Low_resolution_Thesis_CDD_221009_public - Visual Optics and ...

CHAPTER 2
thickness map, the same base sphere (typically the one corresponding to the anterior
cornea) has to be substracted from both surfaces. The shape of the lens appears more
clearly, as a positive or negative meniscus, depending on the lens power. To study the
lens flexure or conformity to the underlying cornea, each of base spheres has to be
substracted to each from the corresponding surfaces.
2.2.2.4. Representing surfaces
Throughout this thesis we have used different graphical representations for analysing
the optical surfaces measured. Three dimensional scattered points plots (as those
shown in Figs. 2.16 and 2.17) are often used to represent raw measurement (or
deviations from a plane or a sphere). Figure 2.18 shows three other representations
used. The same example surface, corresponfing to a highly assymetrical ablation
pattern, is shown in a 2-D color-coded map of elevations (a), a 3-D topography (b)
and a radial profile where only the radial coordinate of the points is plotted vs their
heigh (c). To obtain the representations of Figs. 2.18 (a) and (b) an interpolation of the
measured points to a regular grid is needed. Depending on the application and
variability of the data Zernike polinominal expansions, splines or exact interpolation
was used. As opposed to raw sets of data (scattered points), these interpolated data sets
can be directly compared, point by point. To obtain representations as the one shown
in Fig. 2.18 (c), the data sets have to be previously transformed to cilindrical
coordinates. The position of the origin is critical. In the representation of corneal
ablations a biconic fitting was performed to obtain the center of the ablation, which
was used as origin of the cylindrical coordinates. The representation of Fig. 2.18 (c)
can be used with or without previous interpolation of the poins. In rotationally
symetrical ablations this representation provides a thin curve. In assymetrical surfaces,
as the one shown in Fig. 2.18 (c), a wide region of scattered poins appears.
a) b) c)
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Fig. 2. 18. Different representations of the surfaces used in this thesis. a) Colormap of
elevations. b) Three-dimensional map. C) Radial profile.
2.2.2.5. Operating with surfaces
Calculations are performed on the measured surfaces in different chapters of this
thesis, to estimate physical effects or to obtain different predictions. For example, in
Chapters 3 and 5 efficiency effects are calculated by comparing ablation maps. Also,
theoretical calculations of efficiency effects are applied to ablation patterns in flat
surfaces to predict the ablation shape in curved surfaces, or measurements in plastic
are used to predict the outcomes in corneal tissue. In Chapter 8 the thickness map of
contact lenses is calculated by substracting their base surface, alond the redial
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