The technique we propose here may be seen as a complement to Labeyrie's speckle interferometry for binary stars. The CC is as easy to interpret as the classical AC but provides the absolute PA of the stars as well. The CC is very easy to implement. It has the advantage to give a very simple result in the form of a direct 2D image so that it appears worth it to try that method for a quick analysis of the PA when doing double star observations. The use of a reference star may not be necessary for position measurements. The secondary peaks and their asymmetry are usually easy to see on the double star's CC. In the Fourier plane, the imaginary part of the CS also reveals the position of the brighter star by its slope at the origin. However, a reference star can enhance the asymmetry of the CC for difficult objects (very small or very large magnitude difference).
For relative photometry measurements (the intensity ratio of the couple)
a reference star must be used. A careful attention must then be given to
the bias subtraction. As shown in Sect. 2, the convolution relation
between the double star's CC and the
PSF's CC applies only for zero-mean specklegrams under space-stationarity
hypothesis. If one of these conditions is not fulfilled, the
deconvolution will give a biased result (the intensity ratio
is estimated by the ratio of the heights of the two peaks).
Space-stationarity is generally a wrong assumption for real
specklegrams: they present a finite spatial extent depending
upon seeing conditions. The statistical mean of the speckle
patterns is then a function of the position and cannot be
estimated by averaging the intensity over the whole images,
as it is done
usually. Obtaining zero-mean specklegrams in these conditions
is not simple. For small separations, it can be useful to
process small sub-images extracted around the photocenter
of the specklegrams.
If the dimension of these sub-images is small enough compared
to the size of the speckle patterns, the statistical mean can
be considered as nearly constant. It can then be estimated as
the spatial mean of the intensity over the
sub-images and
subtracted.
The smaller the sub-images are, the better it will work.
A simulation is shown in Fig. 9 (click here).
This is not suitable for large separations. Various algorithms
may be tried in that case. For example subtracting to each
specklegram the corresponding long-exposure image averaged over some
hundreds of instantaneous frames. Or fitting each specklegram by a
smooth function like a Gaussian, then subtracting it. Actually this
will increase in the processing the weight of the small values
of the border of the image, and consequently the noise.
At low light level, the frequency-dependent photon bias can be removed by subtracting the power spectrum to the CS. Here again, this operation is not really necessary for position measurements: the relevant information is contained in the slope at the origin of the unbiased imaginary part of the double star's CS. But it considerably enhances the asymmetry of the two secondary peaks of the CC (as shown by Fig. 6 (click here)).
This technique has been successfully used over about 20 double
stars observed at the Telescope Bernard Lyot between 1994 and 1995.
All the measured PA were compatible with the orbit of the stars.
These results have been submitted to Astronomy and
Astrophysics.
During our last observing run, we discovered a 0
1-separated
binary star (MOAI 1) with almost zero magnitude difference.
Its CC was slightly asymmetric and we predicted a PA for this couple
(Carbillet et al. 1996a).
Acknowledgements
The authors wish to thank J.-L. Prieur (Observatoire Midi-Pyrénées) for the use of his speckle camera and his cooperation during the observations.