Analytic model of energy-absorption response functions in compound X-ray detector materials

Frequency-dependent signal and noise in spectroscopic x-ray imaging

Purpose

We present a new framework for theoretical analysis of the noise power spectrum (NPS) of photon‐counting x‐ray detectors, including simple photon‐counting detectors (SPCDs) and spectroscopic x‐ray detectors (SXDs), the latter of which use multiple energy thresholds to discriminate photon energies.

Methods

We show that the NPS of SPCDs and SXDs, including spatio‐energetic noise correlations, is determined by the joint probability density function (PDF) of deposited photon energies, which describes the probability of recording two photons of two different energies in two different elements following a single‐photon interaction. We present an analytic expression for this joint PDF and calculate the presampling and digital NPS of CdTe SPCDs and SXDs. We calibrate our charge sharing model using the energy response of a cadmium zinc telluride (CZT) spectroscopic x‐ray detector and compare theoretical results with Monte Carlo simulations.

Results

Our analysis shows that charge sharing increases pixel signal‐to‐noise ratio (SNR), but degrades the zero‐frequency signal‐to‐noise performance of SPCDs and SXDs. In all cases considered, this degradation was greater than 10%. Comparing the presampling NPS with the sampled NPS showed that degradation in zero‐frequency performance is due to zero‐frequency noise aliasing induced by charge sharing.

Conclusions

Noise performance, including spatial and energy correlations between elements and energy bins, are described by the joint PDF of deposited energies which provides a method of determining the photon‐counting NPS, including noise‐aliasing effects and spatio‐energetic effects in spectral imaging. Our approach enables separating noise due to x‐ray interactions from that associated with sampling, consistent with cascaded systems analysis of energy‐integrating systems. Our methods can be incorporated into task‐based assessment of image quality for the design and optimization of spectroscopic x‐ray detectors.

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

PURPOSE

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 ε¯(z). 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 ε¯(z) to be quantified on an absolute scale and permits more accurate estimation of the optical Swank factor of scintillators.

METHODS

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 ε¯(z) were used to calculate each scintillator's optical Swank factor.

RESULTS

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 ε¯(z). 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.

CONCLUSIONS

This work uses a modeling approach to remove the noise introduced by the measurement apparatus from measured PHS. This method allows absolute quantification of ε¯(z) 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 ε¯(z) and Swank factor than differences in CsI thickness. Despite large variations in ε¯(z) 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.