Fried Parameter – Naked Eye Obs?

When looking at a bright star with the naked eye, it is possible to relax the eyes so that they diverge, causing a double image with the focus at infinity. I’ve noticed that when doing this, the view of a star in each eye sometimes shows the twinkling to be in sync and so correlated with no time lag, while sometimes the twinkling seen with one eye is uncorrelated with that seen with the other.

It occured to me that this could be a consequence of varying distortion across the incoming wavefront of the starlight, caused by atmospheric turbulence. The scale over which the wavefront is uniform may be quantified by the Fried scale length. In the optical, this scale length tends not to exceed ~20cm at professional sites and will be significantly less than this at amateur sites.

Thus, if the Fried scale is greater than the distance between my eyes, I might expect the twinkling seen with each eye to be in sync with each other. On the other hand, if the Fried scale is less than the distance between my eyes then I might expect the twinkling seen in each eye to be uncorrelated between the two views.

One possible way to back up this explanation could be to place two cameras close together and take video footage of the same star. It ought to be possible to estimate the Fried scale by varying the distance between the cameras and noting when the twinkling in the cameras transitions from being correlated to uncorrelated. Has anyone ever tried this? 

As for the naked eye observations, I would be interested in hearing other possible explanations, e.g. visual, neurological etc. that could explain the lack of correlation between the views of each eye. Qualitatively, the naked eye observations fit with expectation, e.g. no correlation is seen in poor seeing conditions, which supports the turbulence explanation, although I can’t rule out other possible causes.