A variety of detectors and procedures for the measurement of small field output factors are discussed in the current literature. Different detectors with or without corrections are recommended. Correction factors are often derived by Monte Carlo methods, where the bias due to approximations in the model is difficult to judge. Over that, results appear to be contradictory in some cases. In this work, output factors were measured for field sizes from 4 mm up to 180 mm side length with different detectors. A simple linear correction for the energy response of solid state detectors is proposed. This led to identical values down to 8 mm field size, as long as the size of the detector is small against the field size. The correction was of the order of a few percent. For a shielded silicon diode it was well below 1%. A physically meaningful function is proposed in order to calculate output factors for arbitrary field sizes with high accuracy.

The aim of this work was to evaluate the accuracy of dose predicted in heterogeneous media by a pencil beam (PB), a collapsed cone (CC) and a Monte Carlo (MC) algorithm. For this purpose, a simple multi-layer phantom composed of Styrofoam and white polystyrene was irradiated with 10 x 10 cm2 as well as 20 x 20 cm2 open 6 MV photon fields. The beam axis was aligned parallel to the layers and various field offsets were applied. Thereby, the amount of lateral scatter was controlled. Dose measurements were performed with an ionization chamber positioned both in the central layer of white polystyrene and the adjacent layers of Styrofoam. It was found that, in white polystyrene, both MC and CC calculations agreed satisfactorily with the measurements whereas the PB algorithm calculated 12% higher doses on average. By studying off-axis dose profiles the observed differences in the calculation results increased dramatically for the three algorithms. In the regions of low density CC calculated 10% (8%) lower doses for the 10 x 10 cm2 (20 x 20 cm2) fields than MC. The MC data on the other hand agreed well with the measurements, presuming that proper replacement correction for the ionization chamber embedded in Styrofoam was performed. PB results evidently did not account for the scattering geometry and were therefore not really comparable. Our investigations showed that the PB algorithm generates very large errors for the dose in the vicinity of interfaces and within low-density regions. We also found that for the used CC algorithm large deviations for the absolute dose (dose/monitor unit) occur in regions of electronic disequilibrium. The performance might be improved by better adapted parameters. Therefore, we recommend a careful investigation of the accuracy for dose calculations in heterogeneous media for each beam data set and algorithm.

Abbreviations: %dd(10) x , The photon component of the percent depth dose at 10 cm depth in water for a 10 cm 2 × 10 cm 2 field; L∕ w air , Restricted mass collision stopping power ratio of water to air; en ∕ , Spectrum-averaged mass energy-absorption coefficient; AAPM, American Association of Physicists in Medicine; CPE, Charged Particle Equilibrium; DLG, Dosimetric leaf gap; D f msr w,Q msr , Absorbed dose to water at the reference depth z ref in water in the absence of the detector in a field specified by f msr and beam quality Q msr .; f clin , Clinical (clin) non-reference radiation field; f msr , Machine-specific reference (msr) field; f ref , Reference field (ref) specified in dosimetry protocols for which the calibration coefficient of an ionization chamber in terms of absorbed dose to water is provided by a standards laboratory; FWHM, Full-width at half-maximum; GUM, Guide to the expression of Uncertainty in Measurements.; IAEA, International Atomic Energy Agency; ICRU, International Commission on Radiation Units and Measurements; IMRT, Intensity-modulated radiation therapy; k Q,Q 0 , The beam-quality correction factor, which corrects for the differences between the response of an ionization chamber in the reference beam of quality Q o used for calibrating the chamber and the beam of quality Q (defined as k Q . in TG-51 4 ); k f ref Q,Q 0 , Correction factor that accounts for the differences between the response of a detector in field f ref in a beam of quality Q and reference beam quality Q 0 as defined in TRS-483. 1 and Palmans et al 2 ; k fclin,fmsr Qclin,Q msr , The detector-specific correction factor that accounts for the difference between the responses of the detector in fields f clin in a beam of quality Q clin and in fields f msr in beam of quality Q msr as defined by Alfonso et al. 3 ; LCPE, Lateral charged particle equilibrium; M fmsr Qmsr , Detector reading in field f msr and beam quality Q msr corrected for influence of changes in pressure and temperature, incomplete charge collection, polarity effect and electrometer correction factor (TRS-483 1 ); MU, Monitor unit; N D,w,Q 0 , This is N D,w in TG-51, 4 and defined as the calibration coefficient in terms of absorbed dose to water for an ionization chamber at a reference beam of quality,Q 0 and field size f ref ; N f ref D,w,Q 0

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