Digital Signal Processing Reference
In-Depth Information
Figure 10.20. (left) Surface structures of ICF spherical shells measured on the nanometer
scale are a superposition of global-scale variations, isolated bumps and scratches, and
artifacts that look like interference patterns on intermediate scales. (right) Coarsest scale of
the undecimated isotropic wavelet transform of the surface measurements of an ICF target.
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See color plates.
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Vehn 2004). Either way, the aim is to implode the capsule, which contains a shell of
nuclear fusion fuel (deuterium and tritium) ready to ignite if, after it has been im-
ploded, its density is high enough and a hot spot in its center becomes hot enough to
cause a propagating nuclear burn wave to travel through the rest of the fuel. This ul-
timate energy source will not work if, during the implosion, hydrodynamic instabili-
ties develop, which can break apart the shell before it assembles at the center and a
hot spot forms (Lindl 1997). Hydrodynamic instabilities, such as Rayleigh-Taylor in-
stability, occur due to nonuniformities in the laser spatial profile or imperfections in
the composition of the multiple surfaces that make up the layers of thin material that
surround the nuclear fuel. Very small amplitude imperfections initially can result in
the ultimate failure of the target due to the large compression ratios involved in ICF.
It is therefore extremely important to characterize the inner and outer surfaces
of ICF shell targets so as to know whether they are worthy of consideration for ICF
implosions. One day in a reactor setting tens of thousands of targets will have to
be imploded daily so that checking each one is totally out of the question. Instead,
very good target fabrication quality control processes have to be adopted so that
confidence levels in proper performance will be high. A major step along this path
to fusion energy, then, is to understand why imperfections occur and to correct the
systematic elements and control the harm done by random sources.
Fine structures on the surfaces of spherical shells can be measured on the
nanometer scale, among others, by atomic force microscopy or phase shifting spher-
ical diffractive optical interferometry. An example of such measurements is shown
in Fig. 10.20. As can be seen from the figure, there appears to be a superposition
of global-scale variations, isolated bumps and scratches, and artifacts that look like
interference patterns on intermediate scales of localization. The latter must be iso-
lated and eliminated from consideration when deciding the readiness of the target
for implosion.
We achieved morphological feature separation by first doing an isotropic
wavelet transform on the spherical data and subtracting the coarsest-scale informa-
tion. MCA on the sphere was used on the rest of the image using the undecimated
wavelet and the local cosine transforms on the sphere. The isolated bumps were thus
identified, and the artifacts caused by the measurement technique were removed
