Sag and phase descriptions for null corrector certifiers

Null correctors are important in the fabrication of aspheric optics. Although null correctors simplify testing of aspheric surfaces, they can increase the risk of fabricating aspheric surfaces. Undetected errors in the null corrector will result in an aspheric surface that does not meet design specifications. To prevent such problems, a null corrector is certified prior to using it to test an aspheric surface during fabrication. Certification verifies that the null corrector has been produced properly. Current methods of certification that include computer-generated holograms and diamond-turned mirrors require a mathematical description of the certifier. We provide sag and phase formulas for describing such certifiers. The formulas can be used to define certifiers for a broad range of aspheric surfaces. For each aspheric test surface, the specific certifier parameters are found through optimization using default merit functions. Via two different aspheric surfaces, we demonstrate the usefulness and simplicity of our truncated-series sag and phase formulas to define certifiers.