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R. J. Braun, P. E. King-Smith; Why Does Optical Quality Improve After a Blink?. Invest. Ophthalmol. Vis. Sci. 2010;51(13):4149.
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Optical quality measurements after a blink show an improvement for the first few seconds, up to about 6 seconds after a blink. It is hypothesized that this improvement results from the "leveling" of the tear film surface after the blink, as the surface tension of the tear film tends to flatten any surface wrinkles or irregularities.
The equations of fluid motion for the tear film aqueous and lipid layers are applied to small irregularities about a smooth tear film surface. The rate of decay of sinusoidal and other perturbations are found and compared with results from several papers in the literature. Several models will be compared to the experimental results; all of the models will incorporate the surface tension of the tear-air interface and the viscosity of the aqueous layer; the models will incorporate or omit the surface tension variation caused by the polar lipids, the viscosity of the lipid layer and evaporation of the aqueous layer.
Considering the aqueous layer only, we can make use of a result from a classical coating flow called the leveling problem (originally Orchard, 1962). Using that result for tear films, with a mean tear film thickness of 3 µm, a surface tension of 45 dyne/cm, a viscosity of 1.3 centiPoise, a tangential-stress-free tear film surface and a wavelength of the sinusoidal disturbance of 1 mm, then the time for the disturbance to decay to half its original height is 1.4 seconds. There is a fourth-power dependence on the wavelength of the disturbance, and so that, for example, halving the wavelength results in a 16 times shorter decay. Decay time is inversely related to the cube of tear thickness. Subsequent deterioration of optical quality, after it has obtained its optimum value, may be ascribed to non-uniform evaporation of the tears, followed by tear film breakup.
These results and some previous papers suggest that Fourier analysis can be applied to effectively understand the decay of wrinkles or irregularities in the tear film surface that are present just after a blink. The current theory is compatible with the observed time course and spatial characteristics of improvement in optical quality after a blink.
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