Order of analysis of a speckle pattern in high-angular-resolution astronomy

摘要

Abstract: This communication deals with the problem of image reconstruction in astronomy by means of a statistical analysis of the intensity of speckle patterns present at the focus of a large ground-based telescope. It emphasizes the importance of the order of the statistical analysis to be performed. Twofold and threefold statistical analyses are commonly used in speckle interferometry and in speckle masking, this later technique taking advantage of a phase closure effect for full recovery of the astronomical object. The question may arise on the interest of higher order analyses. Making use of simplifying hypotheses, we give a partial answer to this question. Under the assumption that the N points defining the object are well separated one another regard to the telescope resolution, we show that a statistical analysis of order N completely defines the statistical properties of the image speckle pattern. This result is based upon the fact that the characteristic function (CF) of order N $PLU 1 can be written as function of CF's of order N and that the cumulant of order N $PLU 1 is equal to zero. !5