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 gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in these types of domain names.
An vital characteristic of those Advances is that the topics are written in one of these manner that they are often understood by way of readers from different specialities.
Read Online or Download Advances in Imaging and Electron Physics, Vol. 151 PDF
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Additional info for Advances in Imaging and Electron Physics, Vol. 151
Sample text
The object ˆ The dotted lines in point is projected onto different positions indicated by x. Figure 34 correspond to the intersections of the Radon plane with the detector. F IGURE 33. point x. The three IPs of the Radon plane are located within the Pi segment of object RECONSTRUCTION ALGORITHMS 43 F IGURE 34. The planar detector seen from the three IPs y H (s1 ) through y H (s3 ) in Figure 33. ˆ The dotted lines indicated by R correspond to the The object point is projected onto points x. intersections of the Radon plane.
The 3D Radon transform is the set of all plane integrals through a given object function. We parameterize Radon planes by normal vectors ω and scalars ρ, where ρ is the shortest distance of the plane to the origin (Figure 12). With these conventions the Radon transform of object 1 Johann Radon, Austrian mathematician, 1887–1956. 16 BONTUS AND KÖHLER F IGURE 12. An exemplary Radon plane with normal vector ω. The dashed line has the length ρ, which is the shortest distance from the origin to the plane.
They are separated by an angle γ seen from the focal spot. The dashed line is orthogonal to the κ-line and has length . Using the formulas, which compute the area of a triangle, we observe that L = rr sin γ and L = r r sin γ . Hence, r sin γ L = . L r sin γ At the same time L/L = (72) uP /(uP − uP ), such that uP uP r sin γ . = − uP r sin γ (73) Since we are interested in infinitesimal quantities, this yields duP r dγ . = uP − uP r sin γ (74) For the transition to focus-detector coordinates, we realize by comparison with Eq.