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 gamma1 and gamma2 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 E-1 and E-2 (E-1 < E-2) for arbitrary values of gamma1 and gamma2 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-quantum energy ranges considered (0.04-1.25 MeV), the admissible values of E-1 lie on a bounded interval 0.04-0.12 MeV, the optimum values of E2 are related to E-1 by an approximate relation E-2opt/E-1 approximate to 2.5-3.2, and the best characteristics with respect to the thickness measurement errors are reached as E-1 --> E-1min = 0.04 MeV.