Application of Fourier-Galois Spectra Analysers for Rotating Image Analysis

Abstract

It is shown that the analysis of rotating circular images containing n = 2p−1 pixels, the state of which is described by variables of binary logic, and p is an integer, is expedient to carry out using digital spectra obtained using the Fourier–Galois transformation, and the basis corresponding to such a transformation is formed by the method of classical algebraic extensions of the main Galois field GF(2) corresponding to binary logic. It is shown that the use of Fourier–Galois spectra makes it possible to reduce the analysis of a rotating image to the analysis of a still image by using the operation of digital logarithm. It is shown that the proposed approach is of interest, including from the point of view of improving equipment designed to study the rheological properties of liquids, in particular, polymer solutions in which non-trivial branched structures are formed. In this case, the use of the proposed approach provides an opportunity to modernize the classical method of measuring Stokes viscosity, focused on the study of mechanochemical reactions. The design of a viscometer that implements the proposed approach has been developed. In it, a digital image is formed by a set of optoelectronic pairs that track the circular motion of the ball in a cuvette driven by rotation. The electronic circuits of this type of viscometer are based on a Fourier–Galois spectrum analyser and a digital logarithm operation. The possibilities of generalizing the proposed approach to the analysis of rotating images of other types are considered.