Monte Carlo transmission line modelling of multilayer optical coatings for performance sensitivity of exoplanet spectroscopy

Multilayer optical coatings are widely used on the surface of optical components to enhance the transmittance of light in certain spectral regions while reducing it in other regions. Discrepancies between the measured and predicted spectral performance of optical components with such coatings can primarily be attributed to deposition errors and uncertainties in the refractive indices of the materials used for these coatings. Our simulation uses two-dimensional transmission line modelling to evaluate the transmittance of light at a given angle of incidence through multilayer coatings deposited on a substrate material. We perform a number of Monte Carlo simulations to obtain statistical information about the tolerance of the coating performance to systematic and random uncertainties in deposition thickness, refractive index and operating temperature. We present the posterior distributions of the deviations from the nominal performance that result from the propagation of each of these uncertainties for a number of hypothetical scenarios. We find that these uncertainties have the potential to cause significant differences between the designed and achieved performance. Our results indicate that the sensitivity of each layer to the various sources of uncertainties can vary on a case-by-case basis. With the aid of accurate manufacturing recipes and uncertainty amplitudes from commercial manufacturers, this simulation can provide a proficient tool to predict variations in the performance of multilayer optical coatings used in exoplanet spectroscopy.