Theoretical Limits of X-ray Scatter Rejection: A Path Integral Approach

Compton scattering remains a fundamental limit in diagnostic radiology, traditionally mitigatedby physical anti-scatter grids or computational simulations. In this paper, we establish the absolutetheoretical limit of scatter rejection using a pure analytical quantum field-theoretic framework. Bymodeling the inhomogeneous human body as a complex wave vector field, we apply Feynman’spath integral formulation to massless X-ray photons. We introduce a momentum-space Dirac deltafilter to mathematically collapse all non-rectilinear scattered trajectories. Through saddle-pointapproximation, we isolate the real phase oscillation from the imaginary attenuation term, ultimatelyderiving a scatter-free primary intensity equation that perfectly converges to the macroscopic BeerLambert law. This theoretical architecture bypasses conventional particle-based scattering models,providing a definitive mathematical boundary for scatter reduction in medical imaging.