Evolutionary Reverse Engineering Algorithm

 New evolutionary post-production characterization algorithm significantly improves the search for the best fit in the case of multi-scan data. The new option is available in OptiRE through:  Solve --> Random Errors Solve --> Quasi-Random Errors Solve --> Quasi-Random Inhomogeneities Solve --> Random Errors (scientific mode) Solve --> Quasi-Random Errors (scientific mode) In comparison with the previous versions, there is a choice between two algorithms in "Method" field: Simple Refinement and Triangular algorithm. In the case of "Simple Refinement", discrepancy function $$DF$$ is minimized with respect to all "Active" layer thicknesses: $DF^2=\frac{1}{m}\sum\limits_{k=1}^m\frac 1L\sum\limits_{j=1}^L\left[\frac{T(d_1,...,d_m;\lambda_j)-\hat{T}^{(k)}(\lambda_j)}{\Delta T_j}\right]^2,$ where $$m$$ is the number of design layers, $$\{\lambda_j\}, \; j=1,...,L$$ is the wavelength grid, $$\hat{T}^{(k)}(\lambda_j)$$ transmittance scan recorded after the deposition of $$k-$$th layer, $$\Delta T_j$$ are measurement tolerances.  In the case of "Triangular algorithm", partial discrepancy functions $$DF(i)$$ are minimized with respect to all "Active" layer thicknesses among $$d_1,...,d_i$$: $DF^2(i)=\frac{1}{i}\sum\limits_{k=1}^i\frac 1L\sum\limits_{j=1}^L\left[\frac{T(d_1,...,d_i;\lambda_j)-\hat{T}^{(k)}(\lambda_j)}{\Delta T_j}\right]^2,$ where $$m$$ is the number of design layers, $$\{\lambda_j\}, \; j=1,...,L$$ is the wavelength grid, $$\hat{T}^{(k)}(\lambda_j)$$ transmittance scan recorded after the deposition of $$k-$$th layer, $$\Delta T_j$$ are measurement tolerances. Important: At each $$i-$$step, starting approximations of actual layer thicknesses are taken from the result of the $$(i-1)-$$step. This reduces the instability in determination of actual layer thicknesses significantly.

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