| We present a new method for determining the shape parameters, parent radius of curvature (ROC) and conic constant (CC), of a conic surface. This method employs a typical interferometric system setup for testing a spherical surface and directly measures the surface local radii and the wavefront aberrations at characteristic "confocal" positions. The measured wavefront aberrations, particularly the astigmatism and coma, and the local radii are used to determine the parent ROC and CC.; The significance of this method lies in its great simplicity yet with an achievable accuracy comparable to or better than existing methods. The simplicity lies in that it eliminates the need for null optics as typically used in full aperture tests for fast aspheres, and knowledge of the test sub-aperture coordinates as usually needed in local or sub-aperture surface tests. Thus, this method can be applied to surfaces with no fiducial marking such as mirrors that are already installed in a telescope, and will work with conics of any size and any shape, either convex or concave, on-axis or off-axis. The proof-of-concept experiment was performed on a well-figured off-axis parabolic (OAP) mirror. Accuracies of around 0.06% and 2% relative to the nominal values were achieved respectively for the parent ROC and CC. It has been shown that this method is capable of achieving a good accuracy level in determining the parent ROC. The accuracy of CC is mainly limited by the measurement uncertainties in coma. |
