The mediant method for fast mass/concentration detection in nanotechnologies

Abstract

Modern nanotechnologies require methods for registration of variable physical parameters of the environment adjacent to the object. This situation is constrained by very small values, and their fast variation. This paper reports on a theoretical method for the fast parameter-to-frequency conversion (PFC). We introduce the basic formalism of number theory application for rational approximation of an unknown value, which can be naturally represented as the ratio of two independent calculable integer parameters. Mediants (a kind of Farey fractions), as well as its fundamental properties are shown, and their relation with measurement processes in PFC is presented. It is shown that the proposed mediant method is invariant, i.e., strongly independent of any known kinds of timing jitter, which is the most inconvenient kind of noise for any problem requiring the fast variable parameter registration. This method also gives the measurement uncertainty at the rate of time-standard reproducibility. Here, we present the construction of the experimental prototype. We also provide some screenshots of the experimental data obtained using this equipment. Finally, the results of numerical simulation of parameters typical for nano-applications are reported.