An analysis of the performance of simple refractive null compensators was done. Two types of correctors were studied--the Dall compensator and the Offner compensator. A framework was built for determining whether these simple null tests are adequate for a wide range of aspheric surfaces. Variables involved in determining a surface to be null tested are f-number, conic constant, and focal length. Examples are given on how to determine the best null test for several aspheric surfaces. Also of concern in the design of a null compensator was simplicity. Two elements were the maximum used for both compensators and all compensator surfaces were spherical.

Phase shifting interferometry is one of the most promising methods for testing aspheres. However, one will encounter the following problems when it is applied to test an asphere: (1) very tight fringes produced by a strong asphere exceed the test system's resolution, (2) a test wavefront suffers from system aberrations of the interferometer that cause measurement errors, and (3) the wavefront immediately after reflection does not necessarily represent the shape of the test asphere. This thesis used a high density array sensor to detect the dense fringes. In order to solve the system aberration and the ray retrace problems, it is necessary to incorporate a ray trace code and phase shifting interferometry. This measurement principle was applied for an aspheric surface whose asphericity was 100 waves. A phase shifting Fizeau interferometer was incorporated with an optical design program. The attained accuracy was approximately one-tenth of a wave.

The effects of alignment and surface figure errors and their compensation with each other in optical systems are analyzed based on computer simulations with exact ray tracing data. These effects are included in the prediction of system performance and the testing of optics. Several simple systems are used as examples. In the prediction of system performance, a Ritchey-Chretian telescope and a Reflaxicon system are studied. A correct alignment can be found to compensate certain surface figure errors in the system. This will allow larger surface figure errors to be tolerated in the system. In the testing of optics, a method to separate the figure errors from the alignment error contributions is discussed and an off-axis test configuration, the Ritchey-Common test, is studied thoroughly. A figure design approach is suggested and compared with other approaches for reduction of the measured wavefront data in the Ritchey-Common test.