OPTICS FOR LARGE TELESCOPE.

Abstract

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.