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Two new technologies, for polishing and testing large optics, are presented in this dissertation. The first is a new approach to generating and polishing aspheric surfaces which utilizes a full size stressed lap. The lap specifications are chosen to automatically generate a specific amount of spherical aberration. The required comatic distortion of the lap is induced by a system of levers and springs which are stretched and relaxed as the lap moves. A lap was constructed to grind and polish a 20cm glass blank. The resultant polished surface, in agreement with the predicted asphericity, has 28 microns of spherical aberration at its edge, appropriate for a F/2.0 convex paraboloid. The average radial profile has a residual peak-to-valley error of 200nm and an rms error of 60nm. This experiment serves as a first successful test of the stressed lap concept and as a demonstration of a new method for generating aspheric secondary mirrors. The second new technology is concerned with testing large optics where vibrations can be a serious problem. A modification to the usual phase shifting interferometry reduction algorithm permits measurements to be taken fast enough to essentially freeze out vibrations. Only two interferograms are needed with an exact phase relationship; and these can be recorded very rapidly on either side of the interline transfer of a standard CCD video camera, prior to charge transfer readout. The third required interferogram is a null. An analysis of potential phase errors was performed for this "2 + 1" algorithm. In the developed implementation, two frequencies, dν/ν≈10⁻⁸, are generated with orthogonal polarizations. A Pockels cell rapidly switches the frequency entering the interferometer, resulting in a phase shift over the long path difference of the interferometer. The two time critical interferograms are acquired with a 1ms separation resulting in a reduction in sensitivity to vibration of one to two orders of magnitude. Laboratory tests were performed to compare this "2 + 1" system with a commercial phase shifting package. Similar phase determination accuracies were found when vibrations were low. However, the "2 + 1" system also succeeded when vibrations were large enough to wash out video rate fringes.

No description available.

There are two topics in this dissertation: one is to develop new phase reduction algorithms for test interferograms especially of large optics and the other one is to find more accurate analytical expression of surface deflection due to gravity when the mirror is supported in the axial direction. Two new algorithms for generating phase maps from interferograms are developed. Both methods are sensitive to small-scale as well as large-scale surface errors. The first method is designed to generate phase from an interferogram that is sampled and digitized only along fringe centers, as in the case of manual digitization. A new interpolation algorithm uses the digitized data more efficiently than the fitting of Zernike polynomials, so the new method can detect small-scale surface error better than Zernike polynomial fitting. The second algorithm developed here is an automatic phase reduction process which works on test interferograms recorded by CCD camera and transferred digitally to a personal computer through a frame grabber. The interferogram results from interference of the test wavefront with a tilted reference wave-front. Phase is generated by assuming it to be proportional to the intensity of the interferogram, apart from changes of sign and offset occurring every half fringe so as to make the phase increase monotoically. The error of the new algorithm is less than 1/20 waves in the wavefront, which can be reduced further by averaging several phase maps which are generated by interferograms with random phase shifts. The new algorithm is quick and involves no smoothing, so it can detect surface errors on large mirrors on a scale of several centimeters. A new model is developed to calculate analytically the surface deflection of a mirror supported axially on multiple points. It is based on thin plate theory, but considerations of thickness variation of a curved mirror, lightweight honeycomb structure and shear are included. These additions improve the accuracy of the calculated surface deflection, giving results close to those obtained from the accurate but computer intensive finite element model.

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.

No description available.

A subaperture configuration to test aspheric optical components or systems is developed. The method developed has potential for testing rotationally symmetric aspheres without the use of null lenses. The aperture is divided into annular subaperture regions and an interferometer is refocused for each region to reduce the fringe density. Essential mathematical treatments involving annular subapertures, such as annular Zernike polynomials, are provided in detail. Numerical and experimental validations of the algorithm are described. Tolerance analyses on subaperture measurements are given. Computer programs were written to link the subaperture Zernike coefficients and to determine the full-aperture Zernike coefficients.