High-precision optical systems are generally tested using interferometry, since it often is the only way to achieve the desired measurement precision and accuracy. Interferometers can generally measure a surface to an accuracy of one hundredth of a wave. In order to achieve an accuracy to the next order of magnitude, one thousandth of a wave, each error source in the measurement must be characterized and calibrated.Errors in interferometric measurements are classified into random errors and systematic errors. An approach to estimate random errors in the measurement is provided, based on the variation in the data. Systematic errors, such as retrace error, imaging distortion, and error due to diffraction effects, are also studied in this dissertation. Methods to estimate the first order geometric error and errors due to diffraction effects are presented.Interferometer phase modulation transfer function (MTF) is another intrinsic error. The phase MTF of an infrared interferometer is measured with a phase Siemens star, and a Wiener filter is designed to recover the middle spatial frequency information.Map registration is required when there are two maps tested in different systems and one of these two maps needs to be subtracted from the other. Incorrect mapping causes wavefront errors. A smoothing filter method is presented which can reduce the sensitivity to registration error and improve the overall measurement accuracy.Interferometric optical testing with computer-generated holograms (CGH) is widely used for measuring aspheric surfaces. The accuracy of the drawn pattern on a hologram decides the accuracy of the measurement. Uncertainties in the CGH manufacturing process introduce errors in holograms and then the generated wavefront. An optimal design of the CGH is provided which can reduce the sensitivity to fabrication errors and give good diffraction efficiency for both chrome-on-glass and phase etched CGHs.
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