Alfredo Dubra's PhD thesis - Imperial College London

3. Data processing
etc., we ended up having to set this value manually for each individual series of
interferograms.
The algorithm calculates the peak of the correlation between the binarised low-pass
filtered interferogram and the pupil model by changing the radius of the model r model
in steps of one pixel. In order to reduce the number of computations performed,
the algorithm does not actually calculate the correlation for each value in the range
passed to the algorithm. Instead, two series of calculations are performed, first a coarse
estimation in which the step size between consecutive values of r model is set to √ N,
where N is the number of integers in the radii search range, and a second, in which
the step is set to one, and a smaller range of width 2 √ N centered in the value of the
coarse estimation that yielded the maximum normalised correlation. This works on
the assumption of the correlation being a slow-varying function of the value r model , and
reduces the number of correlation calculations from N to 2 √ N. In a typical situation,
the size of the search range needed to be around 100 pixels, and thus the reduction
on the number of calculations achieved by this two-step calculation was 5. As in the
shear estimation algorithm, we make no attempt to achieve sub-pixel position or size
resolution because the integration algorithm is only applicable to integer values.
3.3.3 Tests
In order to illustrate the performance of the method, we show in figures 3.7 and
3.8 raw interferograms with the edge of the pupils that give the highest normalised
correlation indicated by two red circles, the corresponding binarized low-pass filtered
interferograms used for the correlation calculation and the calculated correlation peak
values for the two-step algorithm.
It can be seen from the figures, that the model seems adequate, both visually on the
left column and numerically on the correlation peak value on the right column, but
it is also clear that there is room for improvement both in the pupil model and the
thresholds election. A further step to improve the algorithm would be to consider
fitting elliptical pupils, though the dimension of the search parameter space would
then increase from one to three (ellipse major and minor radii and orientation).
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