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 technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in these kinds of domain names.
An very important characteristic of those Advances is that the themes are written in this kind of approach that they are often understood by means of readers from different specialities.
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Extra resources for Advances in Imaging and Electron Physics, Vol. 151
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. (59), and uP (ϕ ) is given by Eq.
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 . Again, the sign change occurs exactly at the transition from a 3-plane to a 1-plane, since the projected Pi-line is parallel to the vP -axis.
The tangent on the trajectory, is parallel to the planar detector for the trajectories considered. Figure 23 shows exemplary vectors e and ω. The projections of these vectors ˆ In particular, the κ-line is onto the planar detector are denoted as eˆ and ω. parallel to eˆ , while ωˆ is orthogonal to Lω . Here, Lω is the line that results from the intersection of the Radon plane with the detector. Explicit expressions for eˆ and ωˆ can be obtained via eˆ = (e × b) × w (87) ωˆ = (ω × w) × w = ω + w(ω · w).