### Layer Sensitivity

 The Layer Sensitivity option allows you to estimate the design sensitivity to layer thickness variations. OptiLayer provides two possibilities: layer sensitivity with respect to design target and with respect to the theoretical design performance. You can specify relative varialtions in layer thicknesses $$\delta_H, \delta_L$$. The disturbed designs have thicknesses $$d_1,d_2,..., d_i(1+\delta_{H,L}),...,d_m.$$ For each disturbed design, the variations $$\Delta MF_i$$ with respect to design target (Eq. (1)) or to theoretical spectral characteristic $$S$$ (Eq.(2)): $\Delta MF_i=|MF(d_1,...,d_i(1+\delta_{H,L},...,d_m)-MF(d_1,...,d_m)|\;\; Eq. (1)$ $\Delta MF_i=|S(d_1,...,d_i(1+\delta_{H,L},...,d_m)-S(d_1,...,d_m)|\;\; Eq. (2)$ Then, layer sensitivities $$LS(i)$$ are calculated and ranged from 0 to 100%. The corresponding ranges are displayed. The layer ranked number 1 in the Sensitivity order is the layer that is most sensitive to change, it is assigned a relative sensitivity of 100%.  $LS(i)=\frac{\Delta MF_i}{\max_{i=1,...,m}\Delta MF_i}\cdot 100\%$ In the spreadsheet, absolute layer sensitivities are shown. In the Chart, relative layer sensitivities are plotted. Theoretical transmittance of a multilayer design. Crosses represent the design target. Layer sensitivity calculated with respect to design target. Layer sensitivity calculated with respect to the theoretical design performance.

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