Surface reconstruction by using Zernike polynomials

Manon Schilke; Johannes Liebl; Christine Wünsche

doi:10.1117/12.2236305

30 June 2016 Surface reconstruction by using Zernike polynomials

Manon Schilke, Johannes Liebl, Christine Wünsche

Proceedings Volume 10009, Third European Seminar on Precision Optics Manufacturing; 1000910 (2016) https://doi.org/10.1117/12.2236305
Event: Third European Seminar on Precision Optics Manufacturing, 2016, Teisnach, Germany

Abstract

The development of high precision methods for the measurement of plano surfaces became of increasing importance over the last years. Recently accuracies in sub-nanometer range have been achieved on samples up to one meter in diameter. The used measurement method was based on direct deflectometry. The main part of the system was an electronic autocollimator measuring local angular displacements on defined traces along the surface of the plano lens. To stabilize the optical path a pentaprism was used. The measurement accuracy of a similar system was evaluated at the Technologie Campus Teisnach. The used system delivered twenty measurement spots along the profile on one diameter. Four diameters were measured at every 45 degrees. An evaluation algorithm was developed to model the complete threedimensional surface out of a small amount of measurement points. Within this modelling Zernike polynomials were used to reconstruct the surface topography. Two different approaches in using the hierarchy of the polynomials were compared.

At first a reference surface was created by rotating a symmetrical averaged curve of all measured profiles. On the residuals of the original measurements to the symmetrical averaged curve a serial development of the error surface was applied with the help of Zernike polynomials. Different order of Zernike terms were tested because we saw a big influence on the result. This surface was added to the reference surface. The results of the two different approaches were compared. To enable us to compare the results of this measurement method to interferometric and optical 3Dprofilometric measurements the data was converted to xyz-format.

Citation Download Citation

Manon Schilke, Johannes Liebl, and Christine Wünsche "Surface reconstruction by using Zernike polynomials", Proc. SPIE 10009, Third European Seminar on Precision Optics Manufacturing, 1000910 (30 June 2016); https://doi.org/10.1117/12.2236305

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