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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").
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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