Optimization OverviewOptimization is the primary method — but not the only method — by which multi-layer coatings are designed. It works by adjusting the thickness and/or the refractive index of layers so that the coating’s performance (reflectance, transmittance, color, etc.) is close to the desired performance (also called the optimization targets). The difference between the coating’s performance and the desired performance is computed in the merit function
where m is the number of optimization targets, P is the computed performance of the design, PD is the desired performance, and N * Tol is a weighting factor for each target. F is the quantity that the optimization process seeks to minimize. Note that if F = 0, then the coating’s performance is the same as the desired performance. However, in most cases, it is not possible to find a design such that F = 0. Instead, there are methods that attempt to make F as small as possible. In general, there are many coating designs that minimize the merit function. For example, the contour plot below shows the merit function for a two-layer coating design. The X’s mark where the merit function has minimum values.
TFCalc helps the designer locate the designs that minimize the merit function. The designer may use “constraints” to limit the designs found by optimization. That is, the designer may place limits on the range of values that a thickness or index may have. For instance, the designer may want to use constraints to prevent layers from becoming too thin or too thick. Optimizing symmetric designs. TFCalc has the capability of maintaining a symmetry in a design while it is being optimized. This is done using TFCalc’s “group” optimization feature. Each layer is assigned to a group; during group optimization, all of the layers in the same group are shifted together. That is, layers in the same group are multipled by a “group factor” and it is the various group factors that are optimized. |
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