Transmitted intensity through water was measured in a narrow-beam geometry for different energy x-ray beams from commercial accelerators. In order to accurately obtain the attenuation coefficient of the incident beam using transmission data, a novel formula was developed based on consideration of beam hardening in phantom. The value of the attenuation coefficient obtained by fitting transmission data to this formula was found to be independent of the absorber thickness used in experiments, whereas the attenuation coefficient obtained from the traditional formula, I(x) = I0 exp(-mux), changed by up to 7% with absorber thickness for a given beam. The beam hardening coefficient obtained from our formula indicates that the attenuation coefficient in water changes by about 0.33% per cm near the surface for the high-energy photon beams studied. Variations in beam quality with off-axis distance were subsequently investigated using the new formula. Results show that the attenuation coefficient at the water surface increased by about 15% for 15 and 18 MV beams, and by 11%-13% for 6 MV beams, when the off-axis distance at 100 cm from the source was changed from 0 to 18 cm. Consideration of the physics of bremsstrahlung production suggests that these variations should be mainly determined by the shape of the flattening filter, i.e., by the path length of rays traversing the filter in different directions. This expectation was confirmed by observing that the attenuation coefficient at the phantom surface can be related to the ray path of the beam in the flattening filter using the new transmission formula.
Head-scatter factors of symmetric square and rectangular fields (field center on the central beam axis) defined by the upper (Y) and lower (X) jaws for 6 and 15 MV photon beams from 2300CD and 600C accelerators (Varian Associates, Inc., Palo Alto, CA) were measured, as well as those for fields shaped by the Y jaws and the multileaf collimator (MLC) of the 2300CD. For rectangular fields, the head-scatter factor for the field (x = a and y = b) was different from that for the field (y = a and x = b). This difference was 2% -3% for fields defined by conventional collimators when [formula, see text] was large, and became 4%-5% when the MLC and YT jaws were used to shape the fields with the X jaws retracted. In order to calculate values for head-scatter factors of rectangular fields accurately using an equivalent square formalism, the side of the equivalent square should be obtained with different weights for lower and upper jaws, as proposed by Vadash and Bjärngard [Med. Phys. 20, 733-734 (1993)]. Our measurements demonstrate that the relative weight (G) of upper and lower jaws is strongly dependent on their distances from the x-ray source, while the beam energy has little effect on the value of G. We further show that G can be calculated simply from these distances. An analytical representation for head-scatter factors of square and rectangular fields is also developed in this paper. The quality of this representation was judged by the root-mean-square (rms) deviation from measured head-scatter factors, which ranged from 0.11%-0.27%.
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