In this article we report a new wavefront sensor, developed at the Laboratoire de
Spectroscopie Atomique et Ionique, for a full characterization of soft X-ray beams. The
Shack-Hartmann sensor has a theoretical accuracy in the order of $\lambda/100$ at a wavelength
around 13 nm. A cartography of the wave-vectors pointing of laser-pumped soft X-ray laser
has been achieved. It has shown the presence of many ripples probably coming from plasma
instabilities. Capillary discharge soft X-ray laser has been also investigated. For all the
pumping configurations, the wavefront is spherical, divergent with a radius of about 6.5 m at
2.5 m from the plasma end. The best wavefront exhibits an error to a perfect wave of 3λ rms.
Assuming to focus the beam with a f = 50 mm diffraction-limited mirror, a theoretical focal
spot size of 0.5 μm in diameter have been estimated containing 70% of the incident energy. In
that case an intensity of 4 × 1013 W cm−2 should be achieved.