Abstract:
:There are three ways to determine the spectrum of a clinical photon beam: direct measurement, modelling the source and reconstruction from ion-chamber measurements. We focus on reconstruction because the necessary equipment is readily available and it provides independent confirmation of source models for a given machine. Reconstruction methods involve measuring the dose in an ion chamber after the beam passes through an attenuator. We gain information about the spectrum from measurements using attenuators of differing compositions and thicknesses since materials have energy dependent attenuation. Unlike the procedures used in other papers, we do not discretize or parametrize the spectrum. With either of these two approximations, reconstruction is a least squares problem. The forward problem of going from a spectrum to a series of dose measurements is a linear operator, with the composition and thickness of the attenuators as parameters. Hence the singular value decomposition (SVD) characterizes this operator. The right singular vectors form a basis for the spectrum, and, at first approximation, only those corresponding to singular values above a threshold are measurable. A more rigorous error analysis shows with what confidence different components of the spectrum can be measured. We illustrate this theory with simulations and an example utilizing six sets of dose measurements with water and lead as attenuators.
journal_name
Phys Med Bioljournal_title
Physics in medicine and biologyauthors
Armbruster B,Hamilton RJ,Kuehl AKdoi
10.1088/0031-9155/49/22/005subject
Has Abstractpub_date
2004-11-21 00:00:00pages
5087-99issue
22eissn
0031-9155issn
1361-6560journal_volume
49pub_type
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