Cone-beam geometry

To contribute to a voxel (r, s, z) for z 0 in the cone beam geometry, the fan beams must be tilted out of the r, s plane to intersect the particular voxel (r, s, z) from various x-ray source orientations. As a result, the location of the reconstruction point in the tilted system is now determined by a new coordinate system (r, s) (Fig. 26.25). Consequently, the fan beam geometry in these new coordinates will change. Specifically, the new source distance is defined by... 

For CT scanners with 16 and more slices, modified reconstruction approaches accounting for the cone-beam geometry of the measurement rays have to be considered the measurement rays in MDCT are tilted by the so-called cone angle with respect to a plane perpendicular to the z-axis. The cone angle is largest for the shoes at the outer edges of the detector, and it increases with increasing number of detector rows if their width is kept... 

Micro-CT typically utilizes cone-beam geometry and is thus true volume CT . The term volume CT or volumetric CT has been used in association with the Mayo Clinic effort to build the dynamic spatial reconstmctor (DSR) (33). The recent development of multislice row (MDCT) scanners represents a significant movement toward the use of true cone-beam geometry. Micro-CT offers a unique opportunity to test the mathematics and image processing needs of clinical scanners. 

The practical implementation of cone-beam systems requires a choice of scanning geometry and of a reconstruction method. The good answers to both these questions simultaneously can hardly be obtained. 

Multi-row detector systems are referred to as cone-beam systems. With a moving conveyor they become helical cone-beam systems. The cone-beam designation is in contrast to the fan-beam geometry used in Figures 3 and 4, where the source and detectors are aU in a single plane. 

The last twenty years have seen the introduction of novel XDI geometries based on pencil beams [4], cone beams [5], fan beams [6], parallel sheet beams [7] and inverse fan beams [6], These are all, indeed, special cases of a general 3-D arrangement synthesized from a generic 2-D section [6],... 

The Cone Beam Reconstruction. With a cone beam of x-rays, a projection is formed by the illumination of a fixed area of detector cells (Fig. 26.24). A common detector structure in this respect is the equally spaced collinear cell array. The projection data for this geometry is represented by the function R (po, qo). where j3 is the source angle, the horizontal position, and q the vertical position, on the detector plane. 

Fig. 2.6. Typical scattering geometry (vertical cut) showing the intersection of the atomic beam, electron beam, and viewing cone of the analyser. Ai and A2 are the apertures in the detector defining the viewing cone.

Beam Exposure and Research Facility) chamber of the ISL heavy ion accelerator of the Hahn-Meitner-Institute, Berlin, Germany, at a flux of typically 0.1 nA up to fluences of 5><10 cm. The resulting latent SHI tracks produced in the oxide layer were etched by 1.35 wt.% HF solution at 20 1 C for 40 min, until the track opening was detected. The geometry of etched tracks (nanopores) is a truncated cone with the base diameter of 150-200 nm at the Si/SiOa interface and 250-300 nm on the top. The final depth of pores (200 nm) was less than the initial thickness of Si02 layer due to etching process of Si02 film. 

There are several possible factors which may account for the difference between the fee (111) and (110) surfaces. Firstly, the presence of the surface layer relaxation means that, in the one layer incident geometry (Fig. 3), the shadow cone created by the ions incident on the surface atoms is sufficiently narrow at the second layer atoms that the latter become visible to the incident beam. If the surface layer relaxation is different for the (111) and (110) surfaces of CuPd, this may account for some or aU of the extra illumination. The second major factor is potentially the enhanced vibrations of surface atoms. The top layer atoms of the fee (110) surface are only 7 coordinate compared with 9 coordinate atoms on the (111) surface and 12 for atoms in the bulk. A consequence of this low coordination number is that the top layer atoms vibrate with a considerably larger amplitude than those of the bulk. As a result, even in... 

Figure 2.31. The origin of the powder diffraction eone as the result of the infinite number of the completely randomly oriented identical reciprocal lattice vectors, d hki, forming a circle with their ends placed on the surface of the Ewald s sphere, thus producing the powder diffraction cone and the corresponding Debye ring on the flat screen (film or area detector). The detector is perpendicular to both the direction of the incident beam and cone axis, and the radius of the Debye ring in this geometry is proportional to tan20.

Fig. 1.6. Beam directioning during soft-landing the focusing octopole ion guide. The schematics present a 3D view of the newly constructed conical octopole guide. Eight rods shaped as truncated cone (diameter rejuvenates from 3 to 0.5 mm) are arranged in a conical geometry. Two Teflon plates at the ends with four carriage bolts and two metal collars (in the cylindrical part) keep the conical geometry. The ion entrance orifice opens 9 mm in iimer diameter and the exit focuses to around 2-mm spot size [74]...

Upper-layer photographs are usually recorded in equi-inclination geometry (i.e.fi-— v, see equations (A1.8) and (A1.9)). The X-ray beam direction is made coincident with the generator of the cone of the dif-... 

Fig. 4.27 The geometry in the ion beam sputtering unit is shown. Two water cooled ion guns form a cone of ions/atoms of argon which are focused on the metal target. The sputtered metal is then focused onto the rotating specimen.

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