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

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 positive factors prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technology and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in a majority of these domain names.
An vital function of those Advances is that the themes are written in this sort of approach that they are often understood through readers from different specialities.

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2 R (30) From Eq. (29) we determine vP = h¯ 1 + uP R 2 s¯ − (n + 1)π, lower boundary, s¯ + (n − 1)π, upper boundary (31) where we inserted Eq. (30) into the denominator of Eq. (29) and used Eq. (21). Now, using Eq. (30) again and making use of arccot uP /R = π/2 − arctan uP /R, we derive up,low ,n (uP vP ) = ±h¯ 1 + uP R 2 n uP π ∓ arctan 2 R . (32) The latter equation gives the upper and lower boundaries of the n-Pi window on the planar detector. Figure 9 shows the corresponding curves for cases n = 1, 3, and 5.

We could apply just the algorithm defined above for both cases and average the results. More efficiently, we obtain the same output by performing the backprojection over the complete circle using the filter lines defined above. For the line, we filter the data using both sets of filter lines and add the data before backprojection. In other words, we need to 38 BONTUS AND KÖHLER set Ne = 2 in Eqs. (82) and (86). Weights μν must be multiplied by 1/2 for the line part. 3. Proof of Exactness We now prove that the reconstruction algorithm is mathematically exact.

The points of intersection are denoted as Pπ c and Pπ , respectively. For the backprojection segment, which is drawn in bold, the two possibilities are shown in the left and right images. 36 BONTUS AND KÖHLER F IGURE 26. Left: The two Radon planes each have one IP with the backprojection segment. Right: The Radon plane has three IPs. For the other possibility of CBP (x), this plane corresponds to a 1-plane. 2. B can be used to parameterize each filter line using planar-detector coordinates. In particular, we specify pairs of constants v0 and σ , which define a filter line in the sense of Eq.

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


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