Alfredo Dubra's PhD thesis - Imperial College London

6. Tear topography dynamics experiment
0.25
0.25
0.2
0.2
RMS residual
(mm)
0.15
0.1
RMS (mm)
0.15
0.1
0.05
0.05
0
0 5 10 15 20 25
time (s)
0
0 5 10 15 20 25
time (s)
Figure 6.7: Temporal evolution of the estimated wavefront error RMS (b) and residual
wavefront error RMS (a) for 30 data series (around 2300 topography maps) corresponding
to 19 different subjects. The blue dots correspond to the estimated RMS
(b) and residual RMS (a) wavefront aberration introduced by the tear for all the 30
data series. The black lines are the mean RMS at the corresponding time and the gray
areas delimited by the blue lines are the areas within one standard deviation from the
mean. Again, the red horizontal line indicates the diffraction limit at 632.8 nm.
ever, the second moment as defined by Licznerski depends not only on the surface of
the tear, but also on the intensity profile of the image, on the total intensity, on the
shear amplitude, spatial coherence of the source and pupil shape. Thus, monitoring
of the second order moment of the AC term (in the Fourier space) can only be used to
measure relative changes within a series of interferograms from a given subject with
unchanged conditions. The effect of shear amplitude, total intensity and coherence of
the source could be eliminated by defining a normalised second moment,
∫ ∫
f 2 |AC( f)|
M N =
⃗ 2 d 2 f
fR 2 ∫ ∫
|AC( f)| ⃗ 2 d 2 f
(6.6)
where the integral is performed over a circle with radius f R and AC is the part of the
spectrum of the interferogram centered on the carrier frequency. The moment defined
in this way ranges from 0 (when the AC term is a delta function) to 1 (when the AC
term is a ring of radius f R ). In practice, one has a discretised (pixelated) image, and
a discrete Fourier transform, and thus the need for the discrete version of equation
6.6, that is
M N =
∑ m 2 +n 2 ≤R 2
m,n
(
m 2 + n 2) |AC(m, n)| 2
R 2 ∑ m 2 +n 2 ≤R 2
m,n
|AC(m, n)| 2 (6.7)
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