Advances in Imaging and Electron Physics, Vol. 103 by Peter W. Hawkes (Ed.) PDF

By Peter W. Hawkes (Ed.)

ISBN-10: 0120147459

ISBN-13: 9780120147458

Advances in Imaging and Electron Physics merges long-running serials--Advances in Electronics and Electron Physics and Advances in Optical & Electron Microscopy . The sequence good points prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in a majority of these domain names.

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Example text

1 is the Hilkert transformi This expression involves a sum of two real waveforms: 'a1Re 6 and aRZRe 6. YR > 0 but a1 may be any number; if IYI = 0, then (62) is a pure Hilbert transform of (48)]. In order to understand the waveforms involved in (62), we spall express them explicitly in a standard form. Noting that the argument of the 6 function in (62) has an imaginary part, we shall express it symbolically as 6(r - i c ) where E = TO ; C - ' ~ R sin 8 > 0. Expression (62) involves, therefore, the following standard waveforms: i + + 1 & ( t ) = Re6(t - i c ) = - 1 l7€ ( t / € ) 2 t 1 'Hl&(t)= Im6(t - i c ) = - l7E +1 -t/c (f/€)* +1 The amplitude of+the radiation pattern (62) is controlled by the imaginary part of the argument of 6: c = ;To ; c - ' ~ Rsin8 > 0.

The parameters are: F = 9 and DO(@)= F / 9 so that Do(&) = ~ D o ( w zand ) DO(OI) = -~Do(Y). Thus, here the near-to-far transition is essentiallyfrequency independent whereas in (105) it exhibits a low-frequency loss. Following the interpretation given to (l05), it follows that the flat response in the present case is associated with the fact that here all the frequency components stay collimated up to the same collimation distance OIR (see Fig. 13). The time-dependent field corresponding to (107) is given by ( 8 5 ) with 41,2 = O I R .

The expressions in (97) and (98) are the frequency spectra of the PB fields in (80) and (83, respectively, only if I? and a, are frequency independent. This implies that all frequency components in the PB are Gaussian beams with the same waist planes and collimation distances. At a given z , their phasefront curvatures are frequency independent but their widths are proportional to @-‘I2 as described in (99). Thus, the PB can be synthesized by an ultra wideband source distribution (say, in the z = 0 plane) provided that the width of this distribution is proportional to @-1/2.

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Advances in Imaging and Electron Physics, Vol. 103 by Peter W. Hawkes (Ed.)


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