By Peter W. Hawkes
Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This sequence beneficial properties prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photo technology and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in a majority of these domain names.
An vital function of those Advances is that the themes are written in the sort of means that they are often understood through readers from different specialities.
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A Pi-line contains x and two points y H (sπ1 ), y H (sπ2 ) on the helix with sπ2 −sπ1 < 2π. s sπ2 belong to the Pi segment All points y H (s) on the helix with sπ1 of x. The lower and upper Pi-window boundaries are given by Eq. (32) setting n = 1. From every point y H (s) within the Pi segment, x is projected onto the planar detector between these boundaries. For the reconstruction algorithm discussed here, the Pi segment corresponds to the backprojection segment CBP (x). Since the combination of the Pi-line and the Pi segment gives a closed contour, every Radon plane containing x intersects with the Pi segment.
Similar to the factor 1/ cos λ in Eq. (80), it depends only on the detector position. This factor can therefore be taken into account by an object-point– independent modification of the filtered projection data. Functions uP (x, s) and vP (x, s) correspond to the coordinates of the object point x projected onto the planar detector from y(s). These coordinates are given by Eqs. (63) and (64) for γ = 0. 7. Backprojection Using Wedge Detector Geometry The backprojection formula [Eq. (82)] contains a factor 1/|x − y(s)|.
RECONSTRUCTION ALGORITHMS 29 F IGURE 21. The two points P = (uP , vP ) and P = (uP , vP ) on the κ-line are separated by angle γ . The dashed line is orthogonal to the κ-line and has length . The three solid lines originating from the focal spot have lengths r, r , and r . transformed so that the points on the filter lines can be sampled equidistantly in ϕ. With the subsequent derivation we follow Noo, Pack and Heuscher (2003) but aim for a slightly different result. Consider Figure 21. It shows the planar detector and one particular κ-line.
Advances in Imaging and Electron Physics, Vol. 151 by Peter W. Hawkes