Temporal and spatial cross correlation

In order to investigate the temporal properties of the correlation between the left-hand star Strehl ratio and the Strehl ratio of the right-hand star, a temporal cross correlation of the measured Strehl ratios was performed. The peak of this function occurs when the Strehl ratio of the left-hand star is correlated with the Strehl ratio obtained one or two frames later for the right-hand star ($5$--$11$ $ms$ later), as shown in Figure 3.34a.

Figure 3.34: a) The cross correlation of Strehl ratio for the left-hand binary component in the $\gamma$ Leo data with the Strehl ratio for right-hand star in a different exposure. The difference in the exposures used is indicated by the time difference between the acquisition times of the exposures, shown along the horizontal axis. The peak correlation is after a delay of one frame ($\simeq 5.5$ $ms$), suggesting that the wind was blowing refractive index fluctuations from the left-hand side to the right-hand side of the light path through the atmosphere. b) The Strehl ratio obtained for the right hand star using the Lucky Exposures method selecting $1\%$ of the exposures using the left-hand star as the reference. The Strehl ratio and position of the brightest pixel were used to select and re-centre different short exposures to see how the final image was affected - the difference in exposure number used is indicated as a time difference on the horizontal axis.

Figure 3.34b shows the effect of finding the highest $1\%$ of reference star Strehl ratios, but actually selecting exposures an integer number of frames before or after the frame with the high reference star Strehl ratio. The image re-centring was also based on measurements of the reference star in the exposure with the high reference star Strehl ratio, and not the exposure actually used. The Strehl ratio obtained on the binary companion in the final image is plotted against the delay between the Strehl ratio and reference star position measurements and the application of these measurements to the data. The peak Strehl ratio for the companion star is obtained if the delay is $5$ $ms$. The curve has the same general shape as that for self referencing with $\epsilon$ Aquilae, shown in Figure 3.18, except for the time delay.

The observed delay in the response of the binary companion image to fluctuations in the reference star image suggests the presence of an intermediate or high altitude layer of seeing moving with a velocity which has a component along the axis of the binary separation in the plane of the sky. Phase perturbations experienced by the reference star are thus blown into the beam of light from the binary companion between $5$ and $11$ $ms$ later, producing the observed cross-correlation.