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

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Abstract
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.

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