Modified three-flat method using even and odd functions

In a Fizeau interferometer, two flats face each other and form a cavity. The interference fringes detected reveal the flatness of the cavity. In the traditional three-flat method,1,2 the flats are compared in pairs. By rotating the flats with respect to each other, the exact profiles along several diameters of each flat are obtained. A method with more flats and more combinations has been proposed.3 However, with both methods, only the profiles along some straight lines can be solved. Several methods4-8 have been proposed to measure the flatness of the entire surface. These methods involve tremendous least squares calculations. Thus, the fine structure of the surface tends to disappear.