  The pressing need for the detailed wavefront properties of ultra-bright and
ultra-short pulses produced by free-electron lasers (FELs) has spurred the
development of several complementary characterization approaches. Here we
present a method based on ptychography that can retrieve full high-resolution
complex-valued wave functions of individual pulses. Our technique is
demonstrated within experimental conditions suited for diffraction experiments
in their native imaging state. This lensless technique, applicable to many
other short-pulse instruments, can achieve diffraction-limited resolution.
