Abstract
An iterative algorithm has been successfully used to process data from the three-flat test. On the basis of the iterative algorithm proposed by Vannoni, which is much faster and more effective than the Zernike polynomial fitting method, an improved algorithm is presented. By optimizing the iterative steps and removing the scaling factors, the surface shape can be easily computed in a few iterations. The validity of the method is proved by computer simulation, and the interpolation error and principle error are analyzed.
Highlights
The three-flat test method is generally adopted to measure absolute flatness
Schulz and Schwider proposed and developed the earliest three-flat test method, which required three flats to be compared in pairs.[1,2]
The flaw in our method is that the residual error between the reconstructed surface and the measured surface will not decrease after 100 iteration steps, as confirmed by the computer simulation
Summary
The three-flat test method is generally adopted to measure absolute flatness. Schulz and Schwider proposed and developed the earliest three-flat test method, which required three flats to be compared in pairs.[1,2] Three measurements could determine only the profile of one diameter. To reconstruct the three-dimensional surface data, many methods have been introduced in which additional measurements are added, e.g., one of the three plates is rotated at least once Among these methods, the Zernike polynomial fitting method proposed by Fritz is one of the most remarkable.[3,4,5,6,7,8] To cover more frequencies of the reconstructed surface, more polynomials must be fitted, so the computation is much more intensive.
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