Metzler S D, Accorsi R
Department of Radiology, The University of Pennsylvania, Philadelphia, PA 19104, USA.
Phys Med Biol. 2005 Nov 7;50(21):5005-17. doi: 10.1088/0031-9155/50/21/004. Epub 2005 Oct 12.
To account for photon penetration, the formulae used to calculate the geometric resolution of a pinhole collimator use an effective diameter d(e) rather than the physical diameter of the aperture. The expressions commonly used for d(e), however, were originally derived to include penetration in sensitivity calculations. To predict the full width at half maximum (FWHM) resolution of the point-spread function (PSF) of a knife-edge pinhole collimator, we have previously proposed simple expressions for a resolution-effective diameter d(re). Unlike those for d(e), expressions for d(re) predict both a dependence on the polar angle of the source (theta) and a non-isotropic PSF. In this paper, the new theory was tested by measuring experimentally the FWHM of the PSF. Results confirm the theoretical predictions that (a) d(re) provides the best estimates of the experimental FWHM as a function of theta and of the direction in the plane of the pinhole, (b) Paix's expression for d(e) tends to overestimate the FWHM, (c) Anger's is a better approximation, but still cannot predict the dependence on theta, and (d) the FWHM decreases with decreasing theta, i.e. resolution improves for sources at the edge of the field-of-view.
为了考虑光子穿透，用于计算针孔准直器几何分辨率的公式使用有效直径d(e)，而不是孔径的物理直径。然而，通常用于d(e)的表达式最初是为了在灵敏度计算中纳入穿透而推导出来的。为了预测刀口针孔准直器点扩散函数（PSF）的半高宽（FWHM）分辨率，我们之前已经提出了分辨率有效直径d(re)的简单表达式。与d(e)的表达式不同，d(re)的表达式预测了对源极角（θ）的依赖性以及非各向同性的PSF。在本文中，通过实验测量PSF的FWHM对新理论进行了检验。结果证实了理论预测，即（a）d(re)作为θ和针孔平面内方向的函数，能最好地估计实验FWHM；（b）Paix的d(e)表达式往往高估了FWHM；（c）Anger的表达式是一个更好的近似，但仍然无法预测对θ的依赖性；（d）FWHM随着θ的减小而减小，即对于视野边缘的源，分辨率提高。
