Hard x-ray scanning microscopy relies on small and intensive nanobeams. Refractive x-ray lenses are well suited to generate hard x-ray beams with lateral dimensions of 100 nm and below. The diffraction limited beam size of refractive x-ray lenses mainly depends on the focal length and the attenuation inside the lens material. The numerical aperture of refractive lenses scales with the inverse square root of the focal length until it reaches the critical angle of total reflection. We have used nanofocusing refractive x-ray lenses made of silicon to focus hard x-rays at 8 and 20 keV to (sub-)100 nm dimensions. Using ptychographic scanning coherent diffraction imaging we have characterized these nanobeams with high accuracy and sensitivity, measuring the full complex wave field in the focus. This gives access to the full caustic and aberrations of the x-ray optics.