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, photo technology and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kinds of domain names.
An vital characteristic of those Advances is that the topics are written in one of these method that they are often understood via readers from different specialities.
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Additional resources for Advances in Imaging and Electron Physics, Vol. 151
With the line indicated by ωˆ 1 and rotating counterclockwise, the associated Radon plane becomes a 3-plane as soon as the line intersects with the circle. Now, since the filter line is tangential on the circle, ωˆ · eˆ changes sign exactly at the transition from a 1-plane to a 3-plane. The next sign change occurs when the dashed line becomes parallel to the vP -axis—remember that we ˙ = 1. Therefore, we must change ωˆ from pointing to the left to want sgn(ωˆ · y) pointing to the right, once the dashed line becomes parallel to vP .
58) can be evaluated using projections onto the planar detector. 3. Mathematically Complete Trajectories The foregoing discussion showed that we want to define the parameters of our reconstruction algorithms in such a way that Eq. (58) results in a constant value of 1. Here we elaborate on the requirements that the trajectory must fulfill. The result is known as the Tuy condition (Tuy, 1983). 24 BONTUS AND KÖHLER F IGURE 17. Every Radon plane intersects at least once with the helix (left). The circular trajectory is incomplete for object points located outside of the circle plane (right).
Dϕ cos2 ϕ (76) Using this in Eq. (74), we obtain r cos ϕ dϕ dγ = . sin γ r cos ϕ sin(ϕ − ϕ) (77) The latter equation still contains quantities r and r . From Figure 21 we can establish r 2 cos2 ϕ = R 2 + u2P + vP2 cos2 ϕ = R 2 1 + tan2 ϕ + tan2 λ cos2 ϕ cos2 ϕ = R2 , cos2 λ (78) where we have used Eqs. (9) and (10). Now the integration measure can be written as dγ cos λ dϕ = . sin γ cos λ sin(ϕ − ϕ) (79) Comparing this result with Eq. (47) allows us to write the filtering step as π Pν (s, uP , vP ) = −π dϕ cos λ D y(s), uP (ϕ ), vP (ϕ ) , sin(ϕ − ϕ) (80) where vP (ϕ ) = vP uP (ϕ ) , (81) vP (uP ) is defined in Eq.
Advances in Imaging and Electron Physics, Vol. 151 by Peter W. Hawkes