Analytic Model of Energy-Absorption Response Functions in Compound X-ray Detector Materials

Yun, Sangwoon; Kim, Ho Kyung; Youn, Hanbean; Tanguay, Jesse; Cunningham, Ian

doi:10.1109/tmi.2013.2265806

Cited by 13 publications

(26 citation statements)

References 32 publications

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“…Equations (3) and (4) show that I SPC andc are determined by the energy response function R and in turn by the PDF ofd. Yun et al 47 described R for selected x-ray convertor materials, including the effects of random x-ray energy-depositing processes, for deterministic conversion of x-ray energy to secondary quanta with negligible pulse pileup. [48][49][50] Here, we describe a method of obtaining R from the PDF ofd that includes the effects of x-ray reabsorption and stochastic conversion and collection processes.…”

Section: C Determining R From the Pdf Of Image Quantamentioning

confidence: 99%

“…whereξ pe andξ inc represent the relative probabilities of photoelectric absorption and incoherent scattering. 41,47 F. 5.…”

Section: D Liberation Of Secondary Quanta In X-ray Convertormentioning

confidence: 99%

“…where p t θ depends on the interaction type and has been described in detail by Hajdok et al 63 and Yun et al 41,47 for both photoelectric and incoherent interactions, and p z 1 (z 1 ) is given by the exponential PDF µ(E)exp(−µ(E)z 1 ) normalized to unity over the convertor thickness.…”

Section: E3 Pdf Ofñ T =ñ a +ñ B +ñ Cmentioning

confidence: 99%

“…where p inc z 1 ,θ is given by Eq. (63) with p inc θ (θ) described in detail by Hajdok et al 63 and Yun et al 41,47 The first term in Eq. (65) represents the distribution of secondaries collected from energy deposition by the recoil electron and the second term contributes to the photopeak.…”

Section: E5 Incoherent Interactionsmentioning

confidence: 99%

“…In the case of reabsorption, photon energy is converted to secondary quanta at both primaryinteraction and reabsorption sites, resulting in a complicated energy response function. 47 In addition, liberation of secondary quanta (e.g., charges in a photoconductor or optical photons in a scintillator) is a stochastic process and the PDF when energy is deposited at one site differs to that when the same energy is deposited at multiple sites.…”

Section: Introductionmentioning

confidence: 99%

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Detective quantum efficiency of photon‐counting x‐ray detectors

et al. 2015

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The CSA approach is extended to describe signal and noise propagation through photoelectric and Compton interactions in SPC detectors, including the effects of escape and reabsorption of emission/scatter photons. High-performance SPC systems can be achieved but only for certain combinations of secondary conversion gain, depth-dependent collection efficiency, electronic noise, and reabsorption characteristics.

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Section: C Determining R From the Pdf Of Image Quantamentioning

confidence: 99%

“…whereξ pe andξ inc represent the relative probabilities of photoelectric absorption and incoherent scattering. 41,47 F. 5.…”

Section: D Liberation Of Secondary Quanta In X-ray Convertormentioning

confidence: 99%

Section: E3 Pdf Ofñ T =ñ a +ñ B +ñ Cmentioning

confidence: 99%

Section: E5 Incoherent Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Detective quantum efficiency of photon‐counting x‐ray detectors

et al. 2015

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

et al. 2017

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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 ε̄(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 ε̄(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 ε̄(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 ε̄(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 ε̄(z) and more accurate estimation of the optical Swank factor of scintillators. The method was applied to CsI scintillators with different thicknes...

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

Tanguay

Kim

et al. 2020

Medical Physics

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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.

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Analytic Model of Energy-Absorption Response Functions in Compound X-ray Detector Materials

Cited by 13 publications

References 32 publications

Detective quantum efficiency of photon‐counting x‐ray detectors

Detective quantum efficiency of photon‐counting x‐ray detectors

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

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

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