Department of Radiology, Perelman School of Medicine at the University of Pennsylvania, Philadelphia, PA, 19104-4206, USA.
Med Phys. 2019 Feb;46(2):494-504. doi: 10.1002/mp.13313. Epub 2019 Jan 16.
In previous work, a theoretical model of the point spread function (PSF) for oblique x-ray incidence in amorphous selenium (a-Se) detectors was proposed. The purpose of this paper is to develop a complementary model that includes two additional features. First, the incidence angle and the directionality of ray incidence are calculated at each position, assuming a divergent x-ray beam geometry. This approach allows the non-stationarity of the PSF to be modeled. Second, this paper develops a framework that is applicable to a digital system, unlike previous work which did not model the presence of a thin-film transistor (TFT) array.
At each point on the detector, the incidence angle and the ray incidence direction are determined using ray tracing. Based on these calculations, an existing model for the PSF of the x-ray converter (Med Phys. 1995;22:365-374) is generalized to a non-stationary model. The PSF is convolved with the product of two rectangle functions, which model the sampling of the TFT array. The rectangle functions match the detector element (del) size in two dimensions.
It is shown that the PSF can be calculated in closed form. This solution is used to simulate a digital mammography (DM) system at two x-ray energies (20 and 40 keV). Based on the divergence of the x-ray beam, the direction of ray incidence varies with position. Along this direction, the PSF is broader than the reference rect function matching the del size. The broadening is more pronounced with increasing obliquity. At high energy, the PSF deviates more strongly from the reference rect function, indicating that there is more blurring. In addition, the PSF is calculated along the polar angle perpendicular to the ray incidence direction. For this polar angle, the shape of the PSF is dependent upon whether the ray incidence direction is parallel with the sides of the detector. If the ray incidence direction is parallel with either dimension, the PSF is a perfect rectangle function, matching the del size. However, if the ray incidence direction is at an oblique angle relative to the sides of the detector, the PSF is not rectangular. These results illustrate the non-stationarity of the PSF.
This paper demonstrates that an existing model of the PSF of a-Se detectors can be generalized to include the effects of non-stationarity and digitization. The PSF is determined in closed form. This solution offers the advantage of shorter computation time relative to approaches that use numerical methods. This model is a tool for simulating a-Se detectors in future work, such as in virtual clinical trials with computational phantoms.
在之前的工作中，提出了一种用于计算非晶硒（a-Se）探测器中倾斜 X 射线入射的点扩散函数（PSF）的理论模型。本文的目的是开发一个补充模型，该模型包含两个附加功能。首先，在每个位置计算入射角和射线入射方向，假设使用发散 X 射线束几何形状。这种方法允许对 PSF 的非平稳性进行建模。其次，本文开发了一种适用于数字系统的框架，与之前不模拟薄膜晶体管（TFT）阵列存在的工作不同。
在探测器的每个点上，使用射线追踪确定入射角和射线入射方向。基于这些计算，将 X 射线转换器 PSF 的现有模型（Med Phys. 1995;22:365-374）推广到非平稳模型。PSF 与两个矩形函数的乘积卷积，这两个矩形函数用于模拟 TFT 阵列的采样。矩形函数在两个维度上与探测器元件（del）尺寸匹配。
结果表明，可以以封闭形式计算 PSF。该解决方案用于模拟两种 X 射线能量（20 和 40 keV）的数字乳腺摄影（DM）系统。基于 X 射线束的发散，射线入射方向随位置而变化。沿着这个方向，PSF 比匹配 del 尺寸的参考矩形函数更宽。随着倾斜度的增加，变宽更为明显。在高能下，PSF 与参考矩形函数的偏差更大，表明模糊程度更高。此外，PSF 是沿着与射线入射方向垂直的极角计算的。对于这个极角，PSF 的形状取决于射线入射方向是否与探测器的边平行。如果射线入射方向与探测器的任何一个维度平行，PSF 就是一个完美的矩形函数，与 del 尺寸匹配。但是，如果射线入射方向相对于探测器的边成倾斜角，则 PSF 不是矩形。这些结果说明了 PSF 的非平稳性。
本文证明，可以将用于计算非晶硒探测器 PSF 的现有模型推广到包括非平稳性和数字化的影响。PSF 以封闭形式确定。与使用数值方法的方法相比，该解决方案具有计算时间更短的优点。该模型是未来工作中模拟非晶硒探测器的工具，例如在使用计算体模的虚拟临床试验中。
