If we attempt to calculate an operator that will annihilate a hyperbola, this operator should eliminate any predictable part of this hyperbola. The result of filtering the hyperbola with this operator should be our desired output, a whitened hyperbola.
The operator we calculate was expected to have a form like:
The first attempt with the filter above produced hyperbolas that were asymmetric, a result that was unexpected. To make the operator symmetric, we zeroed out the last half of the first row.
By calculating a two-dimensional filter that removes the predictable part of the hyperbola, the filter will be whitened as desired. The evanescent zone is likely to create a problem if we cannot suppress the whitening by providing a small amount of white light.
Since the evanescent zone produces problems shown later in this paper, an operator of the following form could be used.