On the order of analysis of speckle images in optical astronomy

Details On the order of analysis of speckle images in optical astronomy On the order of analysis of speckle images in optical astronomy

Sep 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998papop...7..989a&link_type=abstract

Pure and Applied Optics, Volume 7, Issue 5, pp. 989-1000 (1998).

Physics

Optics

Scientific paper

We show in this paper that the statistical properties of the speckle image formed at the focus of a large telescope can be fully described by a joint statistical analysis at N different spatial positions, where N is the number of resolution cells in the object's support. To obtain this result, the statistical properties are defined using multifold moment-generating functions (MGFs). Simplifying assumptions (discrete one-dimensional geometry, stationarity) are used to make the mathematical formalism simpler; they make the imaging process similar to a moving average process. General expressions are given for the twofold MGF and for MGFs of higher order. These relations are then used to show that an analysis of order N is exhaustive. It is shown that an MGF of order N + 1 can be written as the product of two MGFs of order N divided by an MGF of order N - 1. Alternatively, it is also shown that the cumulant of order N + 1 is equal to zero. A particular comment is made for the case of the double-star speckle pattern.

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