Neutron backscattering spectroscopy with sub-μeV energy resolution has profited over recent years from intensity gains enabled by a phase space transformation (PST) chopper, which is a fast-moving neutron optical component first proposed by Schelten and Alefeld (Internal Report No. Jül1954, KFA Jülich, 1984). Here, we present its principle, the considerations for our technical layout, the related challenges, the mechanical and neutron optical aspects, and tests related to the graphite mosaic crystals, moving with a center velocity of 243 m/s in the scattering plane perpendicular to the reciprocal lattice vector of the reflection. The reported tests of the graphite crystal quality are informative for other neutron optical applications. Our mechanically innovative, most compact PST chopper layout has proven its reliability during user operation in the backscattering spectrometer IN16B, and certain aspects of its design have already been adopted for another backscattering spectrometer. We report the relative intensity gain measured on the backscattering spectrometer IN16B, ILL.