Focus on: Layer Sensitivity

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New in TFCalc 3.0 is the capability of computing the sensitivity of each layer of a coating design. Generally, this should be used only after a design has been optimized. For each layer being refined, it displays how sensitive the merit function is to small changes in the layer thickness. It displays results only for layers being refined. The plot below shows the sensitivity of a 17-layer anti-reflection coating (the same design as in "Focus on: Sensitivity").

Plot of layer sensitivity

To understand this graph, there are two cases to consider: (1) When the analysis is done on a completely optimized design, the first-order sensitivity is very close to zero. In this case, the second order sensitivity tells how steep the sides of the "valley" are. Layer 14, with a second-order sensitivity of about 0.002, is clearly the most sensitivity layer. So if the thickness of layer 14 is changed by dX nm, then the merit function increases by 0.002 dX^2. (2) When the analysis is done on a design that is not completely optimized, then the second-order sensitivity is undefined because we are not at the bottom of a "valley". In this case, the first-order sensitivity shows how the merit function increases or decreases when a thickness changes; if Q is the first-order sensitivity of a layer and dX is the thickness change of that layer, then the merit function changes by Q dX.

The layer sensitivity also gives insight into which classes of designs are easy or difficult to manufacture. For example, the second-order sensitivity of dielectric mirrors is very low; narrow bandpass filters have layers with a very high sensitivity.

The "Compute Sensitivity" and the "Compute Layer Sensitivity" commands complement each other. In the plot produced by "Compute Sensitivity", you may see that the design is sensitive to manufacturing errors. Then the "Compute Layer Sensitivity" graph shows you which layers are to blame. However, note that the two calculations are very different: the layer sensitivity depends on the merit function (i.e., the targets) while the "compute sensitivity" plots the variation of reflectance (or transmittance, etc.).

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