Semi-empirical procedures for correcting detector size effect on clinical MV x-ray beam profiles

The measured radiation beam profiles need to be corrected for the detector size effect to derive the real profiles. This paper describes two new semi-empirical procedures to determine the real profiles of high-energy x-ray beams by removing the detector size effect from the measured profiles. Measured profiles are corrected by shifting the position of each measurement point by a specific amount determined from available theoretical and experimental knowledge in the literature. The authors developed two procedures to determine the amount of shift. In the first procedure, which employs the published analytical deconvolution procedure of other investigators, the shift is determined from the comparison of the analytical fit of the measured profile and the corresponding analytical real profile derived from the deconvolution of the fitted measured profile and the Gaussian detector response function. In the second procedure, the amount of shift at any measurement point is considered to be proportional to the value of an analytical function related to the second derivative of the real profile at that point. The constant of proportionality and a parameter in the function are obtained from the values of the shifts at the 90%, 80%, 20%, and 10% dose levels, which are experimentally known from the published results of other investigators to be approximately equal to half of the radius of the detector. These procedures were tested by correcting the profiles of 6 and 18 MV x-ray beams measured by three different ionization chambers and a stereotactic field diode detector with 2.75, 2, 1, and 0.3 mm radii of their respective active cylindrical volumes. The corrected profiles measured by different detectors are found to be in close agreement. The detector size corrected penumbra widths also agree with the expected values based on the results of an earlier investigation. Thus, the authors concluded that the proposed procedures are accurate and can be used to derive the real profiles of clinical high-energy x-ray beams.