  While Euclid is an ESA mission specifically designed to investigate the
nature of Dark Energy and Dark Matter, the planned unprecedented combination of
survey area ($\sim15\,000$ deg$^2$), spatial resolution, low sky-background,
and depth also make Euclid an excellent space observatory for the study of the
low surface brightness Universe. Scientific exploitation of the extended low
surface brightness structures requires dedicated calibration procedures yet to
be tested.
  We investigate the capabilities of Euclid to detect extended low surface
brightness structure by identifying and quantifying sky background sources and
stray-light contamination. We test the feasibility of generating sky
flat-fields to reduce large-scale residual gradients in order to reveal the
extended emission of galaxies observed in the Euclid Survey.
  We simulate a realistic set of Euclid/VIS observations, taking into account
both instrumental and astronomical sources of contamination, including cosmic
rays, stray-light, zodiacal light, ISM, and the CIB, while simulating the
effects of the presence of background sources in the FOV.
  We demonstrate that a combination of calibration lamps, sky flats and
self-calibration would enable recovery of emission at a limiting surface
brightness magnitude of $\mu=29.5^{+0.08}_{-0.27} $ mag arcsec$^{-2}$
($3\sigma$, $10\times10$ arcsec$^2$) in the Wide Survey, reaching regions 2
magnitudes deeper in the Deep Surveys.
  Euclid/VIS has the potential to be an excellent low surface brightness
observatory. Covering the gap between pixel-to-pixel calibration lamp flats and
self-calibration observations for large scales, the application of sky
flat-fielding will enhance the sensitivity of the VIS detector at scales of
larger than 1 degree, up to the size of the FOV, enabling Euclid to detect
extended surface brightness structures below $\mu=31$ mag arcsec$^{-2}$ and
beyond.
