An alternative to the usual computation of moments in the different speckle interferometry techniques (Labeyrie 1970; Knox & Thompson 1974; Weigelt 1977) is the analysis of the probability density functions (PDFs) at several points in space of the speckle pattern, describing the joint-occurrence of given intensities at several spatial locations.
This original technique--the probability imaging (PI) technique--was firstly proposed by Aime (1987), for binary stars speckle imaging. Extended to the case of a general object (Aime & Aristidi 1991; Aime et al. 1993), this technique is turned out to be rather heavy in its application for objects with more than three elementary components. First and foremost because of the number of dimensions of the PDFs that have to be handled (the exhaustive analysis of the specklegrams of a triple star requires a threefold PDF, and so on), but also because there is no simple separation between a function that depends on the object alone and a function that is relevant to the point-source spread speckle pattern in the result, as in the more classical moment analysis. This led us to focus our attention on the binary star problem, for which a twofold PDF analysis is sufficient. These functions are finally proved to be a powerfull and easy-handled tool, giving really interesting results in the domain of relative photometry (Aristidi et al. 1997b).
We present here a new practical implementation of the PI technique well suited for the image reconstruction of binary systems from visible speckle interferometry data. In that sense, this technique is to be compared to other binary-star-oriented techniques, such as the Directed Vector Autocorrelation (Bagnuolo et al.1992) combined with the fork algorithm, that can be used for binary stars speckle data (Bagnuolo et al. 1990); or to the more recent cross-correlation method proposed by Aristidi et al. (1997a), if coupled to the fork algorithm or to the present Q function computation.
This paper follows the work of Carbillet et al. (1996a) who first obtained--using the PI technique--quantitative results suitable for astrophysical interpretations, from one-dimensional near-infrared data. While the previous approach was parametric and made use of minimization techniques, the present one gives the information required from the binary stars data more directly. As in the first application of this PDFs analysis, we find that the major capability of this technique is to give an accurate relative photometry of binary stars. As a matter of fact, this technique seems to be less sensitive to the variations of seeing conditions than the standard speckle techniques.
The paper is organized as follows. The problem of imaging a binary star by using PDFs is exposed in Sect. 2 (click here). A theoretical model of the PDFs that leads to a relevant quantity is exposed in Sect. 3 (click here), together with the procedure using it as a tool for speckle imaging. A proposal to get rid of the use of a reference star is described in Sect. 4 (click here). Numerical simulations done in order to test the validity and limits of the method are presented in Sect. 5 (click here). An application to real data of the binaries Del, Moaï 1 and Per is performed in Sect. 6 (click here). A discussion of the work (including further planned applications) is given in Sect. 7 (click here), and a conclusion in Sect. 8 (click here).