Alfredo Dubra's PhD thesis - Imperial College London

6. Tear topography dynamics experiment
z
cornea
rotated cornea
Rc
h(x,y)
q
x
y
Rs
sclera
Figure 6.2: Eyeball modelled as two spherical surfaces.
interferograms increased while decreased in the other one and vice-versa when the eye
was too far, providing then a visual aid for alignment. The area illuminated on the
tear film was typically around 3 mm in diameter.
6.2 Eye movements and effect on tear topography measurements
Before presenting the estimated topography maps the effect that eye movements would
have on the tear topography estimation shall be discussed. For the sake of simplicity,
the rotation of the eyeball with respect to the center of the sclera and the movement
of the head will be considered independent.
6.2.1 Effect of eyeball rotation on tear topography experiment
Let us model the eyeball as a rigid body formed by two spherical surfaces, the sclera
with a typical radius (R s ) of approximately 11 mm and the cornea with a radius (R c )
of around 8 mm (typical values range from 7 to 9 mm). It will be also assumed that
the eyeball rotates around the center of the sclera which is a distance d ≈ 6 mm away
from the center of the corneal surface. Now, for the sake of simplicity but without
loss of generality only rotations in the y − z plane around the center of the sclera will
be considered, that as shown in figure 6.2 coincides with the origin of the system of
coordinates. Then, the change in corneal height ∆h with respect to the x − y plane
due to an eyeball rotation of angle θ is given by
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