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3 December 2014 Absolute measurement of square flats with Legendre polynomial fitting method
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Zernike Polynomial fitting method is an effective way to reconstruct absolute surface for three-flat test. However, the Zernike circle polynomials are not orthogonal over the circular area, hence they are not suitable for square flat. We present an absolute testing of a square flat with Legendre polynomial fitting method, which relies on calculating the coefficients of the Legendre terms by least-square fitting method. To obtain the three-dimensional surface data, one additional measurement that rotate the test flat through 90° should be introduced. The formulas are derived theoretically in detail, and validity has been proved by simulated experiment. Vertical profiles of the three surfaces are compared with the measurement results obtained by three-flat test. Good agreement validates our method.
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Bo Gao, Qiang Li, Yuhang He, Liqun Chai, and Xiaohong Wei "Absolute measurement of square flats with Legendre polynomial fitting method", Proc. SPIE 9297, International Symposium on Optoelectronic Technology and Application 2014: Laser and Optical Measurement Technology; and Fiber Optic Sensors, 92970E (3 December 2014);

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