Tomography of laser fusion plasmas Page: 3 of 21
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shadow focuses the incident radiation to a diffraction limited point - the
image of its associated source point. The information contained in the three
dimensional image distribution is retrieved by viewing the image in "sections",
that is, in separate reconstruction planes. Ideally there is a one to one
correspondence between each reconstruction plane and each source plane." In
this way a three dimensional source distribution may be synthesized plane by
Tomographic Resolution Limit
A topographic resolution criterion for the ZPCI technique has been de-
rived from reconstruction calculations fbr an on-axis point source pair of
equal intensity separated by a longitudinal (i.e., normal to the zone plate)
distance, A. Such a criterion, based on point pair resolutions, can at best
serve only as a crude figure of merit for determining the tomographic discrim-
ination capability of ZPCI for a particular three dimensional source distribu-
tion. The precise three dimensional intensity distribution within the source
will significantly affect the tomographic discrimination capability of the
Figure 4 displays results of the reconstruction calculations for a
point source pair. The (on axis) intensity distribution in the reconstructed
image is plotted versus normalized axial distance for four representative
values of the tomographic parameter, a.
a = 23N S + (1)
N equals the total number of zones in the coded aperture, A is the axial
separation of the point source pair, S1 S2 are the source to zone plate and
zone plate to shadowgraph distances respectively. (A << S)
Distance along the horizontal axis is normalized to the nominal point-
pair image separation distance. The nominal reconstruction positions for the
point images in Fig. 4 are at values 2 and 3 along the horizontal axis. Fig.
4 shows that at a = 8.25 the two points are well resolved and the peaks of the
double hump intensity distribution occur at the nominal reconstruction posi-
tions. At a = 3.53 the two points are not resolved. Within the range of
4.71 < a < 7.07 a double hump intensity distribution occurs in the image re-
construction, but interference from sidelobe contributions causes the peak-
to-peak separation to exceed the nominal separation for the reconstructed
points. For the purpose of this discussion a = 4.71 shall be chosen to de-
fine a condition of suitable tomographic resolution.5 This provides an
intensity ratio greater than two between peak and saddle, allowing the clear
identification of the existence of two spatially separated contributions to
the reconstructed image. This yields an expression for the ZPCI tomographic
A(S1 + 2) (2)
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Ceglio, N.M. Tomography of laser fusion plasmas, article, August 2, 1977; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1056429/m1/3/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.