Geometric analysis of light-field position of a multileaf collimator with curved ends

The purpose of this work was to analyze the difference between the light-field edge and the radiation field edge produced by multileaf collimator (MLC) leaves that are constructed with rounded ends. A formula was derived using three-dimensional geometry predicting the location of the ideal point-source light-field edge relative to the geometric projection of the tip of the rounded leaf end. The theoretical edge of the radiation field for a point source was also calculated along the projection of a chord whose length was one Half-Value Thickness (HVT). Analytic solutions were found for the radiation-field edge and the transmission penumbra. The displacement of the light-field edge relative to the projection of the leaf tip varied from 0 mm for the leaf tip projected onto the central axis to approximately 3.2 mm for the leaf tip projected to 20 cm off the central axis. The light-field edge was always displaced into the unblocked area. The location of the projection of the 1 HVT chord was displaced from the light-field edge by a small and essentially constant distance (approximately 0.3 mm) for all field sizes. The transmission penumbra (80%-20%) was about 1.2 mm for all leaf positions. The calibration of the leaf position must account for the nonlinear relationship between the leaf-tip projection and the light-field (or radiation-field) edge.