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10 December 2001 Stitching interferometry of aspherical surfaces
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Sub-aperture stitching interferometry (SASI) is an appropriate method to measure either large optical plane surface topologies or aspheres with strong deviation from the flatness with standard interferometers. Using SASI the surface shape is measured with a higher lateral resolution by multiple adjacent sub-aperture measurements with a sufficient overlap of the neighboring areas. In a second step, the total surface shape is composed with the help of a computer code by stitching the sub-aperture areas together. The overlap areas allow fitting. By means of a regression analysis, tilt and vertical displacement of adjacent areas are calculated and minimized. A confidence band calculated using a MATLAB based code describes the accuracy of the composition. The variance of this estimation is inverse proportional to the peak to valley value (PV) of the measured area and decreases with a 10-3 scaling of the width of the overlapping area. A statistical experimental design method is used to minimize the number of sub-apertures to be measured. The accuracy of the stitched total surface measurement can be increased with the help of model calculations by optimizing (i) the position of the sub-aperture, which was regarded as a standard, and (ii) the sequence of the stitched adjacent areas.
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Thomas Haensel, Andreas Nickel, and Axel Schindler "Stitching interferometry of aspherical surfaces", Proc. SPIE 4449, Optical Metrology Roadmap for the Semiconductor, Optical, and Data Storage Industries II, (10 December 2001);

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