Transmitted intensity through water was measured in a narrow-beam geom
etry for different energy x-ray beams from commercial accelerators. In
order to accurately obtain the attenuation coefficient of the inciden
t beam using transmission data, a novel formula was developed based on
consideration of beam hardening in phantom. The value of the attenuat
ion coefficient obtained by fitting transmission data to this formula
was found to be independent of the absorber thickness used in experime
nts, whereas the attenuation coefficient obtained from the traditional
formula, I(x)=I-0 exp(-mu x), changed by up to 7% with absorber thick
ness for a given beam. The beam hardening coefficient obtained from ou
r formula indicates that the attenuation coefficient in water changes
by about 0.33% per cm near the surface for the high-energy photon beam
s studied. Variations in beam quality with off-axis distance were subs
equently investigated using the new formula. Results show that the att
enuation coefficient at the water surface increased by about 15% for 1
5 and 18 MV beams, and by 11%-13% for 6 MV beams, when the off-axis di
stance at 100 cm from the source was changed from 0 to 18 cm. Consider
ation 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 diff
erent 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 transmissi
on formula. (C) 1997 American Association of Physicists in Medicine.