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The steps of a 2-D image reconstruction from its 1-D projections shown in Figure 42 are as follows: 1 Obtain 180 1-D projections of f (x, y), p(x, ) where = 1, , 180 2 Perform the FT on each 1-D projection 3 Arrange all these 1-D FTs according to their corresponding angles in the frequency domain The result is the 2-D FT of f (x, y) 4 Perform the 2-D IFT, Inverse of the 2-D FT, of step 3, to obtain f (x, y) The Fourier projection theorem forms the basis of tomographic image reconstruction Other methods to reconstruct a 2-D image from its projections are discussed later in this section We emphasize that the reconstructed image from projections is not always exact; it is only an approximation of the original image A different reconstruction method will give a slightly different version of the original image.

aperture before entering the ampli er system through polarizing beamsplitter P1. An anamorphic telescope takes the input from its 25 25-mm2 size to the 7 120mm2 used in the glass ampli er aperture. The input beam enters the regenerative ampli er ring in p-polarization through polarizing beamsplitter P2 and undergoes two gain passes. The polarization is then rotated 908 by a quartz rotator and the beam re ects from the same beam splitter in s-polarization, undergoing two more gain passes. When the polarization is returned to the original p-state after the second pass through the rotator, the beam is coupled out through polarizer P3 and directed into the SBS phase conjugate mirror. The re ected beam from the phase conjugator retraces the path of the input beam, adding four more gain passes for a total of eight. The polarization rotation of the 458 Faraday rotator and the 458 quartz rotator cancel each other in the input direction, but now, in the output direction, they add, resulting in a full 908 rotation. The ampli ed beam is therefore re ected by polarizer P1 and enters the doubler. Since the output beam passes back through the anamorphic input telescope, the 25 25-mm2 beam size is restored before reaching the doubler. 5.4.2.2 Long-pulse energy extraction For a given laser ampli er chain, it is possible in theory to generate any desired output temporal pulse shape by correctly tailoring the input pulse shape, taking into account the effects of energy extraction and total system gain. In order to determine this optimal input shape for a 500-ns rectangular pulse, a straightforward numerical treatment of the long-pulse extraction problem can be made. In the case of a solid-state energy storage medium such as Nd:glass, the uorescence lifetime of *300 ms and ashlamp pulse duration of

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5.6 DESIGNS WITH TRUNCATED CORNERS The technique of truncating the patch corners of a simple square microstrip patch to obtain single-feed CP operation of microstrip antennas has been widely used in practical designs. In this section, we demonstrate that such a technique can also be applied to single-feed microstrip antennas with a triangular patch [14], a square-ring

Since all these methods require extensive computation, specially designed image reconstruction hardware is normally used to implement the algorithm The term computerized (computed) tomography (CT) is often used to represent that the image is obtained from its projections using a reconstruction method If the 1-D projections are obtained.

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Increasing k for the conventional methods did increase the amount of communication. However, for the fractional method, the amount of communication increased only marginally with a larger Q. Data migration was slightly worse for the fractional method. While the number of boxes grew linearly with k for the conventional methods, it grew only marginally for the fractional method. Moreover, the average number of boxes per processor was close to one for all Q.

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