多層膜の自動設計 (I)

抄録

For multilayer dielectric films of given refractive index illuminated by a beam of parallel ray, their optimum thickness is determined by a modified steepest ascent method. If a merit function, which represents the difference in spectral characteristics between the ideal case and the case of films of arbitrary thickness, is introduced by taking optical thickness as a variable, the problem of finding the optimum condition (synthesis) is reduced to that of finding the extreme value of the merit function.
When optical thickness values approach to optimum ones, the secondary approximation theory becomes applicable by which the optimum values are uniquely determined as solution of simultaneous linear equations. These equations are obtained by differentiation of Taylor series expansion of the merit function in which the terms of higher than third order derivatives are neglected.
A high pass filter of nine-layer film and a band pass filter of eleven-layer film with alternate high and low refractive indices are presented as designed samples. By introducing a weighting function given by the product of spectral distribution of light source multiplied by spectral sensitivity of a receptor, antireflection films of double layer were designed. Antireflection films of triple layer were also designed by the use of the secondary approximation theory.