  We derive accurate formulas for thermal fluctuations in multilayer
interferometric coating taking into account light propagation inside the
coating. In particular, we calculate the reflected wave phase as a function of
small displacements of the boundaries between the layers using transmission
line model for interferometric coating and derive formula for spectral density
of reflected phase in accordance with Fluctuation-Dissipation Theorem. We apply
the developed approach for calculation of the spectral density of coating
Brownian noise.
