Homometry in the light of coherent beams

Two systems are homometric if they are indistinguishable by diffraction. A distinction is first made between Bragg and diffuse scattering homometry, and it is shown that in the last case coherent diffraction can allow the diffraction diagrams to be differentiated. 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. This study provides evidence that long-range order in high-order correlation functions has a measurable effect on the speckle statistics.