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We derive accurate formulas for thermal fluctuations in multilayerinterferometric coating taking into account light propagation inside thecoating. In particular, we calculate the reflected wave phase as a function ofsmall displacements of the boundaries between the layers using transmissionline model for interferometric coating and derive formula for spectral densityof reflected phase in accordance with Fluctuation-Dissipation Theorem. We applythe developed approach for calculation of the spectral density of coatingBrownian noise.

Accurate calculation of thermal noise in multilayer coating