A new approach to solve the three flat problem
Abstract:The problem of absolute interferometric testing of circular, plane surfaces is investigated by separating the measured wavefronts into a pure rotational symmetric part and the remaining rotational non-symmetrical part. It is shown, that the pure rotational symmetric part can be derived absolutely free from the classical three flat test. This is very useful, because now the mean radius of curvature of the entire flat can be computed! In a variation of the classical three flat-test, where one of the mirrors is allowed to rotate during the test either continuously or in several steps for one complete revolution, the other part of the wavefront error, which does not contain the information about the mean radial profile but in contrary the rotational non-symmetric errors, can be derived too. The influence of the number of steps within 2π on the residual error is investigated and it is found, that already a small number of rotation positions leads to reasonable accurate results for the rotationally non-symmetric part.
In addition to that, a second procedure is briefly given, which does not need the change in the coordinate systems from the Cartesian measurement grid of the CCD-camera to polar coordinates, but can work purely with the original data set. It is shown heuristically, that the residual error for the rotational non-symmetric part is even smaller by about a factor of 10 with this procedure. Further work will be dedicated to the combination of both procedures.