2 Journal of observations

2.1 Instrumentation

P Cyg was observed, in the context of a dark-speckle run ([Boccaletti et al. 1998]). The AO bench of the ONERA (Office National d'Études et de Recherches Aérospatiales) was installed at the Coudé focus of the 1.52 m telescope. The 90 actuators of BOA and its 1 kHz closed loop bandwidth enable a compensation of atmospheric turbulence in visible light ([Conan et al. 1998]) and provide typical Strehl ratio of $10\%$ to $30\%$ depending on seeing conditions.

The restored wavefront feeds a dark-speckle optics designed to detect faint companions around bright objects. The beam is then focused onto the detector with an f/976 aperture, giving a fine pixel sampling of 144 pixels/arcsec or 0.007 arcsec/pixel (this oversampling of the images was imposed for the dark-speckle experiment). The detector is a cooled CP20 photon-counting camera ([Abe et al. 1998]) allowing single photon detection with a very low dark count ( <5 10^-3 photon/pix/s). The quantum efficiency of CP20 is less than 10% at 700 nm.

Near diffraction-limited images of P Cyg (m_v=4.81, $S_{\rm p}$ = B1Ia+) and 59 Cyg (m_v=4.74, $S_{\rm p}$ = B1.5V) have been obtained (Fig. 1) using a broadband H$_{\alpha }$ filter ( $\lambda_0=6563~$Å, $\Delta\lambda=100~$Å) (Fig. 2).

2.2 Data analysis

The data consist of two sequences of 20 ms short exposures, for P Cyg, and the reference star 59 Cyg of similar magnitude and spectral type. In a preliminary step, the short exposures recorded by CP20 were cleaned for photon-centroiding electronic artifacts and then co-added to generate an equivalent long exposure of 99 s for P Cyg and 370 s for 59 Cyg. Despite the Coudé configuration of the 1.52 m telescope, rotation of the field between the two sequences was found to be negligible. We checked for non-linear effects introduced by the so-called photon-centroiding hole and camera saturation ([Thiébaut 1994]). It appears that the incoming flux is greatly below the saturation limit, the double-photon occurrence is absent. The total number of detected photons for the two images are very similar: 481563 for P Cyg and 416309 for 59 Cyg. A coherent peak and a broken ring, featuring a triple coma aberration, are clearly visible, but 59 Cyg's image is sharper, indicating that P Cyg's envelope is possibly resolved. This is quite visible in Fourier space, as shown in Fig. 3. The envelope of P Cyg clearly appears as the well resolved low frequency part in the visibility curve. High angular information is obtained up to about 80% of the cut-off frequency. The visibility curve is indeed clearly dominated by noise beyond that limit.

Figure 3: Representation in contour plots of the modulus of the Fourier transform of P Cyg (top), 59 Cyg (middle) and their ratio, the visibility curve of P Cyg (bottom). The zero frequency is at the center of the images. The representations are in logarithmic scale. The circle gives the theoretical cut-off frequency of the telescope

   

Table 1: Turbulence characteristics derived from the wavefront sensor data of the adaptive optics system. Atmospheric parameters are given for the visible band

Star name	P Cyg	59 Cyg
Time	20:30 TU	21:23 TU
Average intensity	51.567	42.830
in sub-apertures (photons)
r0 (cm), open loop	5.83	5.92
calculated with L0
r0 (cm), open loop calculated	$\sim$5.4	$\sim$5.4
with L0 and Zernike coef.
L0 (m)	2.96	2.57
Zernike coef. (2,3), $\sigma^2$ (rad2)	70	40
Zernike coef. (4,44), $\sigma^2$ (rad2)	10	9

Since 59 was observed 53 minutes later than P Cyg, a variation of atmospheric conditions and/or a poor correction could be responsible for a noticeable change in the Point Spread Function (PSF) shape. From open/close loop data recorded by the wavefront sensor of BOA, we have derived seeing conditions (F.C.): intensity in sub-apertures, Fried parameter evolution, noise evolution, Zernike coefficient variance evolution, etc. Some of these relevant parameters are summarized in Table 1 for both stars. In particular, the Fried parameter (r₀) exhibits no temporal variation and remains stable around 5.4 cm between the 2 data sequences. Also, high order correction (Zernike coef. (4,44)) have similar variances in both cases, indicating similar adaptive mirror corrections for P Cyg and 59 Cyg. The largest difference appears for the tip-tilt corrections (Zernike coef. (2,3) of the Table 1). However we confirm that during the observations no saturation was detected, and we expect these modes to be correctly compensated for both stars. Furthermore, parameters such as turbulent layers altitude, mean isoplanetic angle and wind velocity indicate a very good stability of the atmospheric conditions during the two records.

Moreover, the photon flux stability can be checked on the short exposures statistics. For 59 Cyg, the flux is stable with a perfect Poisson variance. P Cyg's behavior is roughly the same, except for some localized empty exposures, due to electronic saturation, which have been removed.

This preliminary analysis permits us to assume that 59 Cyg can be confidently considered as P Cyg's PSF and a successful deconvolution becomes possible.