“A priori” estimates in problems of the synthesis of interference coatings

Problems of the synthesis of interference coatings under the action of electromagnetic waves are treated in a variational formulation. A priori estimates for the bounds of the change in the thickness and the number of layers of the optimal system are obtained on the basis of a constructive analysis of the necessary conditions of optimality. A knowledge of such estimates enables one to reduce substantially the number of permissible versions of the multilayer structures which are analysed for optimality.