The MUlti-slit Solar Explorer (MUSE) is a NASA medium-class explorer mission that is currently in phase B and scheduled for launch no earlier than 2027. The MUSE science investigation aims to use high-resolution and high-cadence spectroscopic and imaging EUV observations of the solar atmosphere to understand the multi-scale physical processes that heat the multi-million-degree solar corona, drive the source of the solar wind, and cause solar activity (flares and coronal mass ejections) that lead to space weather that impacts Earth. MUSE will consist of an EUV context imager and an EUV spectrograph, both requiring normal incidence mirrors with a very high level of polishing and figuring, in order to allow high-resolution imaging and spectroscopy. The mission is led by Lockheed Martin Solar and Astrophysics Laboratory (LMSAL). The payload is being developed by LMSAL and the Center for Astrophysics (CfA) at the Harvard Smithsonian Astrophysical Observatory, while INAF-OAB will produce the focusing mirrors with the financial support of the Italian Space Agency (ASI). In this paper, we describe the first steps that are being taken in the procurement of the focusing mirrors in Zerodur, the work plan with the ion beam figuring and the pitch tool aimed at bringing the surface defects within the specification. Additionally, we describe the metrology system that we are setting up to detect the residual deviation to the final shape.
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