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By Dana H. Ballard, Christopher M. Brown

The publication is prepared into 4 components, in accordance with descriptions of gadgets at 4 varied degrees of abstraction. 1. Generalized images-images and image-likeentities. 2. Segmented images-images equipped into subimagcs which are more likely to correspond to "interesting gadgets. three. Geometric structures-quantitative types of imageand global buildings. four. Relational structures-complex symbolic descriptions of snapshot and international buildings.

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Here A(z) = - i a / ( z - ia)so that AR = [al(a~ + z ) +cr:]/[(a~ z ) ~ a:] and A / = - ~ R z / [ ( u I z)* a:]. JNote that the astigmatic PB in (66) is a special case of this example with f ( t ) + S(r - TO)]. , the waists in both principal directions are at z = 0). Here the waveforms change from f,,in the z = o plane to z-',/-'Flf, as z + 00. - + + + + + 37 SPACE-TIME REPRESENTATIONOF ULTRA WIDEBAND SIGNALS 4. The Aperture Field The PB distribution in the aperture plane is found from (80) (89) For simplicitylet us assume that Im I'(0) = 0, so that the initial wavefront is planar.

For simplicity we take a = a~ to be real. As discussed in (98), a~ is the (frequency-independent)collimation (or diffraction) distance. The width of the distribution is given by Do of (99), and thus changes with frequency like w - ' / ~(see Fig. 13). 2 = a ~ Thus, . z. - .... ,.... -__ - .. -... p l , . -2 , ,,, -. - ___ _-_. -----------; , . -. - IF i'p -- . __. ~ .. , __ - . 15 ~ _ 2. FIGURE 13. Radiation from an ultrawideband isodiffracting aperture with a Fresnel distance F . The figure depicts the beamwidth in the ( p .

Are the propagation lines [see discussion in connection with (83)l. The thick line in the z = 0 plane represents the rigorous source distribution for the globally exact complex source pulsed beam [30]. A. General Solution We consider pulsed beam (PB) solutions u(r, t ) of the time-dependent wave equation (a:, + a2: +a: - c-*a:)u(r, t ) = o (71) in a medium with uniform wave velocity c. It is assumed that the PBs propagate along the z-axis in the coordinate frame r = (x,z), x = ( X I , x 2 ) (Fig.

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