4 PSF reconstruction: Results

We present now the results of our reconstruction algorithm applied for different observing conditions:

• bright reference sources under good seeing conditions (0.9-1 arcsec);
• faint reference sources under very bad seeing conditions (1.5-2 arcsec);
• faint reference sources under very good seeing conditions (0.6-0.7 arcsec).

Table 2 summarizes the experimental conditions and the results of the PSF reconstruction. For each case, Figs. 7 to 9 compare the observation (continuous line) to the reconstruction (dashed line).The left columns are the radial mean of the OTF in logarithmic scale. The central and right columns are the cuts of the PSF for two perpendicular directions in linear scale. The dotted lines represent the reconstruction error in linear scale.

4.1 First examples: Bright reference sources and good seeing

Figure 7: Comparison between the observation (continuous line) and the reconstruction (dashed line) for examples A1 and A2. Left column: radial mean of the OTF in logarithmic scale. Central and right columns: cuts of the PSF for two perpendicular directions in linear scale. The dotted lines represent the reconstruction error in linear scale

We observed a bright reference source with two slightly different neutral densities (7.4 et 7.7 mag) and under good seeing conditions (0.9 to 1 arcsec). The correction was good leading to observed Strehl ratios of about 25%. Since we did not calibrate the non-common path aberrations, we took the ideal instrumental OTF for the reconstruction. The results are shown in Fig. 7. For both examples, the maximum reconstruction error on the OTF is about 10 to 20% at low frequencies. The maximum error on the PSF is located at the first-diffraction ring. In contrast to the reconstructed PSF, the observed one is not centro-symmetric. Note that this asymmetry has changed from one observed PSF to the other for the x-direction. Non-common path aberrations, which we did not calibrate, can in principle produce an asymmetry in the PSF, but it is difficult to imagine how they could have changed on such a short time scale without moving the telescope (see also Sect. 5.2 and Fig. 17).

4.2 Second examples: Faint reference sources and very bad seeing

Figure 8: Comparison between the observation (continuous line) and the reconstruction (dashed line) for examples B1 and B2. Same legends as in Fig. 7

Figure 9: Comparison between the observation (continuous line) and the reconstruction (dashed line) for examples C1, C2 and C3. Same legends as in Fig. 7

These examples were obtained with the EBCCD under very bad seeing conditions (1.5 to 2 arcsec). The magnitudes of the reference sources are between 10 and 12 and the observed Strehl ratios vary from 4 to 10%. Since the correction was very partial, we estimated the measurement noise on the CL data. Figure 8 shows that, for both examples, the reconstructed OTF is underestimated by at least 20 to 30% at low frequencies. This was the case for each source, all faint, observed during the same night. The non-common path aberrations were calibrated by taking an image of a fiber source at the beginning of the night. However, we found that using either the ideal or the measured instrumental OTF does not change significantly the quality of the PSF reconstruction.

4.3 Third examples: Faint sources and very good seeing

The last examples correspond to reference sources of 10 to 12 magnitudes, obtained under very good seeing conditions (0.6-0.7 arcsec). The observed Strehl ratios are between 20 and 30%. Since the residual aberration visible on the first diffraction ring is stable from one image to another one, we calibrated OTF $_{{\rm sta}}$by comparing the observed OTF of the same reference source taken before with its reconstructed OTF (Véran et al. 1997b).

The results are shown in Fig. 9. The error on the reconstructed OTF of examples C1 and C3 is less than 10% at low and medium frequencies. The asymmetry of the PSF is quite well reproduced within a mean error between 5 and 10%. In example C2, the reconstruction error is much larger. In this case, the average measured flux per sub-aperture on the WFS is about 4.5 photoelectrons. A closer look to the corresponding set of measurements reveals, from time to time, fluxes of just 2, 1 or even no photoelectrons at all. In these cases the center of gravity on the WFS is poorly estimated.