Design correction criteria

On-line re-optimization is based on the results of on-line characterization, which is quite complicated problem, especially in the case of coatings with many layers. From a mathematical point of view the on-line characterization problem belongs to the so-called inverse recognition problems and has all specific features typical for these problems. One of these features is possible instability of inverse problem solution which exhibits itself in growing solution inaccuracy. OptiLayer software mathematical routines incorporate all latest achievements of the theory of inverse problems in order to minimize solution instability. Nevertheless this potential threat always exists because of the specific nature of the on-line characterization problem.

Accuracy of the on-line characterization is severely affected by errors in measurement data. Thus all possible efforts should be applied to providing the maximum accuracy of input photometric data. But even with high accuracy data the solution instability may grow dramatically if design corrections are performed too many times. Thus the decision on whether to perform the design correction or not should be done very carefully basing on several specific criteria.

First of all it is not advisable to perform the design correction if registered thickness errors are small enough. In this instance the threshold error level should be specified so that all thickness errors not exceeding this level are ignored. It is impossible to indicate the universal threshold error level suitable for all designs. We recommend using the analysis options of OptiLayer in order to find an acceptable error level for your specific design.

It is possible that the OptiReOpt re-optimization procedure provides only an insignificant improvement of the merit function value. In such situations it is also not advisable to perform a design correction because this correction may raise the instability of subsequent on-line characterization and re-optimization procedures. Thus the merit function variation threshold level should be specified so that the current theoretical design is not corrected if the re-optimization procedure provides the merit function variation below this level.

References:

1. A. V. Tikhonravov, M. K. Trubetskov, Online characterization and reoptimization of optical coatings, Proc. SPIE. 5250, Advances in Optical Thin Films 406 (2004)
2. 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).
3. 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.
4. 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.