Merit function 
Merit function estimates the closeness between target and current spectral characteristics. In the simplest case when target reflectance on the wavelength grid \(\{\lambda_j\}\) is specified: \[MF=\left[\frac 1L \sum\limits_{j=1}^{L}\left(\frac{R(X,\lambda_j)\hat{R}(\lambda_j)}{\Delta R_j}\right)^2\right]^{1/2} \] where \(\Delta R_j\) are tolerances, \(X\) is a vector of layer thicknesses. 
Optimization methods 
Hyper Newton method is a modification of the Newton method based on the ideas used by the Damped Least Squares method. It requires considerable computer memory but has a fast convergence. Modified damped least squares (Modified DLS) is a powerful method which offers a rapid convergence at early stages of the refinement procedure, but may be slowly converging near the end of the refinement procedure, especially in the case of complicated designs with many design layers. Newton method is a 2nd order optimization method which uses full analytic second order derivatives of the merit function. It is especially well suited for problems with a large number of optimization parameters and poor convergence of the merit function. Newton’s second order method is one of the most powerful optimization methods, but not necessarily the most rapidly converging at the initial stages of the refinement procedure. It is usually a good choice at the end of the refinement procedure. QuasiNewton DLS method is utilizes full information on partial Jacoby matrices for a merit function being a sum of squares. It has a fast convergence, but is not available for problems with targets having qualifiers. Sequential QP method is based on a sequential approximations of the optimization problem by a set of Quadratic Programming (QP) problems. It has a good convergence and can be recommended for complicated problems. Conjugate gradients method is a wellknown and widely used method. It is a stable method which typically exhibits faster convergence than the Steepest descent method. Steepest descent method is the simplest and historically the first to be applied to optimization problems. This method converges quite slowly compared to other methods 
Degree of bulk inhomogeneity \(\delta\) 
\( \delta=\displaystyle\frac{n_in_0}{n}\cdot 100\%, \;\; n=\frac{n_i+n_0}{2} \) where \(n_i, n_0\) are refractive indices at the outer boundary and substrate boundary, respectively. 
Admittance \(A\) 
\(\displaystyle\frac{dA}{dz}=ik\left[n^2(z)A^2\right], \) \(r(k)=\displaystyle\frac{1A(z_a,k)}{1+A(z_a,k)},\;\; A(0,k)=n_s \) where \(r(k)\) is the amplitude reflectance, \(n(z)\) is refractive index profile, \(k\) is the wavenumber. \(A(0,k)=n_s\) Admittance is a complex value. Geometrically it can be represented as a point on a complex plane (admittance phase plane). For more details, see, for example, this book , pages 3446. 
Group delay (GD) and group delay dispersion (GDD) 
The first and the second derivatives of the total phase shift with respect to angular frequency: \(GD=\displaystyle\frac{d\varphi}{d\omega},\;\;\; GDD=\frac{d^2\varphi}{d\omega^2} \) 
Cauchy model 
Refractive index wavelength dependence is specified: \(n(\lambda)=A_0+\displaystyle\frac{A_1}{\lambda^2}+\frac{A_2}{\lambda^4} \) 
Sellmeier model 
In OptiLayer, Sellemeier model is represented in different forms. Refractive index wavelength dependence is specified:

Arbitrary dispersion  Arbitrary dispersion model assumes Cauchy model for the refractive index. The coefficients of the Cauchy model vary in arbitrary way in the course of the characterization process. 
Exponential model for extinction coefficient 
Dispersion behavior of extinction coefficient is described by exponential formula: \(k(\lambda)=B_1\exp\{B_2\lambda^{1}+B_3\lambda\}\). 
Drude model 
Refractive index and extinction coefficient are connected: \(2n(\lambda)k(\lambda)=\displaystyle\frac{A_1A_2\lambda^3}{\lambda^2+A_2^2}\) \(n^2(\lambda)k^2(\lambda)=A_0\displaystyle\frac{A_1 A_2^2\lambda^2}{\lambda^2+A_2^2}\) 
Hartmann model  \( n(\lambda)=A_0+\displaystyle\frac{A_1}{\lambdaA_2} \) 
Bruggemann’s formula  \(n=\displaystyle\frac 12\sqrt{(3p1)n_b^2+(23p)n_\nu^2+\sqrt{((3p1)n_b^2+(23p)n_\nu^2)^2+8n_b^2n_\nu^2}}\), where \(n\) is the refractive index of the composite; \(p\) is porosity of the layer material; \(n_b\) and \(n_\nu\) are refractive indices of the bilk material and voids, respectively. 
Average Weighted Value of Permitiviteis  \(n^2=pn_b^2+(1p) n_\nu^2\), where \(n\) is the refractive index of the composite; \(p\) is the volume fraction of voids; \(n_b\) and \(n_\nu\) are refractive indices of the bilk material and voids, respectively. 
Average Weighted Value of Refractive indices  \(n=pn_b+(1p) n_\nu\), where \(n\) is the refractive index of the composite; \(p\) is the volume fraction of voids; \(n_b\) and \(n_\nu\) are refractive indices of the bilk material and voids, respectively. 
Look our video examples at YouTube
OptiLayer videos are available here:
Overview of Design/Analysis options of OptiLayer and overview of Characterization/Reverse Engineering options.
The videos were presented at the joint Agilent/OptiLayer webinar.