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 positive factors prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in most of these domain names.
An vital function of those Advances is that the themes are written in this type of method that they are often understood through readers from different specialities.
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Extra resources for Advances in Imaging and Electron Physics, Vol. 151
We begin with some general observations. Remember that line L1 is the asymptote on the helix. Line L1 is parallel to y˙ H (s). We denote the line of intersection of the Radon plane and the planar detector as R. Now, we argue that projecting x into the Pi window from the first point of a 3-plane, the point of projection must be above L1 . Line R must intersect twice with the CBP (x)part of the upper Pi-window boundary seen from the first IP (compare with Figure 34). If x is projected below L1 , line R must be steeper than line L1 in order to have an intersection with the upper Pi-window boundary.
Perform the backprojection along IBP (x)—evaluate Eq. (46). Steps 1 and 2 follow from Eq. (47): the filtering is performed along γ with kernel 1/ sin γ . The filtering depends on x only via b(s, x). Now, all object points on one particular line from the focal spot to the detector share the same b. Consider two vectors b1 and b2 , where b2 is located in the κ-plane of b1 . In many cases, b1 is also located in the κ-plane of b2 . Now the filtering step RECONSTRUCTION ALGORITHMS 25 is shift invariant.
Explicit expressions for eˆ and ωˆ can be obtained via eˆ = (e × b) × w (87) ωˆ = (ω × w) × w = ω + w(ω · w). C and b is defined in Eq. (44). Furthermore, we used the relation a × (b × c) = b(a · c) − c(a − b) above. Now, using the general formula (a × b) · (c × d) = (a · c)(b · d) − (b · c)(a · d) (89) twice and applying b · ω = 0, we derive eˆ · ωˆ = (w × ω) · (e × b) = −(b · w)(e · ω). (90) 34 BONTUS AND KÖHLER F IGURE 24. The planar detector seen from y(s2 ) in Figure 16. The intersection of the Radon ˆ The backprojection segment is drawn plane results in line Lω .
Advances in Imaging and Electron Physics, Vol. 151 by Peter W. Hawkes