Rectifying the isophote to second order by homothetic transofrmation

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I'm writing a Python script following a research paper's algorithm (https://articles.adsabs.harvard.edu/pdf/1990A%26A...233...82C). I've got my isophote points and the points of the closest-fitted ellipse. The paper says: "First, the isophote is rectified to the second order by a homothetic transformation in z (axis ratio of the best-fitted ellipse)". I don't understand that question at all. Homothetic transformation means just multiplying by the scaling factor, right? I understand that as just elongating/shortening my isophote in the z-axis, but how is this "rectifying to the second order"?