Numerical optimization of longitudinal collimator geometry for novel x-ray field

Abstract

Objective: A novel X-ray field produced by an ultrathin conical target is described in the literature. However, the optimal design for an associated collimator remains ambiguous. Current optimization methods using Monte Carlo calculations restrict the efficiency and robustness of the design process. A more generic optimization method that reduces parameter constraints while minimizing computational load is necessary. A numerical method for optimizing the longitudinal collimator hole geometry for a cylindrically-symmetrical X-ray tube is demonstrated and compared to Monte Carlo calculations. 
Approach: The X-ray phase space was modelled as a four-dimensional histogram differential in photon initial position, final position, and photon energy. The collimator was modelled as a stack of thin washers with varying inner radii. Simulated annealing was employed to optimize this set of inner radii according to various objective functions calculated on the photon flux at a specified plane. 
Main results: The analytical transport model used for optimization was validated against Monte Carlo calculations using Geant4 via its wrapper, TOPAS. Optimized collimators and the resulting photon flux profiles are presented for three focal spot sizes and five positions of the source. Optimizations were performed with multiple objective functions based on various weightings of precision, intensity, and field flatness metrics. Finally, a select set of these optimized collimators, plus a parallel-hole collimator for comparison, were modelled in TOPAS. The evolution of the radiation field profiles are presented for various positions of the source for each collimator.
Significance: This novel optimization strategy proved consistent and robust across the range of X-ray tube settings regardless of the optimization starting point. Common collimator geometries were re-derived using this algorithm while simultaneously optimizing geometry-specific parameters. The advantages of this strategy over iterative Monte Carlo-based techniques, including computational efficiency, radiation source-specificity, and solution flexibility, make it a desirable optimization method for complex irradiation geometries.