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

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, snapshot technology and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kind of domain names.
An vital characteristic of those Advances is that the topics are written in this kind of manner that they are often understood via readers from different specialities.

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All Radon planes are considered, which contain x. RECONSTRUCTION ALGORITHMS 17 F IGURE 13. Two-dimensional cut parallel to ω and containing x and the origin O. The Radon plane R is a straight line in this view, since ω is normal to R. We show that all Radon values that must have to be taken into account are located on the surface of a sphere in Radon space (Figure 13). This figure shows a 2D cut parallel to ω containing x and the origin O. The Radon plane R defined by ρ and ω is perpendicular to this view since ω is orthogonal to R.

Projection of the object point x into the xy-plane. While angle s is measured from the rotation axis, angle t is measured from the object point. Using this result, the backprojection formula Eq. (82) becomes μ(x) = −1 2π 2 I˜BP (x) dt R cos ϕ Ne μν P˜ν t, u (x, t), v (x, t) . ν=1 (86) Here, P˜ν (t, u , v ) corresponds to the filtered projection data rebinned into wedge geometry. Functions u (x, t) and v (x, t) yield the coordinates of the object point projected onto the wedge detector, and I˜BP (x) is the backprojection interval of x in parallel geometry.

C [see Eq. (15)]. Here, we have used the fact that y · w = R for the trajectories considered in this chapter. The point of intersection is parameterized by λ0 . From the latter equation we derive λ0 = −R . cos γ b · w + sin γ e · w (62) With these results points on the κ-line can be parameterized by angle γ as cos γ b · u + sin γ e · u , (63) cos γ b · w + sin γ e · w cos γ b · v + sin γ e · v vP (γ ) = (λ0 , γ ) · v(s) − yz (s) = −R , (64) cos γ b · w + sin γ e · w uP (γ ) = (λ0 , γ ) · u(s) = −R where we have used y · v − yz = 0.

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