GEOMETRICAL THEORY OF ACCURACY OF COORDINATE INSTRUMENTS

Abstract

There the theoretical foundations for estimation of accuracy of coordinate instruments have been developed on the basis of representations of Riemannian geometry. The uncorrectness of expansion of traditional representations for the coordinate measurements, the necessity of attraction of concept of metric tensor have been showed. The connection between the confluence of numerical space of instrument and its accuracy of operation has been ascertained. The new interpretation of Abbe's principle has been given, the theorem about comparator straight line has been proved. Two-dimensional diffraction gratings as the reference coordinate systems have been studied by theory and by experiment. The direct comparison of two coordinate mesuring systems of coordinates, the vector field of coordinate errors on the basis of like comparison has been constructed for the first time. The properties of systematic errors in the units to be applied for the coordinate and customary instruments have been studied, the correcting algorithms have been constructed for them. The rebuilding algorithms of Euclidean metrics in the work space of coordinate instrument have been offered.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio