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Design Study of a VUV Microscope at 121.6 nm with the Sample in AirThe design of a custom VUV microscope is studied. The microscope is designed around a custom high brightness, spectrally narrow VUV source operating at the Hydrogen-Lyman-α (HLA) transition characterized by the emission wavelength of 121.6 nm. The incentive for microscopy at 121.6nm is a transparent window in the air absorption spectrum coinciding with 121.6nm light. This allows for the sample to be in air while the microscope is in an enclosed vacuum or nitrogen environment. A microscope is built consisting of the VUV source, a low noise, x-ray camera, a custom 120 magnification, 0.3 numerical aperture objective lens, and an assortment of vacuum flanges, nipples, and crosses. The camera is verified to detect the HLA output from the source. The objective lens is capable of achieving an intrinsic resolution of 247 nm with a wavelength of 121.6 nm if the proposed alignment procedure is followed and the fabricated mechanical tolerances are within the specified range. The objective lens mirrors and the primary mirror cell are fabricated out of specification. Therefore, the best expected optical performance is 0.3 Strehl ratio. In order to improve the optical performance, a few design changes are discussed, including increasing the primary mirror thickness to improve surface figure error and increasing the back thickness of the primary mirror cell in order to reduce the force on the primary mirror from radial adjustment screws.