On an invariant of surface mapping as applied to metallic mesh tailoring

As in previous publications, the authors establish a goal to study tailoring of a metallic mesh to form an axially symmetric parabolic reflector. The tailoring is identified with a one-to-one mapping of a plane onto a part of a paraboloid of revolution. This representation of tailoring has a strong but inevitable idealization. The issue of a comparison criterion for two tailoring schemes is deemed important. In general terms this refers to a criterion of mapping a surface to surface. The mapping defect criterion proposed by the authors is not perfect — like any other criterion. In any case, it makes it possible to answer the question: in what sense one mapping is preferable to another. The article gives examples of the criterion’s application.