Alfredo Dubra's PhD thesis - Imperial College London

3. Data processing
3.3 Pupil position and size estimation
There are three parameters to estimate from the interferograms that are crucial for
the phase map estimation and wavefront integration algorithms: the position, size and
shape of our region of interest (pupil) on the raw interferograms. Ideally, the pupils at
the detector plane would be circular. However, in practice the recorded interferograms
have shapes which are not exactly circular, sometimes clearly elliptical, due to corneal
astigmatism, and some times very irregular due to very rough tear surface and tear
break-ups. Despite this asymmetry, to first approximation, the pupils can in general
be modelled as circular and the algorithm proposed below is based on this assumption.
3.3.1 Algorithm
To estimate the pupil position and radius, a normalised correlation between a binarised
low pass-filtered version of the raw interferograms and a model of a pupil was
maximized, by varying the parameters of the model.
The raw interferograms are low-pass filtered to remove the AC term and then binarised
to eliminate the non-uniformities in illumination, then they are correlated with a series
of models consisting of binarised sums of pairs of circles shifted with respect to each
other by the estimated shear, with different radii (r model ). Finally, we take the value
of r model that maximizes the normalised correlation as the pupil size.
3.3.2 Implementation details
Again, as with the shear estimation, it is convenient for speed and ease of filtering to
use the DFT and the correlation theorem, again padding as before. The low-pass filter
is a circular binary mask in the Fourier space, with a radius equal to the minimum
modulation frequency we considered for all the algorithms.
The intensity profiles of the interferograms change from one series of data to the next,
due to fluctuations of intensity of the source, eye position, etc., requiring different
threshold values to binarize the low-pass filtered images. Despite several attempts
to find a satisfactory automated method for determining the threshold value (e.g.
histogram based) that was able to cope with diffraction rings, tear film features,
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