  We established a new approach to hard-X-ray photoelectron spectroscopy
(HAXPES). The instrumental key feature is an increase of the dimensionality of
the recording scheme from 2D to 3D. A high-energy momentum microscope can
detect electrons with initial kinetic energies more than 6 keV with high
angular resolution < 0.1{\deg}. The large k-space acceptance of the special
objective lens allows for simultaneous full-field imaging of many Brillouin
zones. Combined with time-of-flight parallel energy recording, this method
yields maximum parallelization of data acquisition. In a pilot experiment at
the new beamline P22 at PETRA III, Hamburg, count rates of more than $10^{6}$
counts per second in the d-band complex of transition metals established an
unprecedented HAXPES recording speed. It was found that the concept of
tomographic k-space mapping previously demonstrated in the soft X-ray regime
works equally well in the hard X-ray range. Sharp valence band k-patterns of Re
collected at an excitation energy of 6 keV correspond to direct transitions to
the 28th repeated Brillouin zone. Given the high X-ray brilliance
(1.1x$10^{13}$ hv/s in a spot of less than 20x15 $mu^{2}$), the 3D bulk
Brillouin zone can be mapped in a few hours. X-ray photoelectron diffraction
(XPD) patterns with < 0.1{\deg} resolution are recorded within minutes.
Previously unobserved fine details in the diffractograms reflect the large
number of scatterers, several $10^{4}$ to $10^{6}$, depending on energy. The
short photoelectron wavelength (an order of magnitude smaller than the
interatomic distance) amplifies phase differences and makes hard X-ray XPD with
high resolution a very sensitive structural tool. The high count rates pave the
way towards spin-resolved HAXPES using an imaging spin filter.
