Optimality of thin film optical coating design

The dependence ot permittivity of coating on its thiclrness determines merit ftnction related to the problem or synthesis of optical coatings. From mathematical point of view, synthesis problem can be regarded as a specIal kind cf extreme problems. Theorems, which provide optimum conditions for synthesis prooedure, have been obtained. Taking into account these theorems, one can deduce that at normal incidence optimum optical coating appears to he double-component. Based on the results and principles of optimal control theory, special synthesis methods were elaborated. These methods don't use any starting design.