| Aspheric optical surfaces provide superior performance in the design of optical systems. The introduction of computer controlled fabrication processes allows the manufacture of aspheres, yet the lack of flexible metrology often prevents cost-effective solutions. Null interferometry is an accurate tool for the testing of spherical surfaces. Extending this capability to aspheres, however, requires the design and fabrication of special null optics. Removing this requirement would allow wider application of aspheric surfaces.; This research identifies the barriers to non-null interferometry. The assumptions of null interferometry are invalid, and the individual interferometer components influence the measurement accuracy in different ways. The effects are evident in both data acquisition and interpretation. Each are modeled theoretically in software to ascertain their character. The predictions are then studied in a simplified interferometer arrangement.; Conventional null tests directly measure the surface errors, while a non-null test additionally measures surface sag. The fundamental limits of the dynamic range of an interferometric measurement are defined. An optical surface is represented with two types of spatial frequencies: those physically present on the surface and those observed from sag interference. Surface error measurements are fundamentally limited to the Nyquist frequency, while sag measurements are not. The theory of sub-Nyquist detection and two-wavelength methods are presented.; Data interpretation is a more serious limitation. Under the common-path condition, the measured wavefront is twice the surface profile. The interferometer optics introduce systematic errors in a non-null configuration. A ray-based aberration model is developed to predict the effects of non-null interference. The model expresses the interference error in terms of the conventional parameters of the imaging system optics. The wavefront at the detector is predicted for a wide variety of situations with this theory.; The theory proves most useful for simple imaging systems (with few degrees of freedom). The first-order characteristics of the interferometer are employed to predict interference imaging effects as a function of test surface slope. Interference measurements are taken on defocused spheres and a slow parabola. The results agree well with the theoretical prediction, and the residual errors are within experimental uncertainties and noise. |
