Method and device for characterizing the surface shape of an optical element

A method for characterizing the surface shape of an optical surface of an optical element, wherein

• the optical element is incorporated as a test object in an interferometric test device such that the surface is arranged completely within a measurement region of the test device,
• a plurality of interferometric measurements are carried out on the test object, and
• between the measurements a rotational position of the test object relative to the test device is changed by limited rotation of the test object about a test object rotation axis, and wherein
• in order to form a first measurement series with first measurements, M first measured values are captured for M rotational positions with a rotation angle difference of 360°/M and in order to form a second measurement series, N second measured values are captured for N rotational positions with a rotation angle difference of 360°/N, where M and N are relatively prime natural numbers, and
• in an evaluation operation, measured values are evaluated jointly in order to ascertain shape information for characterizing the surface shape of the optical surface,
• wherein the evaluation operation, in an iterative process, comprises:
• (A) calculating a first figure based on the first measurements, wherein the first figure is a common concomitantly rotating figure of the first measurement series;
• (B) subtracting the first figure from the first measured values in order to determine a first test set-up error containing common non-concomitantly rotating errors of the first measurement series;
• (C) using the first test set-up error for calculating a corrected first figure, which results from the first figure by subtraction of the first test set-up error;
• (D) subtracting the corrected first figure from the second measured values in order to determine a second test set-up error;
• (E) using the second test set-up error for calculating a corrected second figure, which results from the second measured values by taking into account the second test set-up error;
• (F) using the corrected second figure for correcting the first test set-up error by subtracting the corrected second figure from the first measured values in order to determine a corrected first test set-up error containing common non-concomitantly rotating errors of the first measurement series and of the second measurement series;
• (G) using the corrected first test set-up error for calculating a first figure corrected once again;
• and
• (H) comparing the result with a convergence criterion and optionally repeating steps (A) to (H) depending on a result of the comparison.