Looking sharp: Data analysis with superb accuracy

A cost-saving method with wide application in science and technology / publication in new eletronic journal

The method is always applicable when so-called "inverse problems" are involved. Identifying the effects of a known cause - say, possible shadow images of a given body - is usually a simple matter, but the inverse process is difficult: In this case it is the effects - the shadow images - that are known and one has to deduce from them the cause - the shape of the shadow-casting body. The possibly huge number of solutions available sometimes even makes it impossible to answer this question. Inverse problems abound in science, technology, and industry: e. g. in medicine when evaluating computer tomographies, in astronomy when calculating images with optimum focus from satellite data, or in materials technology when applying a variety of testing procedures.

The wide spectrum of such problems has hitherto been treated with a broad diversity of special methods. A universally applicable method that filters out the best, i. e. most probable, solution from all those possible has now been developed by the Surface Physics Division of IPP. The new "multi-resolution method" utilizes Bayes's probability theory. Description of the problem should be as simple but also as informative as possible: Just as an artist paints the small details in a picture with a finer brush than is used for the background, the new method provides better resolution in the areas where the measured data afford more information. Futhermore one can introduce additional information into the evaluation in a mathematically exact manner and hence from the outset eliminate useless, but mathematically admissible results. This obviates many difficulties which would otherwise make it impossible to solve inverse problems. Improved evaluation allows in many cases to overcome experimentally imposed resolution limits or else to reduce implementation of measuring equipment, this possibly leading to appreciable cost saving for the measurements.

Application in fusion research
The performance of the method was demonstrated in a problem from nuclear fusion research: The aim here is to develop a power plant which - like the sun - derives energy from fusion of atomic nuclei. This is done by heating the fuel, a low-density hydrogen plasma, to temperatures of up to 100 million degrees and confining it in magnetic fields. Individual particles from the hot plasma can, however, always escape from the magnetic cage and then impact at the enclosing vessel walls. In order to investigate the changes produced there, material samples were placed at particularly exposed sites in the ASDEX Upgrade fusion device at IPP.

Before and after exposure to the plasma the samples are investigated in the Surface Physics Division of IPP. Of particular interest is detecting where the surface is eroded under the influence of the plasma and where the particles thereby released are redeposited. To analyze the sample, it is bombarded with high energy helium ions. These can penetrate a few micrometers into the plasma until they are finally reflected by the sample material. As the helium particles loose more or less energy, depending on the penetration depth and mass of their collision partner, the energy of the repulsed particles then provides information on the composition of the sample. Determining the depth distribution from the test signals is now a typical inverse problem whose solution has hitherto been awkward and not always reliable. The multiresolution method - in conjunction with the mathematical description of the measuring process - has now provided a computer-aided solution. This yields the concentration profile sought and exact information on its reliability.

In the present case, it was found that, although there is erosion at the site investigated, even more material from other regions of the plasma vessel is deposited. In effect, this leads to layer formation, which is just as undesirable as damage to the wall, but has to be prevented by other means.

Not only the method itself, but also the publication was innovative: the report was published in a new purely electronic journal, the New Journal of Physics. There it recently appeared as the eleventh contribution (New Journal of Physics 1 (1999) 11). The journal was launched in the end of 1998 jointly by the German Physical Society and the British Institute of Physics. The new journal avoids the high costs of printed publications and provides free access everywhere and at all times to reputed research papers from the entire field of physics through the World Wide Web.

Isabella Milch