Measurement of a photon penumbra-generating kernel for a convolution-adapted ratio-TAR algorithm for 3D treatment planning

Daniel A. Low, Xiao Rong Zhu, William B. Harms, James A. Purdy

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


A method has been developed to measure a photon penumbra-generating kernel using dosimetry equipment available in most radiation therapy departments. The kernel is used in a convolution-adapted ratio-TAR algorithm in our three-dimensional treatment planning system. The kernel is assumed to be invariant with respect to off-axis position, axially symmetric, and is divided into short- and long-range components, with a different measurement technique for each. The data required to obtain the short-range component are measured by scanning across a split-field geometry incident on a water phantom. The derivative of the measured profile is proportional to one-dimensional projections across the kernel. Because the kernel is axially symmetric, only one profile measurement is required for each depth. A CT reconstruction technique is used to extract the radial dependence of the kernel from the strip integrals. Electronic noise in the acquisition system yields significant uncertainties in the kernel shape for distances beyond 3 cm. The long-range portion of the kernel is obtained by examining tissue-air ratios (TARs). The derivative of the TAR at the center of a circular field is proportional to the kernel value at the distance corresponding to the radius of the field. The kernel measurement method was tested by comparing measured and calculated square-field profiles at a variety of depths. Agreement was within 1% within the field boundary and 3% outside the field boundary for all depths.

Original languageEnglish
Pages (from-to)1395-1403
Number of pages9
JournalMedical physics
Issue number9
StatePublished - Sep 1995


  • measurement
  • photon dose calculations
  • photon kernel
  • three-dimensional treatment planning


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