Deriving depth-dependent light escape efficiency and optical Swank factor from measured pulse height spectra of scintillators

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Pulse height spectroscopy has been used by investigators to deduce the imaging properties of scintillators. Pulse height spectra (PHS) are used to compute the Swank factor, which describes the variation in scintillator light output per x-ray interaction. The spread in PHS measured below the K-edge is related to the optical component of the Swank factor, i.e., variations in light escape efficiency from different depths of x-ray interaction in the scintillator, denoted Symbol. Optimizing scintillators for medical imaging applications requires understanding of these optical properties, as they determine tradeoffs between parameters such as x-ray absorption, light yield, and spatial resolution. This work develops a model for PHS acquisition such that the effect of measurement uncertainty can be removed. This method allows Symbol to be quantified on an absolute scale and permits more accurate estimation of the optical Swank factor of scintillators.


The pulse height spectroscopy acquisition chain was modeled as a linear system of stochastic gain stages. Analytical expressions were derived for signal and noise propagation through the PHS chain, accounting for deterministic and stochastic aspects of x-ray absorption, scintillation, and light detection with a photomultiplier tube. The derived expressions were used to calculate PHS of thallium-doped cesium iodide (CsI) scintillators using parameters that were measured, calculated, or known from literature. PHS were measured at 25 and 32 keV of CsI samples designed with an optically reflective or absorptive backing, with or without a fiber-optic faceplate (FOP), and with thicknesses ranging from 150–1000 μm. Measured PHS were compared with calculated PHS, then light escape model parameters were varied until measured and modeled results reached agreement. Resulting estimates of Symbol were used to calculate each scintillator's optical Swank factor.


For scintillators of the same optical design, only minor differences in light escape efficiency were observed between samples with different thickness. As thickness increased, escape efficiency decreased by up to 20% for interactions furthest away from light collection. Optical design (i.e., backing and FOP) predominantly affected the magnitude and relative variation in Symbol. Depending on interaction depth and scintillator thickness, samples with an absorptive backing and FOP were estimated to yield 4.1–13.4 photons/keV. Samples with a reflective backing and FOP yielded 10.4–18.4 keV−1, while those with a reflective backing and no FOP yielded 29.5–52.0 keV−1. Optical Swank factors were approximately 0.9 and near-unity in samples featuring an absorptive or reflective backing, respectively.


This work uses a modeling approach to remove the noise introduced by the measurement apparatus from measured PHS. This method allows absolute quantification of Symbol and more accurate estimation of the optical Swank factor of scintillators. The method was applied to CsI scintillators with different thickness and optical design, and determined that optical design more strongly affects Symbol and Swank factor than differences in CsI thickness. Despite large variations in Symbol between optical designs, the Swank factor of all evaluated samples is above 0.9. Information provided by this methodology can help validate Monte Carlo simulations of structured CsI and optimize scintillator design for x-ray imaging applications.

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