Data processing for atomic resolution holography

In photoelectron holography, the intensity of the angular distribution of photoelectrons is measured to obtain a hologram. Thus, a hologram can be defined as a function on a sphere. X-ray fluorescence holography is similar to photoelectron holography. In this study, we describe methods for representing spherical functions that are suitable for atomic resolution holography, and the theory of conversion from the coordinate system of measurement to the various projections. We describe methods for rotational transformations and symmetry operations for atomic resolution hologram and the image composition from measured hologram fragments. In addition, several ways to remove the background from the raw hologram data are discussed.