  Skimmed supersonic beams provide intense, cold, collision-free samples of
atoms and molecules are one of the most widely used tools in atomic and
molecular laser spectroscopy. High-resolution optical spectra are typically
recorded in a perpendicular arrangement of laser and supersonic beams to
minimize Doppler broadening. Typical Doppler widths are nevertheless limited to
tens of MHz by the residual transverse-velocity distribution in the
gas-expansion cones. We present an imaging method to overcome this limitation
which exploits the correlation between the positions of the atoms and molecules
in the supersonic expansion and their transverse velocities - and thus their
Doppler shifts. With the example of spectra of
$(1\mathrm{s})(n\mathrm{p})\,^3\mathrm{P}_{0-2}\leftarrow
(1\mathrm{s})(2\mathrm{s})\,^3\mathrm{S}_1$ transitions to high Rydberg states
of metastable triplet He, we demonstrate the suppression of the residual
Doppler broadening and a reduction of the full linewidths at half maximum to
only about 1 MHz in the UV. Using a retro-reflection arrangement for the laser
beam and a cross-correlation method, we determine Doppler-free spectra without
any signal loss from the selection, by imaging, of atoms within ultranarrow
transverse-velocity classes. As an illustration, we determine the ionization
energy of triplet metastable He and confirm the significant discrepancy between
recent experimental (Clausen et al., Phys. Rev. Lett. 127 093001 (2021)) and
high-level theoretical (Patk\'os et al., Phys. Rev. A 103 042809 (2021)) values
of this quantity.
