Isoplanatic angle

In order to investigate the size of the isoplanatic patch, observations of binary stars with a range of separations were also undertaken on 2001 July 26. All of the stars used were bright enough that the ``over resolution'' effect described in Chapter 5.4 due to the selection of noise features is expected to be small. The seeing conditions were good for all the observations (seeing FWHM $\sim0.5$ $as$), and frame rates greater than $70$ $Hz$ were used for the data presented here.

For each observation, one of the binary components was used as a reference star, and the image FWHM and Strehl ratio of the other component was measured in the final Lucky Exposures image. Figure 5.14 shows the fractional reduction in Strehl ratio (i.e. the companion star Strehl ratio divided by the reference star Strehl ratio) for the binary stars HD 203991, 8 Lacertae and 61 Cygnii with separations of $0.6$, $22$ and $30$ $as$ respectively.

Figure 5.14: The Strehl ratio of each science object divided by the Strehl ratio for the corresponding reference star is plotted against the angular separation between science object and reference star.

As in Chapter 3.5.6 I will define the isoplanatic angle $\theta_{e}$ as that at which the Strehl ratio falls to $\frac{1}{e}$ of the value obtained close to the reference star. A model for the anisoplanatism is required in order to calculate the size of the isoplanatic patch from measurements such as these. For both the best fit Gaussian model (shown in Figure 5.14) and for a fit of the form of Equation 2.20 a value of $30$ $as$ is obtained.

The $30$ $as$ separation for 61 Cygnii was close to the measured $\theta_{e}$, and it is of interest to look at the image quality obtained on this star. The Lucky Exposures image on one component generated using the other binary component to select and re-centre the best $1\%$ of exposures is displayed alongside the seeing-limited average image in Figure 5.15. The FWHM of $130$ $mas$ obtained for the Lucky Exposures image represents a substantial improvement over the FWHM of $450$ $mas$ for the seeing-limited image. The halo around the core of the Lucky Exposures image is very compact, and it is clear that this PSF would provide good quality high resolution imaging. Any differential motion between the images of the two stars must have been extremely small. The FWHM of the companion star in the Lucky Exposures image increases to $230$ $mas$ when the best $10\%$ of exposures are selected using the reference star. For a shift-and-add image using all of the exposures the FWHM of the companion star is $300$ $mas$.

Figure 5.15: Panel a) shows the image quality obtained $30$ $as$ from a reference star using the best $1\%$ of exposures. One component of the binary 61 Cygnii was used as the reference star for exposure selection and re-centring. The other component of the $30$ $as$ binary is shown here. The image FWHM of $130$ $mas$ represents a very substantial improvement over the FWHM of $450$ $mas$ for the seeing-limited image shown in b). This image was generated from the same data, but without selecting or re-centring the exposures based on the reference star.

An isoplanatic angle of $30$ $as$ is impressively large for observations at I-band. Previous authors have predicted much smaller values of isoplanatic angle, both for speckle imaging and non-conjugate adaptive optics (typically $2$--$15$ $as$ - see e.g. Roddier et al. (1982a); Vernin & Muñoz-Tuñón (1994); Roddier et al. (1990); Marks et al. (1999)). Observations at other wavelengths can be scaled to give a corresponding value for I-band using the dependence of $r_{0}$ on wavelength given in Equation 2.9.

On several nights in June and July 2003 high frame-rate observations of the globular clusters M13 and M15 were obtained covering fields which were $20$ $as$ across. It is hoped that these datasets will provide a set of isoplanatic angle measurements which can be used to determine whether the result obtained in 2001 is unusual or typical of the summer seeing conditions at the NOT. Initial results from these observations look very promising, but detailed analyses will not be presented here.