aPIE: an angle calibration algorithm for reflection ptychography

Reflection ptychography is a lensfree microscopy technique particularly promising in regions of the electromagnetic spectrum where imaging optics are inefficient or not available. This is the case in tabletop extreme ultraviolet microscopy and grazing incidence small angle x ray scattering experiments. Combining such experimental configurations with ptychography requires accurate knowledge of the relative tilt between the sample and the detector in non-coplanar scattering geometries. Here, we describe an algorithm for tilt estimation in reflection ptychography. The method is verified experimentally, enabling sample tilt determination within a fraction of a degree. Furthermore, the angle-estimation uncertainty and reconstruction quality are studied for both smooth and highly structured beams.