Autocorrelation-based reconstruction of two-dimensional binary objects

A method for reconstructing two-dimensional binary objects from its autocorrelation function is discussed. The objects consist of a finite set of identical elements. The reconstruction algorithm is based on the concept of class of element pairs, defined as the set of element pairs with the same separation vector. This concept allows solving the redundancy introduced by the element pairs of each class. It is also shown that different objects, consisting of equal number of elements and the same classes of pairs, provide Fraunhofer diffraction patterns with identical intensity distributions. However, the method predicts all the possible objects that produce the same Fraunhofer pattern.