Detector line spread functions determined analytically by transport of Compton recoil electrons

To achieve the maximum benefit of conformal radiation therapy it is necessary to obtain accurate knowledge of radiation beam penumbras based on high-resolution relative dosimetry of beam profiles. For this purpose there is a need to perform high-resolution dosimetry with well-established routine dosimeters, such as ionization chambers or diodes. Profiles measured with these detectors must be corrected for the dosimeter's nonideal response, caused by finite dimensions and, in the case of an ionization chamber, the alteration of electron transport and a contribution of electrons recoiled in the chamber wall and the central electrode. For this purpose the line spread function (LSF) of the detector is needed. The experimental determination of LSFs is cumbersome and restricted to the specific detector and beam energy spectrum used. Therefore, a previously reported analytical model [Med. Phys. 27, 923-934 (2000)] has been extended to determine response profiles of routine dosimeters: shielded diodes and, in particular, ionization chambers, in primary dose slit beams. The model combines Compton scattering of incident photons, the transport of recoiled electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. It yields the traveling direction and the energy of electrons upon incidence on the detector surface. In the case of ionization chambers, geometrical considerations are then sufficient to calculate the relative amount of ionization in chamber air, i.e., the detector response, as a function of the detector location in the slit beam. In combination with the previously reported slit beam dose profiles, the LSF can then readily be derived by reconstruction techniques. Since the spectral contributions are preserved, the LSF of a dosimeter is defined for any beam for which the effective spectrum is known. The detector response profiles calculated in this study have been verified in a telescopic slit beam geometry, and were found to correspond to experimental profiles within 0.2 and 0.3 mm (full width at half-maximum) for a Wellhoefer IC15 chamber in a 6 and 25 MV-X x-ray beam, respectively. For a shielded diode these figures were found to be 0.2 and 0.1 mm, respectively. It is shown that a shielded diode in a primary beam needs only a small size-based correction of measured profiles. The effect of the LSF of an IC15 chamber on penumbra width has been determined for a set of model penumbras. The LSFs calculated by the application of the analytical model yield a broadening by 2 mm of a 3 mm wide penumbra (20%-80%). This is 0.5 mm (6 MV-X) to 1 mm (25 MV-X) smaller than found with the experimental LSFs. With a spatial correction based on the LSFs that were determined in this study, this broadening of up to 2 mm is eliminated, so that ionization chambers like the IC15 can be used for high-resolution relative dosimetry on a routine basis.