Fan beam projection

Figure 2.5. The transverse field of view determined by the acceptance angles of individual detectors in a PET scanner. Each detector is connected in coincidence with as many as half the total number of detectors in a ring and the data for each detector are acquired in a fan beam projection. All possible fan beam acquisitions are made for all detectors, which define the FOV as shown in the figure. (Reprinted with the permission of The Cleveland Clinic Center for Medical Art Photography 2009. All Rights Reserved).

Positron scanners comprised of BGO or LSO detectors are arranged in full or partial rings, and each detector is connected to a number of opposite detectors in coincidence. If there are N detectors in the scanner, what is the maximum number of fan-beam projections available for coincidence counting ... 

A sinogram is a (a) hie containing individual annihilation events, (b) a matrix of parallel projection data, (c) a matrix of fan beam projection data, and (d) reconstructed image. 

FIGURE 26.21 Fan beam projection with varying angle. 

The Fan Beam Reconstruction. With a slit collimated fan beam of x-rays, a projection is formed by the illumination of a fixed line of detector cells. A common detector structure in this respect is the equally spaced collinear array. The projection data for this geometry is represented by the function P ), where )3 is the projection angle of a typical ray path SB and p is the distance along the detector line D,D2 to a point at B (Fig. 26.22). To simplify the algebra, the fan beam projection R ) is referred to the detector plane moved to DJ/Dj. The ray path integral along SB is now associated with the point A on this imaginary detector line aXp = OA (Fig. 26.23). 

Using the geometric relations (26.74), the reconstruction (26.76) can be expressed in terms of the fan beam projection R ), to give... 

If the fan beam projection data set is represented as PaiiPi), where and a represent the detector position and rotation angle of the beam, respectively (Fig. 2), then the relation between parallel and fan beam projection data with coordinates x, cp) and ai, P ) can be represented as... 

Fig. 18. Geometry of fan-beam coherent scatter computed tomography. A fan beam is used to illuminate one object slice. The central detector row (in the plane of the drawing) receives the transmitted radiation while the out-of-plane rows receive only scattered radiation. The coordinate represents the projection angle whereas...

If a parallel projection were impressed upon this geometry, the ray SA defined by (r, 9) would belong to the one-dimensional image Pfr). The relationship between the parallel-beam and fan-beam cases is given by... 

The third generation scanners a fan beam of X-rays is rotated 360° around the patient. A curved detector array consisting of several hvmdred of independent detectors is mechanically coupled opposite to the X-ray source, and both rotate together. No translation motion is used. The fan beam must be wide enough to completely contain the patient. The projection data for a single image are acquired in as little as 1 s. 

Leng S, Zhuang T, Nett BE, Chen GH (2005) Exact fan-beam image reconstruction algorithm for truncated projection data acquired from an asymmetric half-size detector. Phys Med Biol 50 1805-1820... 

The entire DSR system is conveniently divided into the DSR scanner section, the reconstruction section, and the data analysis section. The reconstruction system utilizes a filtered back-projection fan beam reconstruction system based on a floating point array processor (Robb et ai, 1980). Most important to the... 

Early spiral-CT scanners (34) provided stacks of cross-sectional CT sections. However, the slices were separated in time. The DSR acquired all the slices simultaneously but cone-beam reconstructions required a prohibitive amount of computation time. Tomography slices in medical CT have, until recently, been generated from one-dimensional projections via fan-beam methods. 

The fan beam reconstruction algorithm given in Eq. (8) consists of three parts (1) weighting the projection data with J Pi), (2) convolution with g P ), and (3) weighted backprojection with weight l/V. ... 

The project of vortex zone replacement is shown in Figure 12. The technological parameters of replacement management is determined by the parameters of pneumatic fan, the details are as follows ) The center angle corresponding to the arc AC is 60°, 2) The vertical distance of AB is 3.0 meters, 3) The horizontal distance of BC is 2.0 meters, 4) The height of airtight wall and replacements equals the roof of upper roadway, 5) The normal distance from pneumatic fan to BC is 5.0 meters, 6) Pneumatic fan is fixed on the posterior column of end support, and 5 meters away from the upper beam, 7) The type of pneumatic... 

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