Homometry in the light of coherent beams

Two systems are homometric if they are indistinguishable by diffraction. This article mainly discusses the issue of diffuse scattering homometry and its relation to high-order correlation functions. The study of the Rudin-Shapiro sequence, homometric to random sequences, allows one to manipulate independently two-point and four-point correlation functions, and to show their effect on the statistics of speckle patterns.