Bal Girish, Acton Paul D
Department of Radiology, Thomas Jefferson University, Philadelphia, PA 19107, USA.
Phys Med Biol. 2006 Oct 7;51(19):4923-50. doi: 10.1088/0031-9155/51/19/013. Epub 2006 Sep 18.
The point spread function (PSF) of a pinhole collimator plays an important role in determining the resolution and characterizing the sensitivity of the accepted photons from a given point in the image space. The focus of this paper is to derive an analytical expression for the PSF of two different types of focusing pinhole collimators that are based on (1) right-circular double cones and (2) oblique-circular double cones. Conventionally, focusing pinhole collimators used in multi-pinhole SPECT were designed using right-circular double cones, as they were easier to fabricate. In this work, a novel focusing collimator consisting of oblique-circular double cones was designed and its properties were studied in detail with respect to right-circular double-cone based collimators. The main advantage of determining the PSF is the fact that they can be used to accurately model the PSF during the reconstruction, thereby improving the resolution of the reconstructed image. The PSF of the focusing collimators based on oblique-circular cones were found to be almost shift invariant for low and medium energy photons (below 200 keV). This property is very advantageous as algorithms such as slice-by-slice reconstruction can be used for resolution recovery thereby drastically reducing the reconstruction time. However, the PSF of focusing oblique-circular double cones (FOCDC) for higher energy photons were found to be asymmetric and hence need to be modelled more accurately during the reconstruction. On the other hand, the PSF for the right-circular cone based collimators were found to be asymmetric for all energy levels. However, due to the smaller acceptance angle used, the number of penetration photons was found to be far less than that observed for oblique-circular cones. This results in a smaller PSF making right-circular cone based collimators preferable for high-resolution small animal imaging, especially where very small pinhole diameters are used. The analytically derived PSF for both collimators were validated using a ray-tracing based Monte Carlo approach and found to agree well with a mean square error of less than 1%.
针孔准直器的点扩散函数（PSF）在确定分辨率以及表征图像空间中来自给定一点的接收光子的灵敏度方面起着重要作用。本文的重点是推导两种不同类型聚焦针孔准直器的PSF的解析表达式，这两种准直器分别基于：（1）右圆形双锥，以及（2）斜圆形双锥。传统上，多针孔单光子发射计算机断层显像（SPECT）中使用的聚焦针孔准直器是用右圆形双锥设计的，因为它们更容易制造。在这项工作中，设计了一种由斜圆形双锥组成的新型聚焦准直器，并针对基于右圆形双锥的准直器详细研究了其特性。确定PSF的主要优势在于，在重建过程中它们可用于精确模拟PSF，从而提高重建图像的分辨率。基于斜圆锥的聚焦准直器的PSF对于低能和中能光子（低于200keV）几乎是平移不变的。这一特性非常有利，因为诸如逐片重建等算法可用于分辨率恢复，从而大幅减少重建时间。然而，发现基于斜圆形双锥的聚焦准直器（FOCDC）对于高能光子的PSF是不对称的，因此在重建过程中需要更精确地建模。另一方面，发现基于右圆锥的准直器在所有能量水平下的PSF都是不对称的。然而，由于使用的接受角较小，发现穿透光子的数量远少于斜圆形圆锥的情况。这导致PSF较小，使得基于右圆锥的准直器更适合用于高分辨率小动物成像，特别是在使用非常小的针孔直径的情况下。使用基于光线追踪的蒙特卡罗方法验证了两种准直器的解析推导PSF，发现其均方误差小于1%，吻合良好。
