In engineering, plasma – an ionised gas – is used for processing materials; in chemistry, it is used for synthesizing new compounds and nanostructures, and in physics, for performing study of lightning discharges. In each case, it is important to control the properties of the plasma – temperature, electron density and distribution of particles in space. To estimate these parameters, scientists photograph the ionized gas, and then record its emission spectrum. At the last stage, computer algorithms reconstruct spatial distribution of various parameters in a plasma plume. However, in this case we obtain 2D images.
To obtain the volumetric structure of plasma from flat images, such algorithms use a mathematical tool called the inverse Abel transform. The only obstacle is the “noise” arising from experimental measurements and affecting the accuracy of the model. To solve this problem, the scientists of Lomonosov Moscow State University have analyzed 14 algorithms that work with low-quality (“noisy”) experimental data. The researchers also tested combinations of algorithms with the noise suppression methods: smoothing, filtering and regularization.
Smoothing is an approach in which experimental data are averaged: highly outliers are cut off in a similar way to the knife that removes the thorns from a rose stem. Filtering, on the other hand, is based on the idea that “noise” and useful information in the data have different frequencies: as a consequence, the frequency corresponding to the noise is removed. Finally, regularization is a way to find incorrectly posed problems: a small term (penalty) is added to the solution: the more noise, the more the penalty term.
The researchers conducted a numerical experiment, processing with all 14 algorithms “noisy” data sets that can theoretically describe the state of plasma. The most accurate models were obtained by using the algorithm of Piessens-Verbaeten, because it has built-in filtering mechanisms. At the same time, regularization as a method of suppressing “noise”, practically erased the differences between the algorithms: their error decreased to 8-12%, whereas, without regularization, it reached almost 100% in some cases.
“Plasma sources are widely used not only in scientific research, but also in processing materials, application of various protective coatings, laser welding and cutting, as well as in studying the combustion processes. Therefore, the obtained results can help optimize the technological processes in which plasma with strictly defined characteristics must be generated,” the Russian Science Foundation quotes Timur Labutin, Ph.D. in Chemical Sciences.
