Since Labeyrie's invention of stellar speckle-interferometry
(Labeyrie 1970; Dainty 1975), high angular resolution techniques have
been able to attain the diffraction limit of existing large telescopes both
in the visible and infra-red wavelengths. Using the more recent technique of
speckle-imaging like the bi-spectral analysis (Weigelt 1977), one can
have access to the morphological structures of various galactic and
extra-galactic objects such as T Tauri stars or NGC 1068 (Thiébaut et al. 1995;
Weigelt 1977). A practical problem often encountered in reducing
speckle-interferometric data is the so-called "photon-centroiding hole"
(Foy 1987), PCH hereafter, which degrades the power spectra or bi-spectra
of short exposures recorded by intensified cameras (Thiébaut et al. 1995). This
hole is due to the spatial/temporal coincidence of photon-events and appears
as a depression at the center of the average auto-correlation, AC hereafter,
of clipped speckle-interferograms. Consequently, the observed Fourier
components are biased at different spatial frequencies and make the restored
AC or reconstructed image of the object unreliable. Different remedies have
been proposed to overcome this problem such as calibrating it on a
laboratory source having photometric properties close to those of the star
under study or by comparing the raw power spectra to a priori models from
which the hole can be removed (Hoffman 1993). A different but most
effective technique consists in spatially splitting the
speckle-interferograms in two optical replicas which are later
cross-correlated by software (Thiébaut 1994). If these replicas are
strictly balanced, the cross-correlation, CC hereafter, is identical to the
AC with the extra bonus of obtaining an unbiased power-spectrum after
Fourier transformation. The counterpart is doubling the number of pixels on
the detector and penalizing the signal to noise ratio by a factor 
.
In this paper we propose a different approach which consists in correcting the artifact of the PCH directly from the power-spectrum itself provided a partial coverage of the Fourier space due to a sparse pupil distribution. This is precisely the case of a diluted optical interferometer such as the GI2T (Grand Interféromètre à 2 Télescopes), where the power-spectrum support is limited to one low frequency component and two high-frequency symmetrical components with respect to the zero frequency.
In the first section we recall briefly the instrumental characteristics of the GI2T and its detector relevant to this study. We describe also the proposed technique to overcome the PCH. In the second section, we present the theoretical expressions of the standard deviation of the power and cross-power spectra, which are used to estimate the quality of the PCH correction. Next we present the correction results on numerical simulated interferograms. Our method is then applied to data from actual observations on the sky where reliable visibilities have been obtained for two stars with different magnitudes. Finally we discuss the limitation of our method and its use on future interferometers.