Efficient Validation of Photon Output Factors Using a Continuous Two-Dimensional Surface Model
Abstract
Purpose
To develop and validate a continuous two-dimensional output-factor (OF) model and to identify a measurement strategy that achieves accuracy and efficiency.
Methods
High-density OF datasets (729 field sizes) were acquired using automated XML-driven beam delivery and continuous electrometer logging for a 6 FFF MV beam. Multiple modeling approaches including polynomial regression, neural-network regression, and an extended log–log surface model were evaluated using the high-density dataset as the reference. To assess measurement efficiency, several geometric subset strategies (published reference field sizes, Edge + X, Directional Rays, Perimeter + Diagonals + Midlines, Radial Expansions, and 5 Rays) were compared at varying measurement densities. Model performance was quantified using root mean squared error (RMSE), mean absolute percent error (MAPE), maximum percent deviation, and the coefficient of determination (R²). Measurement uncertainty was quantified through controlled perturbation tests involving MU dependence, electrometer effects, geometric setup deviations, jaw calibration sensitivity, and measurement repeatability.
Results
The extended log–log model produced the most accurate and stable performance across all subset strategies (RMSE 0.14–0.21%, R² ≥ 0.998). Agreement between modeled and measured OFs was consistently limited by measurement uncertainty (≈0.26% at 1σ), rather than modeling error. Subset geometry strongly influenced efficiency: the Edge + X sampling pattern achieved sub-percent accuracy with only 22 measurements (RMSE 0.16%, MAPE 0.13%).
Conclusion
Photon output factors for a 6 FFF beam can be accurately reconstructed from a small, strategically selected subset of measurements using a robust continuous surface model. By recognizing measurement variability as the dominant limitation on achievable accuracy, this approach enables efficient and reproducible output factor validation while maintaining commissioning-grade accuracy, providing a practical alternative to conventional table-based methods.