Modelling phase errors induced by multilayer optical coating using Monte Carlo transmission line modelling and PAOS for performance sensitivity of the Ariel mission

The primary requirement of a manufactured optical surface is a combination of an optimized spectral performance to minimize spectral losses and an accurate mathematical definition of its surface form. Variations in the thicknesses of the coating layers of a dichroic beamsplitter can introduce deviations in the observed phase of the reflected and transmitted beams. Here, we use transmission line modeling to explore the effect of high- and low-spatial frequency variations in the thicknesses of the layers to assess the subsequent impact on the resulting phase of the outgoing beams of a dichroic. We apply our methodology to an extreme broadband dichroic designed to comply with the spectral requirements of a dichroic on the ARIEL telescope. We obtain estimates of the expected phase variations when subjected to high- and low-spatial frequency errors in thickness. We show that these non-uniformities introduce a wavelength-dependent shift in the observed phases of the outgoing beam, which may subsequently degrade the point spread function (PSF) using physical optics simulator (PAOS), an open-source, generic Physical Optics Propagation code, to assess the consequent impact on the PSF at the focal plane of the Fine Guidance System 2 (FGS2) photometer.