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MTF of columnar phosphors with a homogenous part: an analytical approach

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Abstract

A method for the theoretical estimation of the MTF of columnar phosphors with a homogeneous part at the end used in X-ray imaging has been developed. This method considers the light transport inside the scintillator through an analytical modelling, the optical photon beams distribution on the scintillator–optical sensor interface, and uses the definition of the PSF and a Gauss fitted LSF to estimate the MTF of an indirect detector. This method was applied to a columnar CsI:Tl scintillator and validated against experimental results found in literature, and a good agreement was observed. It was found that, by increasing the pixel size of the optical detector and the thickness of the scintillator, the MTF decreased as expected. This method may be used in evaluating the performance of the columnar phosphors used in medical imaging, given their physical and geometrical characteristics.

Graphical abstract

(a) Side view of a part of the scintillator where five crystal columns with homogeneous ends attached to an optical sensor is shown.

(b) Propagation of two random optical photon beams emitted from point K with different angles of emission is shown. All the symbols are explained analytically in the text.

(c) MTF of a 140-μm length scintillator attached to a 22.5-μm pixel size optical sensor.

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Authors and Affiliations

  1. Department of Medical Physics, School of Medicine, University of Patras, 26500, Patras, Greece

    Konstantinos Psichis & George Panayiotakis

  2. Department of Biomedical Engineering, University of West Attica, 12210, Athens, Greece

    Nektarios Kalyvas & Ioannis Kandarakis

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  1. Konstantinos Psichis
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Appendix

Appendix

According to reference [36], DOG can be calculated as

$$ DOG=\frac{I_{tot}}{\sum \limits_Ef(E)} $$
(33)

where Itot is the total number of optical photons refracted in the optical sensor given by the following relationship:

$$ {\displaystyle \begin{array}{c}{I}_{tot}=\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{0 ff}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vff}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t{I}_{0 ff}\left(E,t,0\right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vff}\left(E,t,0\right)+\\ {}\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{fT I}\left(E,t,\varphi \right)\\ {}+\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{0 ff H}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vff H}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t{I}_{0 ff H}\left(E,t,0\right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vff H}\left(E,t,0\right)+\\ {}\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{fT1H}\left(E,t,\varphi \right)\\ {}+\sum \limits_E\sum \limits_t\sum \limits_{m=0}^4{I}_{Shm}\left(E,t,\varphi \right)\\ {}+\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{0 bf}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t\sum \limits_{\varphi}\sum \limits_{v=1}^7{I}_{vbf}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t{I}_{0 bf}\left(E,t,180\right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vbf}\left(E,t,180\right)\\ {}+\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{sbT1h}\left(E,t,\varphi \right)+\\ {}\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{0 bf H}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t\sum \limits_{\varphi}\sum \limits_{v=1}^7{I}_{vbf H}\left(E,t,\varphi \right)+\sum \limits_E\sum \limits_t{I}_{0 bf H}\left(E,t,180\right)+\sum \limits_E\sum \limits_t\sum \limits_{v=1}^7{I}_{vbf H}\left(E,t,180\right)+\\ {}\sum \limits_E\sum \limits_t\sum \limits_{\varphi }{I}_{Lb}\left(E,t,\varphi \right)\end{array}} $$
(34)

where the subscript H accounts for emission in the homogeneous part and φ ϵ (−90°, 0°) and φ ϵ (0°, 90°). f(E) is the number of X-ray photons that impinge on the DA side of the crystalline column.

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Psichis, K., Kalyvas, N., Kandarakis, I. et al. MTF of columnar phosphors with a homogenous part: an analytical approach. Med Biol Eng Comput 58, 2551–2565 (2020). https://doi.org/10.1007/s11517-020-02243-4

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