**1. Introduction**

Optical monitoring techniques can be applied in the production of optical coatings in almost all deposition plants. Both commercial and homemade optical monitoring devices are widely used all over the world, and choosing a good optical monitoring strategy is a key issue for the production of high-quality optical coatings. There is a great variety of optical monitoring techniques, and they are divided into monochromatic and broadband techniques [1]. In the case of monochromatic techniques, the question of having a proper monitoring strategy was raised many decades ago. The most impressive example of this was the production of narrow band-pass filters using turning point optical monitoring [2–4]. The production of very complicated optical filters became possible due to the presence of a very strong error self-compensation effect associated with this type of monitoring. The physics of the error self-compensation effect was explained many years later [5], and it was shown that the advantage of turning point monitoring appears only in the case of filters with resonant filter cavities. For other types of optical coatings, monochromatic-level monitoring was proposed many years ago in various forms [6–9]. For monochromatic-level monitoring, the choice of monitoring strategy is usually decided by the specifications of monitoring wavelengths and signal termination levels or swing [10] termination levels for all coating layers. The choice of monochromatic monitoring strategy is not a straightforward task, and recent efforts have been made to automate this choice [11,12].

In the case of broadband monitoring, various monitoring strategies are also possible. The first alternative is the choice between direct and indirect monitoring strategies [1,10]. The main advantage of direct monitoring was indicated by Macleod [7]. In this case, we monitor one of the samples that we want to produce. Unfortunately, direct broadband monitoring can lead to the development of a strong, cumulative effect of thickness error growth. This effect was even noticed in the first works done on broadband monitoring [13,14] and was later investigated in detail [15]. Indirect broadband monitoring allows one to use several monitoring chips and, thus, prevent the fast growth of thickness errors. However, with this type of monitoring, we lose the previously noted advantage of direct monitoring. The recent progress in monitoring hardware arrangements [16,17] allows one to combine the advantages of direct and indirect monitoring. In the arrangement reported in these works, the monitor holder has several monitoring chips and is located on the main wheel of the deposition chamber with the same radial position as those of the deposited samples. Thus, the cumulative effect of thickness errors can be reduced by using several monitoring chips during the coating deposition.

The negative cumulative effect of thickness error growth is connected with the correlation of thickness errors by optical monitoring procedures [15]. Although, the correlation of errors can also lead to a positive effect of self-compensation of influence of errors in various layer thicknesses. In the case of broadband monitoring, this effect was first noticed four decades ago [13,14]. However, a comprehensive study of the error self-compensation effect associated with direct broadband monitoring began only recently, after the presence of a very strong effect was detected in the production of Brewster's angle polarizers for high-fluence optics [18]. The mathematical investigation of the error self-compensation mechanism in the case of broadband monitoring was performed in Ref. [19]. The results of this investigation were formulated in terms of singular values of rectangular matrices describing the correlation of errors in the course of broadband monitoring. Unfortunately, this form of representation is not convenient for practical applications, and the degree of correlation between the thickness errors and the strength of the error self-compensation effect can be calculated using computational experiments on optical coating production simulations [20,21].

The recent progress in broadband monitoring hardware [16,17] allows one to apply different direct monitoring strategies. In particular, direct broadband monitoring can be performed using several monitoring chips. It is also possible to remove monitoring chips and bring them back to the measurement position many times during the coating deposition. This strategy was previously applied in the case of indirect broadband monitoring, and it was shown that it had a certain advantage in monitoring some types of optical coatings [22].

Despite the obvious progress in monitoring arrangement, choosing the optimal strategy in the case of broadband monitoring is still an open question. When studying this question, we should take into account the negative and positive effects connected with the correlation of thickness errors. On the one hand, the use of several monitoring chips prevents rapid development of the cumulative effect of thickness errors. On the other hand, it can also reduce the degree of correlation of thickness errors and the associated positive effect of error self-compensation. The goal of this paper is to present a computational approach that can be applied for the comparison of various monitoring strategies while also taking into account the above-mentioned effects. We hope that such a comparison will be useful in practice to help select the optimal monitoring strategy for a given coating design.
