5 Effective performance of AIC

The efficiency of the coronagraph can be measured by comparing images of the same object respectively on-axis and off-axis (Fig. 3). When the star is set off-axis by 4 or 5 times the distance of the first Airy ring (this is about 2 arcsec here) the nulling process no longer applies. Thus as shown in Fig. 3 (image on the left), the photometry of the star is available through the twin images (the summed energy in the twin images is half the energy reaching the beamsplitter). When the star is on-axis a halo of residual energy appears (as shown in Fig. 3). Basically the ratio of the energy in the residual halo to the incident energy determines the extinction capabilities, and this led to the criterion: normalised integrated residual energy. In the following we use this criterion to evaluate the effect of AIC on AO typical images. We also compare two reduction techniques for AIC images and we show how AIC reaches a higher close-sensing capability than does the Lyot coronagraph.

   
5.1 Integrated residual energy

Let's call w₀ the total energy that hits the AIC beamsplitter (i.e., the total energy collected on the star by the telescope taking into account optical transmission before the AIC). This quantity is twice the total energy from the twin images. From the derivation in Paper I, the normalised integrated residual energy is given by:

$g_J=p_J.\left(\frac{D}{r_0(\mathrm{vis})}\right)^{\frac{5}{3}}$

where D is the diameter of the telescope, r₀ is the Fried parameter in the visible and p_J is a coefficient depending on J, the index of the last Zernike polynomial corrected.

Figure 4: residual energy rejection rate (gJ) in vertical versus $\frac{D}{r_0(\mathrm{vis})}$ in horizontal. Filled circles stand for calculation with the whole set of images of a star. The squares use only selected best images of a star. The error bars show the $1\mathrm{~}\sigma$ dispersion

In Fig. 4 we plot the value of the integrated residual intensity g_Jversus the factor $\frac{D}{r_0(\mathrm{vis})}$ for a sample of data collected during the observation run. The filled circles stand for g_J measured when adding the whole set of images of a star and the squares stand for g_J measured when adding only selected best images of a star. The selected best images for each target represent between 8% and 15% of the total number of images (in Sect. 4.2 we have explained why the number of images varies from quality-class to another). The best regression lines (whole set and selected set) are also drawn. They yield respective estimates of p_J via the expression: $g_J=p_J.\left(\frac{D}{r_0(\mathrm{vis})}\right)^{\frac{5}{3}}$. For the whole set of images we find p_J=0.009 (solid line in Fig. 4) while for the selected images p_J=0.0065 (dashed line in Fig. 4). The theoretical coefficient p_J for BOA is 0.0025. In comparison the AO acts as if it was an AO completely efficient up to radial mode N=7 (36 polynomials). The error bars show the 1$\sigma$ dispersion. Vertically the precision has been estimated taking into account the temporal variation of the extinction and of the total energy collected w₀. Horizontally the limitations come mainly from the temporal variation of the r₀ during the observations. This variation of r₀ is estimated from the BOA measurements taken on each star.

Figure 5: Mean radial profile of a star (vertical) versus angular separation (in arcsecond). a) theoretical diffraction pattern. b) profile without AIC. c) profile with AIC and the whole set of images of the star. d) profile with AIC and a selection of the best images of the star

   
5.2 Radial profiles of residual energy

We have to take into account the shape of the halo because it makes the detection capability variable with the location of the image of a companion. In addition we want to visualize the shape of the halo of residual light effectively obtained from the observational data. For that matter we consider the case where AIC has given its best results (here $\frac{D}{r_0(\mathrm{vis})}=17$). In Fig. 5 we show profiles of the normalised flux pertaining respectively to the diffraction pattern of the telescope, central obscuration taken into account (profile a), to the observed image without coronagraph and where AO provides a Strehl Ratio of 90% in K band (profile b, 150 images), to the residual light averaged over the whole set of images (profile c, 1200 images) and to the residual light averaged over the set of selected best images (profile d, 150 out of 1200 images). In Paper I, we suggested that the residual energy is spread over an extended halo, what is effectively found from our data. Unsurprisingly the coronagraphed profile from the selected set is lower and less extended than the profile from the whole set. This change brings in a reduction of the integrated energy from 7.5% to 5.5% that is a lowering factor of 0.73 and reduces the height of the central peak from 2.6% to 2.1% that is a lowering factor of 0.8. Those numerical figures illustrates the interest of a selection process and the presented profiles show where and how the situation is thus improved.

However, we should have observed a depression at the origin in the coronagraphed profiles, as expected from the analysis in Paper I. and this is clearly not confirmed by our profiles from data. This discrepancy between expected and observed profiles is well explained on the theoretical ground by unstabilities affecting OPD (see Paper I) and this situation has been clearly met in our observations, as commented in Sect. 3.2 (specific conditions of observation). In addition, the central hole expected from the theoretical extinction profile can yield full extinction only over an area smaller than the pixel size. Therefore a small fraction of the residual energy is constantly present and prevents the "full darkening" of the central pixel. This also contributes to the observed central peak (but significantly less than OPD variations do).

Figure 6: Detection capabilty in magnitude versus separation with the main star (horizontal scale). curve a and b respectively $\Delta K$ accessible without and with AIC (both raw data). Curve c is the $\Delta K$ accessible without AIC with substraction of a comparison star (also without AIC)

5.3 Magnitude difference reachable from raw data

In this section, to demonstrate more quantitatively the effect of AIC, we compare the magnitude difference ($\Delta K$) detectable at a given angular resolution with AIC and without AIC. The $\Delta K$ values correspond to the lower limit of the detectable flux of the companion at the level of 3$\sigma$. The noise is evaluated by integration of the energy over a $0.36''\times 0.36''$ patch (Paper I, Close et al. 1998) and this patch is radially moved to determine the variation of the noise level versus the angular distance to the axis. The total flux of the companion is determined by the energy enclosed within the patch centered on each image of the companion. One must notice that the total flux recorded from the companion depends also on the angular separation but the effect of the dependency is visible only close to the star (see Paper I). Roughly AIC diminishes the flux from the companion when this one is closer to the star than 0.18'' while there is practically no attenuation beyond.

In Fig. 6 we show the $\Delta K$ accessible from raw data without and with AIC (curve a curve b) for typical conditions of turbulence ( $\frac{D}{r_0(\mathrm{vis})}=25$). Substracting the comparison star from the target star profile (both obtained without AIC) yields the curve c. It is apparent from the graph that curve b and c correspond to nearly the same detection sensitivity, what means that working with raw data of AIC is as good as working with "cleaned'' data without AIC. Such a situation shows that processing raw data is necessary to improve the detectivity and ultimately to recover the expected performance.

   
5.4 Comparison between two reduction methods

In this section we compare the $\Delta K$ given by 2 different reduction processes:

1.

substracting a comparison star (comparison process);

2.

substracting the mean radial profile (radial process).

Substracting the mean radial profile is possible as soon as the correction by AO is good enough (Strehl Ratio (SR) larger than 50%) what is the case here. In Fig. 7 the $\Delta K$ is calculated as described in Sect. 5.2. In this figure we show for comparison the $\Delta K$ detectable from raw data (curve a in Fig. 7). The curves b and c (Fig. 7) shows the $\Delta K$ accessible respectively for the radial process and for the comparison process (both curves uses the whole set of images available for the target star and the comparison star).

Figure 7: Vertically: magnitude difference accessible. Horizontally: separation with the main star in arcseconds. See text for details

For this configuration (star magnitude, number of frames, exposure time and high noise of the camera), the detectability is limited to $\Delta K=5$ beyond 1 arcsec separation. We can note that close to the star the radial process is more efficient than the comparison process. In fact, close to the star the shape of the profile is very similar to the theoretical radial profile (large SR). This leads to a shape of diffraction pattern very similar to the theoretical one. Since this pattern is radial the radial process works well. Besides, the comparison process is not very efficient close to the star because of the possible incidental on-axis pointing shift between the target star and comparison star. This slight angular shift makes the respective mean patterns unequal close to the axis, and limits the efficiency of the comparison process.

In the comparison process used far from the star the detectivity is reduced because noises from target and comparison contribution are added, then decreasing the detectable $\Delta K$.

As described in Paper I one specific interest of AIC is its capabilities of detection close to the star. Then to study the efficiency of the AIC close to the star, we calculate the $\Delta K$ accessible with a selection of the best images of both target and comparison star for the two reduction processes we are interested in (curve d for radial process and curve e for comparison process, both in Fig. 7). When using the selection of best images we keep about 150 images while with the whole set of data we use 900 images.

Using a reduced number of images tends to decrease the detectable $\Delta K$ far from the star. Conversely, close to the star this $\Delta K$ is increased because the selection tends to favor images with the highest wavefront quality which results in removing residual energy around the axis first.

We have shown in this section that the selection of images helps increasing detectability of faint structures close to the axis. The use of reference stars does not seem necessary from the averaged radial curves we show. However, when searching for faint structures, one can be misled by fixed speckles mainly coming from aberrations in the wavefront sensor unit or in the optical set-up standing between the AO output beamsplitter and the AIC entrance. Reference sources are then still necessary.

Figure 8: Image of the double star HD 211673 off-axis and on-axis. Separation of the two components is 1.4 times the distance of the first Airy ring (0.53 arcsec). Difference of magnitude in K is estimated at about 0.36

5.5 Close-sensing capabilities

To evaluate the close-sensing capability of AIC we have recorded images of several double stars of various angular separations. In Fig. 8 we present the case of the double star HD 221673 (72 Peg) where the separation is 1.4 times the angular distance of the first Airy ring (0.53 arcsec). From the recorded images (K band) we have estimated the magnitude difference between components at $\Delta K=0.36$. Hipparcos (ESA 1997) gives a difference of magnitude of $\Delta Hp=0.46$ (Hipparcos magnitude Hp, visible-near infrared, Martin 1996).

Though, for this star, the magnitude difference to deal with is not very challenging it shows how AIC works. A more challenging star is HD 211073 for which we have to face magnitude differences $\Delta Hp=3.46$ (Hipparcos Catalogue ESA 1997), $\Delta R=2.9$ and $\Delta I=2.2$ (Ten Brummelaar et al. 1996) and a separation of 0.4'' (Hartkopf et al. 1996). For this star the best results have been obtained with the radial process, because the superimposition of target star and comparison star was not good enough. No faint companion appears clearly but at the position given by Hipparcos Catalogue (ESA 1997) and Hartkopf et al. (1996) two symmetrical bright speckles appear at the level of the residual fixed speckle noise. The difference of magnitude derived from the level of these speckles is $\Delta K=6.4$. This result is not in agreement with a low mass companion hypothesis derived by Ten Brummelaar et al. (1996).

Figure 9: Image of the faint component of the double star HD 213310. Separation of the two components is the third of the diffraction limit. Difference of magnitude in K is estimated at about 3.5

To show that the AIC can detect companions as close to the star as half of the distance of the first Airy ring we observed the star HD 213310 (5 Lac). The two components of the star are only about 0.11 arcsec appart (one third of the first dark Airy ring). This companion is too close to the star to be resolved by the telescope, but as shown in Paper I, it should be possible to detect this companion with AIC. Figure 9 shows that this possibility is effective and that a sensing of the environment as close as a third of the Airy angular radius has been achieved with AIC. Let us give few comments regarding this point. The image of a companion closer than the first Airy ring appears as two spots symmetrically located at 0.6 times the distance of the first dark Airy ring (Paper I), i.e. 0.22 arcsec here, even if the true separation is different. Actually the true separation governs the apparent flux, not the location of the image. The bright spots (twin images) from HD 213310 effectively appear at the expected location, with a Signal to Noise (SNR) of 5 (Fig. 9). Both the radial and comparison processes give the same result. The intensity ratio between the main star and these spots is 42. From this estimate and taking an average separation of 0.11 arcsec (Hartkopf et al. 1996) a magnitude difference $\Delta K=3.5 \pm 0.5$ is found. The uncertainty $\Delta K$ comes from the uncertainty regarding the angular separation and also from the low level of detection (SNR = 5). This magnitude difference is consistent with the spectral types of the 2 stars. Markowitz (1969) gives for these stars M0II+B8V (see also Ginestet et al. 1997 for more references on this star).

Classical Lyot coronagraph can not image a companion so close to the main star. Actually, the masks used in Lyot-type coronagraphs cover 2 to 10 times the distance of the first Airy ring (Malbet 1996) and most of the time they cover 4 or 5 times this distance (Beuzit et al. 1997; Mouillet et al. 1997). As we have shown in this section, AIC can image the faint companion at one third of this distance (first dark Airy ring).