Alfredo Dubra's PhD thesis - Imperial College London

1. Introduction
1.2 Tear film
It is accepted that the tear film consists of three layers [76, 79], the outermost being the
lipid layer of around 50 nm thickness, followed by the aqueous layer with a thickness
of around 4 − 8 µm and finally a mucous layer of around 20 − 50 nm. Each of the
layers has a different function, but from the optical point of view we should only be
concerned with their thickness and refractive indices. Actually, from the refractive
index point of view, we will assume, to a first approximation, a mean refractive index
n tear = 1.337 [80], so that we can concentrate on the tear thickness only. What is
more, in the rest of this thesis, we will estimate the topography of the front surface
of the film, assuming an unchanged back surface, which is reasonable given the time
scales involved in our experiments (a few seconds).
The first question we should ask ourselves is whether the tear film is thick enough
to produce optical path length differences that are significant in terms of the other
sources of variability of wavefront sensing in the eye measurements. Let us begin by
assuming that the difference between two tear topography maps at two given instants
is a parabolic surface that can be described by the defocus Zernike polynomial. We can
then relate the sag s of this parabolic surface to the wavefront error RMS amplitude
(a 2,0 ) it would produce in the eye through the formula
(
2 √ )
3
s =
a 2,0 (1.1)
n tear − 1
≈ 10 a 2,0 (1.2)
Therefore, if we assume even the most conservative reported values of tear thickness
[81, 82, 83, 84, 85, 86, 87, 88, 89], that is around 3 µm, then a sag of only 15 % of the
tear thickness (which seems plausible) would be enough to take a perfect eye out of the
diffraction limit. To see, under the same assumptions, the sag required to introduce
a defocus amplitude comparable to the intervals in spectacle prescription, we can use
the following
s =
d 2 Φ s
8(n tear − 1)
(1.3)
where d is the pupil diameter and Φ is the prescription in diopters. Therefore, for the
tear to play a noticeable role in vision (let us say a quarter of a diopter) in daylight
conditions with a typical value for d of 3 mm, the sag would have to be 0.8 µm –a
value physically plausible.
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