High-resolution imaging with coherent X-rays

In the last decade, the development of techniques commonly grouped under the name ``coherent diffractive imaging'' (CDI) has greatly expanded the means whereby spatial information can be collected using radiation. These imaging techniques, which can be described as ``microscopy without lenses'' or ``crystallography without crystals'', present a great potential for diffraction-limited imaging with short wavelength radiation. After giving an overview of the current state of the field, I will describe recent results obtained at the Swiss Light Source with a scanning method called ``ptychography''. CDI techniques typically require much more data processing than traditional microscopy methods. Special emphasis will be put on the algorithmic developments that accompany and often enable new coherent imaging schemes.