Optimization of Parameters of the Gamma-Absorption Method of Measuring the Layer Thickness of a Two-Layer Composition

Mathematical relations are obtained and a technique of determining the requirements for the relative measurement errors γ1 and γ2 in signals recorded for prescribed errors in measuring the composition layer thicknesses is proposed. It is shown that the density fluctuations of materials affect the thickness measurement errors. Analytic expressions determining the optimum gamma-quantum energies E1 and E2 (E1 < E2) for arbitrary values of γ1 and γ2 are derived. On the basis of these expressions, it is concluded that the optimum energies are independent of the densities of the materials and their dimensions. With reference to an Al{C composition, it is shown that for the gamma-quantumenergy ranges considered (0.04–1.25 MeV), the admissible values of E1 lie on a bounded interval 0.04–0.12 MeV, the optimum values of E2 are related to E1 by an approximate relation E2opt/E1 ≈ 2.5–3.2, and the best characteristics with respect to the thickness measurement errors are reached as E1 → E1min = 0:04 MeV.