Một cách dễ dàng để đại diện cho đồ họa hình học hình ảnh để biểu thị mỗi chiếu pq, f (u, v) là một dấu chấm trên một quả cầu đơn vị, tương ứng với các góc độ hình cầu q và f. Cầu đơn vị này còn được gọi là của lĩnh vực Orlov (89). Vẽ hình học hình ảnh trên mặt cầu Orlov giúp xác định liệu các điều kiện cần và đủ hài lòng, trung thành xây dựng lại | 158 Chapter 10 Coincidence Imaging W. An easy way to graphically represent the imaging geometry is to denote each projection p0f u v as a dot on a unit sphere corresponding to the spherical angles 0 and f. This unit sphere is also called Orlov s sphere 89 . Plotting the imaging geometry on the Orlov sphere helps to determine whether the necessary and sufficient conditions are satisfied to faithfully reconstructf x . The imaging geometry W can be considered to be complete and a faithful reconstruction can be obtained by inverting Equation 1 provided the imaging geometry W intersects every great circle on the Orlov sphere. Let us now illustrate some of the 3D imaging geometries used in PET as well as in GCPET on the Orlov sphere. The simplest 3D imaging geometry is the one obtained by using a parallel slat collimator and rotating the GCPET system around the longitudinal axis of the patient for 360 degrees. The data are acquired in the 2D mode and the projection data is rebinned as a set of 2D parallel projections. If we assume the longitudinal axis of the patient as the z-axis on the Orlov sphere then this geometry corresponds to an equatorial circle perpendicular to the z-axis on Orlov s sphere. The center of this equatorial circle coincides with the center on the sphere as shown in Figure . This equatorial circle is also called a great circle and the geometry is mathematically denoted as W2p 0 0 p 2 fe 0 2p . A popular PET geometry is the equatorial band on the Orlov sphere that can be obtained by either rotating an uncollimated 2D planar GCPET detector around the longitudinal axis of the patient or using a stationary truncated spherical cylindrical PET detector. For the GCPET system the data are acquired in the fully 3D mode with the oblique rays considered as parallel ray projections. As shown in Figure the parallel projections are obtained for the polar angle 0 ranging from p 2 - y to p 2 y and for the azimuthal angle f varying from 0 to 2p. .
