  We present scattered light images of the TW Hya disk performed with SPHERE in
PDI mode at 0.63, 0.79, 1.24 and 1.62 micron. We also present H2/H3-band ADI
observations. Three distinct radial depressions in the polarized intensity
distribution are seen, around 85, 21, and 6~au. The overall intensity
distribution has a high degree of azimuthal symmetry; the disk is somewhat
brighter than average towards the South and darker towards the North-West. The
ADI observations yielded no signifiant detection of point sources in the disk.
  Our observations have a linear spatial resolution of 1 to 2au, similar to
that of recent ALMA dust continuum observations. The sub-micron sized dust
grains that dominate the light scattering in the disk surface are strongly
coupled to the gas. We created a radiative transfer disk model with
self-consistent temperature and vertical structure iteration and including
grain size-dependent dust settling. This method may provide independent
constraints on the gas distribution at higher spatial resolution than is
feasible with ALMA gas line observations.
  We find that the gas surface density in the "gaps" is reduced by 50% to 80%
relative to an unperturbed model. Should embedded planets be responsible for
carving the gaps then their masses are at most a few 10 Mearth. The observed
gaps are wider, with shallower flanks, than expected for planet-disk
interaction with such low-mass planets. If forming planetary bodies have
undergone collapse and are in the "detachted phase" then they may be directly
observable with future facilities such as METIS at the E-ELT.
