  We developed a method to make GEM foils with a spherical geometry. Tests of
this procedure and with the resulting spherical GEMs are presented. Together
with a spherical drift electrode, a spherical conversion gap can be formed.
This eliminates the parallax error for detection of x-rays, neutrons or UV
photons when a gaseous converter is used. This parallax error limits the
spatial resolution at wide scattering angles.
  Besides spherical GEMs, we have developed curved spacers to maintain accurate
spacing, and a conical field cage to prevent edge distortion of the radial
drift field up to the limit of the angular acceptance of the detector. With
these components first tests are done in a setup with a spherical entrance
window but a planar readout structure; results will be presented and discussed.
  A flat readout structure poses difficulties, however. Therefore we will show
advanced plans to make a prototype of an entirely spherical double-GEM
detector, including a spherical 2D readout structure. This detector will have a
superior position resolution, also at wide angles, and a high rate capability.
