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.
