Focal Spot Design Optimization for High-Resolution CT

Recent advances in improved detector resolution including photon counting CT has helped to enable high-resolution diagnostic computed tomography (CT). However, the finite size of the X-ray tube focal spot has emerged as a dominant limitation on spatial resolution. While reducing focal spot size improves resolution, it also limits photon fluence. This can result in unacceptable levels of noise, particularly for larger patients. Novel x-ray tube designs may be required to overcome these fluence limitations. Previous work has shown that using structured focal spots, multiple x-ray sources, and advanced reconstruction models has the potential to overcome classic noise-resolution trade-offs. In this work, we write down general expressions for the imaging performance of a multi-focal spot CT system and use those predictors to design structured focal spots based on specific imaging tasks. Specifically, an analytic performance model is developed that explicitly links extended focal spot shape to the system modulation transfer function (MTF) and noise power spectrum (NPS) through local Fourier-based approximations. This model enables efficient prediction of a task-weighted detective quantum efficiency (DQE) and supports gradient-based optimization of focal spot emission patterns under physical fluence constraints. Focusing on high-frequency imaging tasks, we formulate the design problem as minimizing NPS within a prescribed spatial-frequency band and solve it using first-order optimization with multiple random initializations. Simulation studies demonstrate that the optimized focal spot designs substantially suppress high-frequency noise compared to a conventional small focal spot (limited fluence) configuration, yielding marked improvements in task-specific DQE. Analytical NPS predictions closely match empirical estimates from noisy reconstructions, validating the accuracy of the proposed model. These results highlight focal spot shape as a powerful and previously underutilized degree of freedom in CT system design and establish task-based, gradient-driven focal spot optimization as a promising approach for enhancing high-resolution CT performance.