Geometrical Determinations of Photon-Beam Limit Angle (LA) Related to Maximum Pencil-Beam Divergence Angle for Standard Radiotherapy Wedges

Wedge filters constitute a useful type of Beam Modification Devices (BME) in Radiation Therapy. Its use is routinary in both Forward and Inverse Treatment Planning Optimization (ITPO). In previous contributions we presented the exact/approximated path of a Pencil Photon-Beam (AAA Model, Anisothropic Analytic Algorithm), through standard manufacturing alloy wedges. It was found a so-defined Limit-Angle (LA), beyond of which the outpoint of the beam is located improperly at the lateral side of the wedge. LA exists because of the photon-beam physical divergence phenomenon. In this paper we carry out the Geometrical and Analytical determination of the LA in function of the beam divergence angle, collimator output distance, and the size parameters of the wedge filter. Two methods are used, Geometrical and Analytical. A series of Mathematical Formulations for LAs, is shown with basic approximations according to the industrial manufacturing wedge standards. Formulation is verified with Optimization Mathematical Methods.