X-ray lensless optics and ptychography

One of the problems of modern optics is accurate and full description of the object and light fields. Thus, the optical properties of the materials should be characterized not only by their absorption, but also by the refraction, and the light fields near the object and detector — not only by the intensity, but also by the phase. The 1972 the work of Gershberg and Saxton was the first attempt to solve this problem in free space without optical elements, relying only on a quadratic detector and a computer simulation of the wave propagation. Today, such lensless imaging is used at different wavelengths, from terahertz to hard X-rays. The purpose of this work is to give a brief introduction to the theory of lensless imaging which can be applied to the X-ray region. The results of the corresponding experiments in invisible light using He-Ne laser and testing objects are also presented.