## Abstract

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.

© 2017 Optical Society of America

Full Article |

PDF Article

**OSA Recommended Articles**
### Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.

### Equations (14)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$F={\displaystyle \sum _{\lambda}\left\{\text{\hspace{0.17em}}{\left[{T}_{s}(\lambda )\right]}^{2}+{\left[{T}_{p}(\lambda )-1\right]}^{\text{\hspace{0.17em}}2}\right\}}.$$
(2)
$$\delta F=\frac{1}{2}{\displaystyle \sum _{i,j=1}^{m}\frac{{\partial}^{2}F}{\partial {d}_{i}\partial {d}_{j}}\delta {d}_{i}\delta {d}_{j}}.$$
(3)
$$A=\Vert \frac{{\partial}^{2}F}{\partial {d}_{i}\partial {d}_{j}}\Vert .$$
(4)
$$\delta F={\displaystyle \sum _{i=1}^{m}{\mu}_{i}{\u3008{Q}_{i},\Delta \u3009}^{2}}.$$
(5)
$${T}_{j}^{\text{meas}}(d)={T}_{j}({d}_{1}^{a},\mathrm{...},{d}_{j-1}^{a},d)+\delta {T}_{\text{meas}}$$
(6)
$${\Phi}_{j}(d)=\underset{d}{\mathrm{min}}{\displaystyle \sum _{\left\{\lambda \right\}}{\left[{T}_{j}^{\text{meas}}(d)-{T}_{j}({d}_{1}^{t},\mathrm{...},{d}_{j}^{t},d)\right]}^{2}}$$
(7)
$${\Phi}_{j}(d)={\displaystyle \sum _{\left\{\lambda \right\}}{\left[{\displaystyle \sum _{i=1}^{j}\frac{\partial {T}_{j}}{\partial {d}_{i}}\delta {d}_{i}}+\delta {T}_{\text{meas}}\right]}^{2}}$$
(8)
$${\Phi}_{j}({d}_{j}^{t}+\delta {d}_{j})={\displaystyle \sum _{i,k=1}^{j}\left({\displaystyle \sum _{\left\{\lambda \right\}}\frac{\partial {T}_{j}}{\partial {d}_{i}}\frac{\partial {T}_{j}}{\partial {d}_{k}}}\right)\delta {d}_{i}\delta {d}_{k}}+2{\displaystyle \sum _{i=1}^{j}\left({\displaystyle \sum _{\left\{\lambda \right\}}\frac{\partial {T}_{j}}{\partial {d}_{i}}\delta {T}_{\text{meas}}}\right)\delta {d}_{i}}+{\displaystyle \sum _{\text{{}\lambda \text{}}}{(\delta {T}_{\text{meas}})}^{2}}$$
(9)
$${\Phi}_{j}={\displaystyle \sum _{i,k=1}^{j}\left({\displaystyle \sum _{\left\{\lambda \right\}}\frac{\partial {T}_{j}}{\partial {d}_{i}}\frac{\partial {T}_{j}}{\partial {d}_{k}}}\right)\delta {d}_{i}\delta {d}_{k}}.$$
(10)
$${C}_{j}=\Vert {\displaystyle \sum _{\left\{\lambda \right\}}\frac{\partial {T}_{j}}{\partial {d}_{i}}\frac{\partial {T}_{j}}{\partial {d}_{k}}}\Vert .$$
(11)
$$\delta \Phi ={\displaystyle \sum _{i=1}^{j}{\lambda}_{i}^{j}{\u3008{P}_{i}^{j},{D}_{j}\u3009}^{2}}$$
(12)
$$\sum _{i=1}^{j}{\lambda}_{i}^{j}{\u3008{P}_{i}^{j},{D}_{j}\u3009}^{2}}\to \mathrm{min$$
(13)
$${W}_{ij}={\lambda}_{i}^{j}\left\{{p}_{1}^{ij},\mathrm{...},{p}_{j}^{ij},0,\mathrm{...},0\right\}$$
(14)
$$\sum _{i=1}^{j}{\Vert {W}_{ij}\Delta \Vert}^{2}}\to \mathrm{min$$