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OptiLayer:  Your Partner in Design and Post-Production Characterization of Optical Coatings


 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)):

\[ \Delta MF_i=|MF(d_1,...,d_i(1+\delta_{H,L},...,d_m)-MF(d_1,...,d_m)|\;\; Eq. (1)\]

\[ \Delta MF_i=|S(d_1,...,d_i(1+\delta_{H,L},...,d_m)-S(d_1,...,d_m)|\;\; Eq. (2)\]

sensitivity thin film design

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.

sensitivity to thickness errors thin films

layer sensitivity

Theoretical transmittance of a multilayer design. Crosses represent the design target.

multilayer design sensitivity

Layer sensitivity calculated with respect to design target.

thin film design performance variation

Layer sensitivity calculated with respect to the theoretical design performance.

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