Measurement of aspherical surfaces using a test plate and computer generated holograms

Abstract

A major paradigm shift in the design of large telescopes is currently in progress. In order to increase the size of a telescope primary mirror, current designs use mirrors that are comprised of multiple segments instead of one monolithic piece. While this approach allows for larger primary mirrors than the monolithic approach, new challenges arise. One of the primary challenges is to accurately, rapidly, and cost-effectively test the multiple asphere segments. This dissertation provides a thorough design analysis and experimental validation on a novel method, proposed by Burge and Anderson, for measuring off-axis aspherical surfaces using test plate and computer-generated holograms. This new method is optimal for measuring segments of aspheric primary mirrors, and can be applied to any aspheric surface, convex or concave. It interferometrically compares the aspheric surface with a nearly matching spherical reference surface and uses CGH to compensate the aspherical departure. Like other Fizeau-type interferometric tests, high accuracy is achieved economically since the spherical reference is the only surface that directly affects the measurement. This technique is optimal for testing primary mirror segments where all the different off-axis pieces of the asphere can be measured with a single test plate, replacing only the smaller hologram. The most important property of this test for segmented mirrors is the fine control of the curvature provided by using a reference plate in close proximity to the aspherical surface being measured. This allows all the segments to be separately manufactured, assumes that they will fit together to form a single aspheric surface. In this dissertation, I examine, optimize, and validate this novel method, making it readily available for future telescope designers/manufacturers. First, the quantitative analysis on how segmentation tightens the testing requirements during fabrication and alignment provides valuable information in determining essential telescope parameters such as segment size, F/#, fabrication and alignment specifications. Secondly, the detailed optimization processes show how the test system can be designed and built to achieve high accuracy with maximum cost effectiveness. Lastly, the experimental data successfully validate the test and the method of design and analysis.