### On-line characterization

The main goal of the The on-line characterization of thicknesses of already deposited layers requires |
\(\hat{T}^j_1,...,\hat{T}^j_L\) in situ spectral monitoring data collected after the deposition of j-th layer (\(L\) – total number of data points in one spectral scan) |

There are two computational modes of the OptiReOpt characterization routines. These modes are referred to as Discrepancy function (SEQUENTIAL algorithm): \[DF(d_i)=\left(\frac 1L \sum_{j=1}^L\left[ \frac{\hat{T}(\hat{d}_1,...,\hat{d}_{i-1}, d_i;\lambda_j)-\hat{T}^{(i)}(\lambda_j)}{\Delta T_j}\right]^2\right)^{1/2},\] where \(\hat{d}_1,...,\hat{d}_{i-1}\) are the thicknesses of the previously deposited layers that were determined at the previous steps of the algorithm. The discrepancy functions are minimized with respect to only one variable: \[ DF(i)\rightarrow \min \] Because of this fact, this algorithm usually works faster than the triangular algorithm. This is of course an attractive feature of the sequential algorithm. At the same time, this algorithm may suffer from |
In the case of TRIANGLE mode thicknesses of all already deposited layers are determined at each characterization step. Operational time of OptiReOpt DLL in SEQUENTIAL mode is faster than in TRIANGLE mode. At the same time, in general, TRIANGLE mode provides more reliable thicknesses of all already deposited layers. Discrepancy function (TRIANGULAR algorithm): \[DF(i)=\left(\frac 1i \sum_{k=1}^i \frac 1L\sum_{j=1}^L\left[ \frac{\hat{T}(d_1,..., d_i;\lambda_j)-\hat{T}^{(k)}(\lambda_j)}{\Delta T_j}\right]^2\right)^{1/2},\] The discrepancy functions are minimized with respect to thicknesses of the first \(k\) deposited layers: \[ DF(d_1,...,d_i)\rightarrow \min \] |

There are other types of algorithms, for example, hybrid algorithms where at each step errors in several previous layers are determined. Automation tool of OptiLayer can help you to find the algorithm appropriate for your production environment. You can easily create your own program which will call OptiRE from your program with various setting/models and develop the most appropriate optical coating model. This model can be later used in on-line characterization with OptiReOpt. |

References:

- T.V. Amotchkina, M.K. Trubetskov, V. Pervak, S.Schlichting, H. Ehlers, D. Ristau, and A.V. Tikhonravov. "Comparison of algorithms used for optical characterization of multilayer optical coatings," Appl. Opt. 50, 3389-3395 (2011).
- A. V. Tikhonravov, M. K. Trubetskov, "Online characterization and reoptimization of optical coatings", Proc. SPIE. 5250, Advances in Optical Thin Films 406 (2004)
- S. Wilbrandt, O. Stenzel, N. Kaiser, M.K. Trubetskov, and A.V. Tikhonravov, "In situ optical characterization and reengineering of interference coatings," Appl. Opt. 47, C49-C54 (2008).
- S. Wilbrandt, O. Stenzel, N. Kaiser, M. K. Trubetskov, and A. V. Tikhonravov, "On-line Re-engineering of Interference Coatings," in Optical Interference Coatings, OSA Technical Digest (CD) (Optical Society of America, 2007), paper WC10.
- J. Oliver, A. Tikhonravov, M. Trubetskov, I. Kochikov, and D. Smith, "Real-Time characterization and optimization of e-beam evaporated optical coatings," in Optical Interference Coatings, OSA Technical Digest Series (Optical Society of America, 2001), paper ME8.