The emergence of hard X-ray free electron lasers (XFELs) enables new insights into many fields of science. These new sources provide short, highly intense, and coherent X-ray pulses. In a variety of scientific applications these pulses need to be strongly focused. In this article, we demonstrate focusing of hard X-ray FEL pulses to 125 nm using refractive x-ray optics. For a quantitative analysis of most experiments, the wave field or at least the intensity distribution illuminating the sample is needed. We report on the full characterization of a nanofocused XFEL beam by ptychographic imaging, giving access to the complex wave field in the nanofocus. From these data, we obtain the full caustic of the beam, identify the aberrations of the optic, and determine the wave field for individual pulses. This information is for example crucial for high-resolution imaging, creating matter in extreme conditions, and nonlinear x-ray optics.
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