LINEAR METHODS OF COMPUTER CONTROLLED OPTICAL FIGURING.

Abstract

The problem of using a computer to control the figuring of an optical surface is investigated. By assuming a linear, shift invariant figuring process, the amount of material removed during each figuring run can be computed. This is done by convolving a tool removal profile with a dwell function that describes the amount of time the figuring tool spends in each area element on the surface. Four methods of computing a dwell function that will best remove the figure errors are described. The advantages of making surface figure measurements using direct wavefront measurement techniques over the interferogram analysis methods used in previous computer controlled figuring machines are also discussed. The design and construction of a computer controlled optical figuring machine is then reviewed. The machine uses a computer controlled heterodyne interferometer to provide optical testing data on the surface being polished. Two microcomputers are used to analyze the test data and run the machine. Optical figuring is performed by scanning a polishing head with a known removal function over the surface at a rate derived from the surface errors. The operation of the software that computes the run path data and controls the machine hardware is outlined. The performance of each of the machine components is evaluated by comparing the behavior predicted by theory to the measured behavior. Initially, the accuracy of the interferometer is measured. The interferometer is then used to determine the performance of the polishing head by measuring the tool removal function. It is then shown that the machine can be run so that a predictable amount of material is removed from the surface. Finally, the feedback loop is closed and surface figure data from the interferometer is used to correctly polish the central region of a 16 inch diameter mirror. It is shown that the surface figure can be predicted with good accuracy over the entire surface. This work concludes with recommendations for improving the machine hardware and for improving the figuring performance near the edge of the surface being polished.