Non‐stationary model of oblique x‐ray incidence in amorphous selenium detectors: I. Point spread function

Acciavatti, Raymond J.; Maidment, Andrew D. A.

doi:10.1002/mp.13313

Cited by 3 publications

(10 citation statements)

References 38 publications

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“…We model the NGT system with the same acquisition parameters as those described in Part 1 for a digital mammography (DM) image (analogous to the central projection in DBT). To calculate the MTF along any polar angle ( α ), a coordinate transformation can be introduced

f_{x} = f_{r} cos α

f_{y} = f_{r} sin α,

where f r denotes radial frequency.…”

Section: Resultsmentioning

confidence: 99%

“…To determine the MTF of the x‐ray converter, it is first necessary to calculate the two‐dimensional (2D) Fourier transform of P I ; that is, the PSF associated with the interaction point at the height z above the exit surface of the x‐ray converter

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P_{normalI} \cdot e^{- 2 π i (f_{x} x + f_{y} y)} d x d y

where

i = \sqrt{- 1}

and where f x and f y measure the frequency along the x and y directions, respectively. This integral can be transformed from the

(x, y)

coordinate system into the

(v_{1}^{'}, v_{2}^{'})

coordinate system using the equations of Part 1

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} δ [{v^{'}}_{1} - false(l - z false) tan θ] δ false({v^{'}}_{2} false) \cdot e^{- 2 π i [f_{x} (ξ_{1} + {v^{'}}_{1} cos Γ - {v^{'}}_{2} sin Γ) + f_{y} (ξ_{2} + {v^{'}}_{1} sin Γ + {v^{'}}_{2} cos Γ)]} d {v^{'}}_{1} d {v^{'}}_{2}

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}

…”

Section: Methodsmentioning

confidence: 99%

“…These equations presume that r > 0, as was the case in Part 1 . Following Swank, the optical transfer function (OTF) of the x‐ray converter is determined by integrating

{scriptF}_{2} P_{normalI}

over the thickness ( l ) of selenium, and weighting the integrand by the relative number of x‐ray quanta at each depth z .

G_{normalSe} = \int_{0}^{l} N \cdot F_{2} P_{I} \cdot d z

= C_{normalI} e^{\frac{- 2 π i d ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{d - l}} \int_{0}^{l} e^{- μ (l - z) \sqrt{1 + {(\frac{r}{d - l})}^{2}} + \frac{2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{d - l} z} d z

= \frac{e^{- 2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}}{1 - e^{- μ l \sqrt{1 + {(\frac{r}{d - l})}^{2}}}} [\frac{1 - e^{- μ l \sqrt{1 + {()(, \frac{r}{d - l})}^{2}} + \frac{- 2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y}) l}{d - l}}}{1 + \frac{2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{μ r \sqrt{1 + {()(, \frac{d - l}{r})}^{2}}}}]

…”

Section: Methodsmentioning

confidence: 99%

“…Since P z is a convolution of two functions [Eq. , Acciavatti and Maidment], the 2D Fourier transform can be evaluated using the convolution theorem

{scriptF}_{2} P_{z} = {scriptF}_{2} P_{normalI} \cdot {scriptF}_{2} P_{normalTFT}

where

{scriptF}_{2} P_{normalTFT} = sinc false(a_{x} f_{x} false) \cdot sinc false(a_{y} f_{y} false)

and where

sinc false(ν false) \equiv \frac{sin (π ν)}{π ν}

…”

Section: Methodsmentioning

confidence: 99%

“…One limitation of experimental methods used to measure MTF is that spatial anisotropy cannot be quantified, since it is presumed that the MTF is stationary within a region‐of‐interest (ROI). We calculate the MTF using the model of the point spread function (PSF) developed in Part 1 . This model includes the effects of the divergent‐beam geometry and digitization.…”

Section: Introductionmentioning

confidence: 99%

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Nonstationary model of oblique x‐ray incidence in amorphous selenium detectors: II. Transfer functions

Acciavatti

Maidment

2019

Medical Physics

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Purpose One limitation of experimental techniques for quantifying resolution and noise in detectors is that the measurement is made in a region‐of‐interest (ROI). With theoretical modeling, these properties can be measured at a point, allowing for quantification of spatial anisotropy. This paper calculates nonstationary transfer functions for amorphous selenium (a‐Se) detectors in breast imaging. We use this model to demonstrate the performance advantage of a “next‐generation” tomosynthesis (NGT) system, which is capable of x‐ray source motion with more degrees of freedom than a clinical tomosynthesis system. Methods Using Swank's formulation, the optical transfer function (OTF) and presampled noise power spectra (NPS) are determined based on the point spread function derived in Part 1. The modulation transfer function (MTF) is found from the normalized modulus of the OTF. To take into account the presence of digitization, the presampled NPS is convolved with a two‐dimensional comb function, for which the period along each direction is the reciprocal of the detector element size. The detective quantum efficiency (DQE) is then determined from combined knowledge of the OTF and NPS. Results First, the model is used to demonstrate the loss of image quality due to oblique x‐ray incidence. The MTF is calculated along various polar angles, corresponding to different orientations of the input frequency. The MTF is independent of the incidence angle if the polar angle is perpendicular to the ray incidence direction. However, along other polar angles, oblique incidence results in MTF degradation at high frequencies. The MTF degradation is most substantial along the ray incidence direction. Unlike the MTF, the normalized NPS (NNPS) is independent of the incidence angle. To measure the relative signal‐to‐noise, the DQE is also calculated. Oblique incidence yields high‐frequency DQE degradation, which is more pronounced than the MTF degradation. This arises because the DQE is proportionate with the square of the MTF. Ultimately, this model is used to evaluate how the image quality varies over the detector area. For various projection images, we calculate the variation in the incidence angle over this area. With the NGT system, the source can be positioned in such a way that this variation is minimized, and hence the DQE exhibits less anisotropy. To achieve this improvement in the image quality, the source needs to have a component of motion in the posteroanterior (PA) direction, which is perpendicular to the conventional direction of source motion in tomosynthesis. Conclusions In a‐Se detectors, the DQE at high frequencies is degraded due to oblique incidence. The DQE degradation is more pronounced than the MTF degradation. This model is used to quantify the spatial variation in DQE over the detector area. The use of PA source motion is a strategy for minimizing this variation and thus improving the image quality.

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f_{x} = f_{r} cos α

f_{y} = f_{r} sin α,

where f r denotes radial frequency.…”

Section: Resultsmentioning

confidence: 99%

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P_{normalI} \cdot e^{- 2 π i (f_{x} x + f_{y} y)} d x d y

where

i = \sqrt{- 1}

and where f x and f y measure the frequency along the x and y directions, respectively. This integral can be transformed from the

(x, y)

coordinate system into the

(v_{1}^{'}, v_{2}^{'})

coordinate system using the equations of Part 1

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}^{\infty} δ [{v^{'}}_{1} - false(l - z false) tan θ] δ false({v^{'}}_{2} false) \cdot e^{- 2 π i [f_{x} (ξ_{1} + {v^{'}}_{1} cos Γ - {v^{'}}_{2} sin Γ) + f_{y} (ξ_{2} + {v^{'}}_{1} sin Γ + {v^{'}}_{2} cos Γ)]} d {v^{'}}_{1} d {v^{'}}_{2}

{scriptF}_{2} P_{normalI} = \int_{- \infty}^{\infty} \int_{- \infty}

…”

Section: Methodsmentioning

confidence: 99%

“…These equations presume that r > 0, as was the case in Part 1 . Following Swank, the optical transfer function (OTF) of the x‐ray converter is determined by integrating

{scriptF}_{2} P_{normalI}

over the thickness ( l ) of selenium, and weighting the integrand by the relative number of x‐ray quanta at each depth z .

G_{normalSe} = \int_{0}^{l} N \cdot F_{2} P_{I} \cdot d z

= C_{normalI} e^{\frac{- 2 π i d ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{d - l}} \int_{0}^{l} e^{- μ (l - z) \sqrt{1 + {(\frac{r}{d - l})}^{2}} + \frac{2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{d - l} z} d z

= \frac{e^{- 2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}}{1 - e^{- μ l \sqrt{1 + {(\frac{r}{d - l})}^{2}}}} [\frac{1 - e^{- μ l \sqrt{1 + {()(, \frac{r}{d - l})}^{2}} + \frac{- 2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y}) l}{d - l}}}{1 + \frac{2 π i ()(, ξ_{1} f_{x} + ξ_{2} f_{y})}{μ r \sqrt{1 + {()(, \frac{d - l}{r})}^{2}}}}]

…”

Section: Methodsmentioning

confidence: 99%

“…Since P z is a convolution of two functions [Eq. , Acciavatti and Maidment], the 2D Fourier transform can be evaluated using the convolution theorem

{scriptF}_{2} P_{z} = {scriptF}_{2} P_{normalI} \cdot {scriptF}_{2} P_{normalTFT}

where

{scriptF}_{2} P_{normalTFT} = sinc false(a_{x} f_{x} false) \cdot sinc false(a_{y} f_{y} false)

and where

sinc false(ν false) \equiv \frac{sin (π ν)}{π ν}

…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonstationary model of oblique x‐ray incidence in amorphous selenium detectors: II. Transfer functions

Acciavatti

Maidment

2019

Medical Physics

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Recent Developments of Amorphous Selenium-Based X-Ray Detectors: A Review

Huang

Abbaszadeh

2020

IEEE Sensors J.

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Amorphous selenium (a-Se) is a photoconductive material that has been intensively investigated from its early application in xerography to its present application in flat panel X-ray imagers. It can be deposited up to a few millimeters thick over a large area. Its high vapor pressure yields uniform coverage in novel device structures for lowcost and large-area applications. The evidence of avalanche multiplication in a-Se and application of a-Se in high-gain avalanche rushing photoconductor video-tubes goes back to the early 1980s. Over the past decade there has been increasing research interest in novel detector structures and integration of a-Se with new materials to leverage the avalanche properties. We summarize some of the shortcomings of a-Se such as low charge carrier mobility, low charge conversion efficiency, depth dependence, and high dark current at high electric fields. We then highlight recent developments in a-Se-based devices to address these shortcomings and enable picosecond timing performance and high detection efficiency.

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