Rigaut et al. have observed (1991) an enhancement of the speckle transfer function by up to a factor 7 using the AO prototype Come-on. From AO calculations and simulations in the partial correction regime, Roggemann & Matson (1992) and Conan et al. (1993) showed that the speckle transfer function with AO yields a significant gain in signal and signal to noise ratio compare to the ones obtained without AO. From AO simulations, Roggemann & Matson (1992) have also shown that bispectral analysis yields a significant gain for the partially compensated case.
Tessier & Perrier (1996) have carried out some Come-on+ observations in speckle mode. A critical value for the Strehl ratio is observed for long exposure AO images. In the images with a Sr lower than about 5%, the diffraction-limited coherent peak is lost as the optical transfer function does not show anymore high spatial frequencies (dashed line in Fig. 16 (click here)). The use of short exposure times allows to recover the high spatial frequencies part in the modulation transfer function (MTF) shown in solid line in Fig. 16 (click here). In our case, the 250 ms exposure time in J was quite long in comparison to the typical speckle coherence time estimated from the wavefront sensor data. This suggests that a speckle analysis improves the high frequencies even with exposure times larger than the speckle coherence time. By contrast, in case of good Sr (), this mode does not yield so much gain and is not relevant.
The behavior of the signal to noise depends more on the quality of the MTF calibration possibly achievable. We have completed the observation of a close binary (0.2 arcsec) using this technique. The data have been reduced with the IRAF package c128 (see Appendix B; Tessier et al. 1994). From the rms residual of the reconstructed complex visibility, we can conclude that the phase is much less sensitive to seeing effects than the modulus is. The rms residual for the phase is about 0.03 radians from 500 frames. The rms residual for the visibility in modulus is 3% in the high spatial frequency range but some seeing effects affect up to 20% the low spatial frequency region ().
To conclude, the field of application of speckle with AO applies essentially to low corrections (a few per cent). This occurs when, e.g., going short-wards in wavelength for given conditions. We should be able to observe fainter sources with a higher resolution than in speckle without AO because of the gain in signal and the possibility to use longer exposure times.
Figure 16: Speckle transfer function of short exposures AO images (exposure time is 0.25s in J band) under poor correction compared to the square optical transfer function of the long-exposure AO image. From COP data
Speckle imaging is a post-processing technique based on sets of short exposure
images. When a set of AO images is available from the science
object and its
calibration psf, it may be useful to test some techniques drawn from the speckle experience before applying the deconvolution. First, it could be necessary to recenter the frames on their centroid before averaging the sets. Roddier et al. (1995) have used the median operator in place of the mean on their sets of images with some success. Other operators could be tested. The rebinning technique initially used in speckle (Perrier 1988) may be applied here and should improve the sequential calibration procedure accuracy by minimizing the "correction'' effects (due to the seeing fluctuations e.g.). It consists in binning object and psf AO images with the same level of correction. This technique requires the object-independent estimation of the Strehl ratio in the AO images. Incidentally, the AO system ADONIS has been providing this feature recently: the Strehl ratio is estimated from the WFS data (E. Gendron, private communication), so that this technique could be now tested. Some best estimator should yield the final AO image and its calibration psf from these bins. The selection technique is another possibility which aims to increase the sharpness in the images by discarding the bad images in the set (Tessier et al. 1994). However to get a good calibration psf, the same operations must be carried out on the set of the psf images. In fact, this technique is equivalent to the rebinning technique where the bad bins are rejected.