Energy calibration based on ridge lines in scatter plots

Abstract In applications such as PET and proton therapy monitoring, MVT and TOT methods have played a significant role. However, these methods face issues such as energy nonlinearity and inconsistent performance across different energy ranges. The challenge of investigating and resolving these issues has become urgent. This paper proposes a nonlinear calibration framework based on a 3D energy spectrum surface and diffusion equations, significantly improving the energy resolution and calibration accuracy of high-energy radiation detection systems. To address this challenge, this work establishes a foundation using the joint probability density surface of the acquisition system's input and output energies, along with the probability density and energy transfer equation. From this foundation, a transfer equation describing the energy input-output relationship is derived, and subsequently, a ridge line equation is developed for energy calibration. This approach results in an improvement in linearity from -5.11%, obtained via empirical scatter plot fitting, to -1.18%.