## Abstract

The refining method described in this paper is based, unlike the methods known up to now, on the combination of a special relaxation algorithm and a broad-band interpolation with respect to the layer parameters. It is shown that this combination is an essential requirement for the excellent convergence provided by this method, which is therefore applicable to rather complicated filter functions and gives useful solutions even for very rough initial filter designs. This algorithm is employed in the program package CALMIC (Calculation of Multilayer Interference Coatings) with considerable success. Two examples of applications illustrate the efficiency of the program.

© 1973 Optical Society of America

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### Equations (4)

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(1)
$$R=1-\{1/[{a}_{0}+{a}_{1}\xb7\text{cos}(\phi +4\pi nt/\mathrm{\lambda})]\}.$$
(2)
$${D}_{\text{lin}}=\frac{1}{L}\sum _{i=1}^{L}{\left[\frac{\mid T({\mathrm{\lambda}}_{i})-{T}_{d}({\mathrm{\lambda}}_{i})\mid -\hspace{0.17em}\mathrm{\Delta}T({\mathrm{\lambda}}_{i})}{\mathrm{\Delta}T({\mathrm{\lambda}}_{i})}\right]}^{2},$$
(3)
$${D}_{av}=\sum _{j=1}^{N}{\left[\frac{\frac{1}{{\mathrm{\lambda}}_{2j}-{\mathrm{\lambda}}_{1j}}\left|{\int}_{{\mathrm{\lambda}}_{1j}}^{{\mathrm{\lambda}}_{2j}}[T(\mathrm{\lambda})-{T}_{d}(\mathrm{\lambda})]d\mathrm{\lambda}\right|-\overline{\mathrm{\Delta}{T}_{j}}}{\overline{\mathrm{\Delta}{T}_{j}}}\right]}^{2}$$
(4)
$$R=1-(1/\sum _{m=0}^{M}{a}_{m}\xb7\text{cos}{\alpha}_{m}).$$