The Mid-infrared ELT Imager and Spectrograph (METIS) is among the first three scientific instruments commissioned at the ELT. It will implement vortex coronagraphy to achieve high-contrast imaging (HCI) at small angular separations from bright, nearby stars. An important unresolved problem with vortex coronagraphy is the vortex center glow (VCG) effect, where the thermal emission from the warm environment around the entrance pupil is partially diffracted into the image of the pupil by the vortex phase mask (VPM), which shows up as a diffuse bright spot in the center of the image. This effect has proven to be a significant nuisance in previous mid-infrared observations. Here, we use physical optics propagation to model the VCG for the first time and evaluate its strength with respect to the background flux in standard noncoronagraphic imaging in the context of ELT/METIS. Through our end-to-end simulations we find that the VCG peaks at about 70% of the standard background flux at an angular separation of 1 λ/D from the star and reduces to about 20% at 5 λ/D from the star. We apply the same method to model the VCG for the VLT/VISIR configuration, and show our model to be in agreement with the actual VCG measured in VISIR data, where the peak of the VCG is about twice as bright as the thermal background. In case the VCG turns out to be larger than anticipated in METIS, we propose two methods to mitigate it: (i) adding pupil stops in the pupil plane upstream to the VPM to block all of the thermal emission, and (ii) adding undersized Lyot stops in the image plane to block part of the diffracted light.
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