The paper proposes an approach for the pre-production selection of the most promising combination of a monochromatic monitoring strategy and a monitoring algorithm used for predicting termination of layer deposition. The approach is based on the previously introduced estimate of the strength of the expected error self-compensation effect and the new estimate, to the best of our knowledge, of the strength of the cumulative effect of thickness error growth presented in this paper. The application of the proposed approach is demonstrated using computational manufacturing experiments with various types of optical coating designs.

Theoretical results are formulated to assess the strength of the effect of self-compensation of errors in layer thicknesses of multilayer optical coatings. They are applicable to any method of optical monitoring of the deposition process. It is shown that considering a possible presence of a strong error self-compensation effect is of great importance for choosing a monitoring method. A comparative analysis of the results obtained to date to assess the strength of the error self-compensation effect for various types of coatings has been carried out. Moreover, in this work, a number of results were obtained directly for the first time. The results obtained can be used to select the optimal method for monitoring the deposition process depending on the type of coating.

The paper proposes to use combinations of two algorithms for the on-line prediction of the termination times of layer depositions in the case of complex optical coatings with large numbers of layers with significantly different layer thicknesses. Notch filters with very thin and thick coating layers are considered as examples of coatings where such combinations of algorithms can be useful. Computational manufacturing experiments are used to estimate expected levels of thickness errors and the strength of the error self-compensation effect for various notch filter designs. It is shown that the estimates obtained can be used to select the optimal combination of the considered algorithms.

It is generally accepted that turning point optical monitoring provides a very strong error self-compensation effect when used to control the deposition of narrow bandpass filters with quarter-wave or multiple-quarter-wave layer optical thicknesses. However, how strong this effect is has never been assessed before, to our knowledge. A recently developed general approach to estimating the strength of thickness error correlation and the strength of the associated error self-compensation effect allows, possibly for the first time, such an assessment. In this work, it is proved that, indeed, in the case of monitoring narrowband filters, the latter effect has enormous strength, many times greater than the strength of the error self-compensation effects when manufacturing all other types of optical coatings using various monochromatic and broadband monitoring techniques.

The main theoretical results related to the investigation of the error self-compensation mechanism associated with direct broad band monitoring of optical coating production are presented. The presented results are illustrated using the production of Brewster angle polarizer where this effect is especially strong. Specific properties of the design merit function required for the presence of the error self-compensation effect are discussed and the mechanism of thickness errors correlation by the direct broad band monitoring is described. It is also discussed how one can check whether a strong error self-compensation effect may be expected for a given coating design and specific parameters of the monitoring procedure that will be used for coating production.

The reverse engineering problem of determining the layer thicknesses of deposited optical coatings from on-line monochromatic measurements is considered. To solve this inverse problem, non-local algorithms are proposed that use all the data accumulated during the deposition process. For the proposed algorithms, the accuracy of solving the inverse problem is compared in the presence of random and systematic errors. It is shown that in the case when the measured data contains only random errors, the best accuracy is provided by the algorithm based on minimizing the discrepancy functional. In the case of systematic errors, the advantage of one the algorithms based on minimizing the variance functionals is demonstrated. Key words: inverse problems, reverse engineering, optical coatings, thin films.

Under consideration is the inverse problem of controlling the deposition of a multilayercoating using optical monitoring. Some new nonlocal algorithm is introduced for data analysis.Using the simulation of deposition process, the errors are compared of the proposed nonlocalalgorithm and the traditional local algorithm. Some scheme of correction of the levels of thedeposition process termination is considered that allows us to improve the accuracy of depositionmonitoring. We show that the nonlocal algorithm is more efficient both for the deposition withoutcorrection of the signal level for the deposition interruption and with correction of this level.

Предложен новый алгоритм определения значений экстремумов измеряемой в процессе напыления многослойного покрытия зависимости значения коэффициента отражения от оптической толщины напыляемого слоя. Алгоритм использует физическую модель процесса напыления, что позволяет использовать все данные измерений, накопленные регистрирующим прибором во время напыления слоя, в отличие от классических подходов, которые хорошо описывают зависимость коэффициента отражения только вблизи ее экстремума. Эффективность предложенного подхода продемонстрирована на примере моделирования процесса напыления 20слойного четвертьволнового зеркала. A new algorithm for determining the extrema in the dependence of the reflection coefficient on the optical thickness of the deposited layer is proposed. This reflection coefficient is measured during the deposition process of a multilayer coating. The proposed algorithm uses a physical model of the deposition process, which makes it possible to use all the measurement data accumulated by a recording device during the deposition of the layer in contrast to the classical approaches that adequately describe the dependence of the reflection coefficient only near its extremum. The efficiency of the proposed approach is shown by an example of modeling the deposition process for a 20-layer quarter-wave mirror.