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5. Performance


The capability to get high-contrast and diffraction-limited images is the strong points of the adaptive optics technique. Performance of AO is usually described in term of Strehl ratio. As shown in Sect. 3 (click here), for Sr higher than 10%, AO images allows a resolution up to the diffraction-limit, for lower Strehl, as the psf widens, the fwhm or r50 should be considered as the new resolution (see Fig. 8 (click here)). As expected, a higher Sr increases the contrast in the image (see Fig. 7 (click here)).

However, Tessier (1995) has shown that the psf calibration is the limiting factor to build up high signal to noise (usually done by integrating longer) in the deconvolved images at a given Sr. We will concern the general case where the psf is known from the sequential calibration procedure. To see the consequences of the calibration noise over the performance, I have used typical observations of a bright binary (Tessier et al. 1994). The deconvolution of the AO image using the sequential calibration psf (done as described earlier) have shown residuals stronger than the expected residuals in case of background, photon, readout or flat-fielding noise. These residuals come from the inaccuracy in the calibration process and appear to be the lower limit of the noise. Figure 13 (click here) shows the limiting magnitude for an unknown companion detection in presence of these residuals levels. The Strehl ratio greatly improves the detection capability. For good Sr, the dynamic range of the detection regularly increases when going away from the central source from 102 at 0.5 arcsec up to 104 at 2 arcsec. An extended source could be defined as a source much larger than the 50% energy radius of the psf. Sensitivity curves for such sources are shown in Fig. 14 (click here) for a pixel of 50 mas. Binning pixels will gain in sensitivity as the binning factor. For the J curves (Sr of 4%), the sensitivity is probably underestimated since we know that the psf calibration was quite poor in this case.

Figure 13:  COP sensitivity curve for the detection of a companion in magnitude difference to the main component as a function of the separation for different Strehl ratios. Plot is rescaled by tex2html_wrap_inline1463. A pixel width of 50 mas is assumed

Figure 14:  COP sensitivity curve for the detection of an extended structure around a point source in magnitude per tex2html_wrap_inline1655 relative to the central source as a function of the radial distance for different Strehl ratios. Plot is rescaled by tex2html_wrap_inline1463. A pixel width of 50 mas is assumed

The visibility defined as the ratio of the AO image Fourier spectrum to the calibration psf one is also concerned by the calibration noise. An unresolved source will show some deviation to the flat visibility: e.g. in the visibility in modulus, a few per cent for good calibration and bias larger than 50% is usual in case of miscalibration.

Science observations have been carried out for a few years and yielded some results which set the current abilities in AO. Resolution up to the diffraction limit is possible on AO images. See e.g. the binary with a separation equal to the diffraction limit in Tessier et al. (1994) and Brandner et al. (1995). However, unpredictable feature on the first Airy ring may limit the detection level in contrast. Léna (1994) has collected current scientific publications from COP data. First, the observation of the R 136 cluster has revealed stars in the field (13 arcsec) as faint as a magnitude difference of 9 relatively to the brightest star in the field (see also Brandl et al. 1995); secondly, a faint companion in K with a flux ratio of 104 at 4 arcsec have been detected around the object HR 4796, and the detection of the disk around tex2html_wrap_inline1667 Pictoris (Lagrange et al. 1996) at 2 arcsec. All these experimental results are consistent with the detectivity curves shown previously. From close binaries observations (a few tex2html_wrap_inline1463) I have personally processed, the relative accuracy is a few milli-arcseconds for astrometry, a few per cent for relative photometry.

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