RPC's analysis of S c data from ϳ90 institutions ͑Fig.12͒ shows that even for the same linac make/model, the data have a large spread of up to 4% ͑max/min͒.
As recommended in TG40, 136 the periodic ͑yearly͒ spot checks of open square field S c values should be performed.One should be able to reproduce the values within 1%.Spot checks of the physical or dynamic wedged fields may not be necessary if open-field checks show an acceptable agreement.Spot checks of the MLC rectangular-field data are recommended for field sizes of 3 ϫ 40 and 40ϫ 3 cm 2 .

VIII. SUMMARY
͑1͒ In-air output ratio, S c , is defined as the ratio of collision kerma to water per monitor unit at a point in free space for an arbitrary collimator setting to that for a reference collimator setting.This definition ensures that S c describes the photon transport only.S c is caused by three physical effects: Source obscuring, headscattering, and monitor backscattering.Interested readers can refer to Sec.IV for details.͑2͒ The in-air output ratio should be measured at the point of interest using a miniphantom with sufficient longitudinal and lateral thicknesses to eliminate electron contamination.The cross section of the miniphantom should be completely covered by the collimator setting of the field.Figure 9 provides recommended geometries for the miniphantoms for normal collimator settings.For small collimator settings, a brass miniphantom ͑Fig.10͒ can be used for collimator setting as small as 1.5ϫ 1.5 cm 2 .Section V C gives procedures for use of the high atomic number miniphantoms.For smaller field sizes, detailed recommendations of the miniphantom and detector combinations are included in Sec.V D. ͑3͒ A correction-factor based formalism ͓Eq.͑31͔͒ is introduced to determine in-air output ratio measured using any geometries of miniphantom ͑or cap͒ composed of any material.This correction should be applied under conditions when a miniphantom of high-Z material with smaller longitudinal and/or lateral dimensions has to be used, e.g., for SRS fields and/or IMRT.Correction factors for common collimator settings can be found in literature.

FIG. 3 .x
FIG.3.Flattening filter scatter profiles ͑normalized to the isocenter primary energy fluence ⌿ 0 ͒ at the isocenter plane for two 15ϫ 40 cm 2 fields defined by the inner ͑IC͒ and outer ͑OC͒ collimators.The profiles are along the 15 cm axis; the machine geometry is shown to the right.The calculation's point eye view of the filter at various positions is shown on top of the chart.Three different distributions of scatter release from the filter are compared; a triangular, a Gaussian and a flat ͑constant͒ distribution, all normalized to yield 8% scatter at isocenter when the entire filter is viewed ͓from Ahnesjö ͑Ref.19͔͒.
FIG. 5. Results of monitor backscattering obtained by a telescopic method with an 18 MV x-ray from a Therac-20 accelerator.Different symbols represent different collimator settings: b-square fields; ϫ-fixed inner jaws; ᭺-fixed outer jaws.͓Adapted from Kubo ͑Ref.90͔͒.

FIG. 7 .
FIG.7.͑a͒ An example of an old style S c measurement using a peak thickness build-up cap.Such measurments allowed charged particle contamination to affect the readings inappropriately.͑b͒ Miniphantom as described by van Gasteren.

FIG. 8 .
FIG. 8. Deviation in the result of S c measurement caused by using high-Z material, relative to that using water-equivalent miniphantom.͓Taken from Weber et al. ͑Ref.108͔͒. h

FIG. 11 .
FIG. 11.The field size dependence of the ratio of headscatter-to-direct radiations on the central axis for ͑a͒ the internal wedge of SL75-5 and ͑b͒ the external wedge of a Varian 2100C.Taken from Zhu et al. ͑Ref.75͒.

FIG. 12 .
FIG.12.Measured S c for various accelerators for ͑a͒ 6 MV, ͑b͒ 15 MV, and ͑c͒ 18-25 MV.The symbols are measurement taken using the waterequivalent miniphantom described in this report.The dashed line is average data submitted by users to RPC.The shaded area represents the variation among various accelerators.The cause of large discrepancy between the curve and the shaded area is most likely electron contamination due to in appropriate build-up cap, especially at energies Ͼ15 MV.

TABLE I .
Summary of terminology used to describe the output radiation.The first column shows the terms used for the sum of the components on respective row, while the bottom row shows the terms used to represent the sum of the components in the column above.Definition of general terms used in the task group report.

MEASURED DATA FOR IN AIR OUTPUT RATIO FOR TYPICAL LINEAR ACCELERATORS Measured
14 ͑4͒ Theoretical analysis is provided to determine the values of S c and its components ͑headscatter, monitor back-scattering͒ in clinical conditions different from that for rectangular fields ͓e.g., irregular ͑MLC͒ fields, wedge fields, and IMRT fields͔.Headscatter at off-axis points are discussed.In addition, the concept of equivalent square for headscatter is introduced to determine S c while accounting for the collimator exchange effect for various field shaping mechanisms ͑MLC replacing jaws, MLC as attachment, and/or blocks͒.Interested readers can refer to Sec.VI for details.͑5͒ A database of S c for rectangular fields is provided for quality assurance of measured S c ."QA" does not imply extensive repeated measurements of S c but is a step ͑not necessarily measurement͒ to verify the measured values of S c .Details are included in Sec.VII.͑6͒ S c defined in this report can be used in meterset and dose calculation as described in Sec.III.It is suitable for TPR-based MU calculation algorithm where the reference depth is typically 10 cm or beyond electron contamination.However, this report does not provide a solution for situations when the historically used "collimator-scatter factor" measured at d max is used for TMR-based MU calculation algorithm.In this case, TG74 recommend using S c ͑in-air output ratio͒ as defined in this report so long as S p = S cp / S c is determined using S cp measured at d max . in air output ratio are included for square open fields ͑Table III͒, square wedged fields ͑Table IV͒, and rectangular open fields ͑Table V͒.

TABLE III .
Measured in-air output ratio versus square collimator settings for open fields.Data are compiled for comparison or quality assurance purpose only and are not to be used for clinical application.Measurement uncertainty is 0.5%.

TABLE IV .
Measured in-air output ratio, S c,w , versus square collimator settings for 60°wedged fields.Data are compiled for comparison or quality assurance purpose only and are not to be used for clinical use.Measurement uncertainty is 0.5%.͑Note: S c,w should not be used simultaneously with field size dependent WF in MU calculation formalism.͒

TABLE V .
Measured in-air output ratio versus rectangular collimator settings for open fields of three major accelerator manufacturers ͑Elekta, Siemens, and Varian͒ for ͑a͒ 6 MV and ͑b͒ 15 ͑or 25͒ MV.Y is always upper collimator and X is always lower collimator.Measurement uncertainty is 0.5%.For the open beam, this alternative formulation for the dose at an arbitrary point can be derived as D͑c,s;x,y,z;d͒ = MU D ref MU ͑s;x,y,z;d ¯͒K inc ͑c;x,y,z͒SF͑s;x,y,z;d ¯͒T͑x,y;d͒ K inc ͑c ref ;x ref ,y ref ,z ref ͒SF͑s ref ;x ref ,y ref ,z ref ;d ref ͒T͑x ref ,y ref ;d ref ͒ = MU D ref MU ϫ K inc ͑c;x ref ,y ref ,z ref ͒ K inc ͑c ref ;x ref ,y ref ,z ref ͒ K inc ͑c;x,y,z ref ͒T͑x,y;d͒ K inc ͑c;x ref ,y ref ,z ref ͒T͑x ref ,y ref ;d ¯͒ K inc ͑c;x,y,z͒ K inc ͑c;x,y,z ref ͒ ϫ ͑s;x,y,z;d ¯͒SF͑s;x,y,z;d ¯͒T͑x ref ,y ref ;d ¯͒ SF͑s ref ;x ref ,y ref ,z ref ;d ref ͒T͑x ref ,y ref ;d ref ͒ SF͑s ref ;x ref ,y ref ,z ref ;d ref ͒T͑x ref ,y ref ;d ref ͒ = MU D ref MU S c ͑c͒ • OAR air ͑c;x,y;d͒ • DIST͑c;x,y,z͒ ͑sЈ;x ref ,y ref ,z ref ;d ¯͒SF͑sЈ;x ref ,y ref ,z ref ;d ¯͒T͑x ref ,y ref ;d ¯͒ SF͑s ref ;x ref ,y ref ,z ref ;d ref ͒T͑x ref ,y ref ;d ref ͒ SF͑sЈ;x ref ,y ref ,z ref ;d ref ͒ SF͑s ref ;x ref ,y ref ,z ref ;d ref ͒ ͑sЈ;x ref ,y ref ,z ref ;d ¯͒SF͑sЈ;x ref ,y ref ,z ref ;d ¯͒T͑x ref ,y ref ;d ¯͒ SF͑sЈ;x ref ,y ref ,z ref ;d ref ͒T͑x ref ,y ref ;d ref ͒ = MU D ref MU S c ͑c͒ • OAR air ͑c;x,y;d͒ • DIST͑c;x,y,z͒ • S p ͑sЈ͒ • TPR͑sЈ;d ¯͒ Ϸ MU D ref MU S c ͑c͒ • S p ͑sЈ͒ • TPR͑sЈ;d ¯͒ • POAR͑x,y;d ref ͒ • DIST͑z͒, ͑B1͒ where POAR͑x,y;d ref ͒ = K inc ͑c max ;x,y,z ref ͒T͑x,y;d ref ͒ K inc ͑c max ;x ref ,y ref ,z ref ͒T͑x ref ,y ref ;d ¯ref ͒ K inc ͑c ref ;x ref ,y ref ,z͒ K inc ͑c ref ;x ref ,y ref ,z ref ͒ ͑B3͒ c ͑c͒ • OAR air ͑c;x,y;d͒ • DIST͑c;x,y,z͒ ͑s;x,y,z;d ¯͒SF͑s;x,y,z;d ¯͒T͑x ref ,y ref ;d ¯͒ c ͑c͒OAR air ͑c;x,y;d͒ • DIST͑c;x,y,z͒ ϫ Notice that the dosimetrical quantity, D͑c , s ; x , y , z ; d͒, implicitly includes the dependence on d ¯since d changes with x, y and equals d ¯on the central axis ͑x ref , y ref ͒.TPR͑sЈ ; d ¯͒, S p ͑sЈ͒, and S c ͑c͒ are the central axis quantities for the open beam.The last line of Eq. ͑B1͒ becomes an approximation due to using the POAR͑x , y ; d ref ͒ instead of OAR air ͑c ; x , y ; d͒ ͑losing the dependence on c and d͒ using only the z dependence for distance function, and ignoring the off-axis change in the TPR.From these equations, we get for the off-axis case with no wedge: