Interferometric optical testing using computer-generated holograms (CGH's) has proven to give highly accurate measurements of aspheric surfaces. New applications of CGH interferometry were developed to support the fabrication of the large, steep mirrors required by the next generation ground-based telescopes. A new test to certify null correctors was designed and implemented that uses small CGH's fabricated onto flat surfaces. This test solves the difficult problem of verifying the accuracy of the null correctors that are used for measuring primary mirrors. Several new techniques for hologram fabrication have been explored for this application. A second new use of CGH's was developed for measuring convex secondary mirrors using test plates with holograms fabricated onto concave spherical reference surfaces. This test provides efficient and accurate measurement of large aspheric convex mirrors. A polar coordinate laser writing machine was built for fabricating these patterns onto curved optical surfaces up to 1.8 meters in diameter and as fast as f/1. These powerful new techniques have been implemented and optimized at the Steward Observatory Mirror Laboratory to guide mirror polishing for large telescope projects. They can also be readily applied for measuring small aspheres to high accuracy.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.