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

The Ariel space mission requires the simultaneous observation of exoplanet systems in visible and infrared wavelengths through spectroscopic and photometric channels. These wavebands are selected and isolated using dichroic beamsplitters. Dichroic beamsplitters, or dichroics, are filters that rely on the optical interference occurring within thin film layers to ensure the transmission and reflection of selective wavelengths from an incident light beam. They aim to facilitate a predetermined pathway of different wavebands by manipulating the separation of precise ranges of wavelengths and play a role in determining the spectral response of an instrument.

The assumption that the layers of coating that comprise the dichroic are entirely uniform may pose a significant limitation to its physical accuracy. Complex dichroic coatings can exhibit phase effects in both transmission and reflection of light, affecting the WaveFront Error (WFE) and, consequently, the point spread function (PSF) as a function of the wavelength. The deviations in the phase observed across the surface of the dichroic are primarily the result of variations in the thickness of a given coating layer, influenced by the accuracy of the technique and equipment used during the deposition process of the coatings.

Here, we use transmission-line modelling to explore the effect of 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 a case study of an example dichroic that has been designed to comply with the spectral requirements of Ariel’s extreme broadband dichroic, D1.

We will show that these non-uniformities introduce a wavelength-dependent shift in the observed phases of the outgoing beam, which may subsequently degrade the PSF. We obtain estimates of the expected phase variations when subjected to low-spatial frequency errors in thickness. The physical distribution of these errors in the form of WFE maps are propagated through the optical chain of Ariel using PAOS, an open-source, generic Physical Optics Propagation code developed by Ariel scientists, to assess the consequent impact on the PSF at the focal plane of the FGS-2 photometer.