Download e-book for kindle: Advances in Imaging and Electron Physics, Vol. 151 by Peter W. Hawkes

By Peter W. Hawkes

ISBN-10: 0123742188

ISBN-13: 9780123742186

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, photo technological know-how and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in a lot of these domain names.
An vital function of those Advances is that the themes are written in this sort of means that they are often understood through readers from different specialities.

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Extra info for Advances in Imaging and Electron Physics, Vol. 151

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94) Due to our choice of parameters the plane intersects with the planar detector at x = 0, such that 0 = 1 + α(cos s − 1) + β(cos 2s − 1) (95) RECONSTRUCTION ALGORITHMS 45 gives the condition for the points of intersection. Solving the latter equation for β results in 1 + α(cos s − 1) 1 + α(cos s − 1) = . (96) 1 − cos 2s 2 sin2 s Inserting this equation into Eq. (94), the y-component corresponds to the uP coordinate of the filter line: sin 2s sin 2s(cos s − 1) uP (α) = R + αR sin s + 2 2 sin s 2 sin2 s (1 − cos s) , (97) = R cot s + αR sin s or uP sin s − R cos s uP − R cot s α(uP ) = sin s = .

For this consider Figure 22. It shows a plane containing x and parallel to the x- and y-axes. The source path y(s) is projected into this plane. Variable ϕ corresponds to the fan angle under which the object point appears from the projected y(s). While s corresponds to the angular variation of the source position, variable t is the angle under which the source is seen from x. From Figure 22 we realize that L dt R ds = . (83) cos ϕ Here, L is the distance from the projected object point to the projected focalspot position.

46). It yields μ(x) ˜ = −1 8π 2 dΩ R μ(ω · x, ω)w(x, ω), (57) RECONSTRUCTION ALGORITHMS 23 F IGURE 16. The backprojection segment CBP (x) associated with IBP (x) for the object point x is drawn in bold along the helix. The Radon plane defined by x and ω has three intersection points with the helix: y(s1 ), y(s2 ), and y(s3 ). It has only one intersection point, y(s2 ), with CBP (x). where NI Ne (k) ˙ k ) sgn(ω · eν ). μν sgn ω · y(s w(x, ω) = k (58) ν=1 The sum over k is different from the sum over k˜ in Eq.

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Advances in Imaging and Electron Physics, Vol. 151 by Peter W. Hawkes


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