We present the MUSE Hubble Ultra Deep Survey, a mosaic of nine MUSE fields covering 90% of the entire HUDF region with a 10-hour deep exposure time, plus a deeper 31-hour exposure in a single 1.15 arcmin2 field. The improved observing strategy and advanced data reduction results in datacubes with sub-arcsecond spatial resolution (0.65 arcsec at 7000 A) and accurate astrometry (0.07 arcsec rms). We compare the broadband photometric properties of the datacubes to HST photometry, finding a good agreement in zeropoint up to mAB=28 but with an increasing scatter for faint objects. We have investigated the noise properties and developed an empirical way to account for the impact of the correlation introduced by the 3D drizzle interpolation. The achieved 3 sigma emission line detection limit for a point source is 1.5 and 3.1 10-19 erg.s-1.cm-2 for the single ultra-deep datacube and the mosaic, respectively. We extracted 6288 sources using an optimal extraction scheme that takes the published HST source locations as prior. In parallel, we performed a blind search of emission line galaxies using an original method based on advanced test statistics and filter matching. The blind search results in 1251 emission line galaxy candidates in the mosaic and 306 in the ultradeep datacube, including 72 sources without HST counterparts (mAB>31). In addition 88 sources missed in the HST catalog but with clear HST counterparts were identified. This data set is the deepest spectroscopic survey ever performed. In just over 100 hours of integration time, it provides nearly an order of magnitude more spectroscopic redshifts compared to the data that has been accumulated on the UDF over the past decade. The depth and high quality of these datacubes enables new and detailed studies of the physical properties of the galaxy population and their environments over a large redshift range.
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