Browse > Article
http://dx.doi.org/10.3807/KJOP.2014.25.5.273

Free-Form Surface Reconstruction Method from Second-Derivative Data  

Kim, Byoung Chang (Department of Mechanical Engineering, Kyungnam University)
Kim, DaeWook (2College of Optical Science, University of Arizona)
Kim, GeonHee (Center for Analytical Instrumentation Development, Korea Basic Science Institute)
Publication Information
Korean Journal of Optics and Photonics / v.25, no.5, 2014 , pp. 273-278 More about this Journal
Abstract
We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x- and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.
Keywords
Profilometry; Second derivative; Surface reconstruction; Free-form surface;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. W. Kim, B. C. Kim, C. Zhao, C. J. Oh, and J. H. Burge, "Algorithm for surface reconstruction from curvature data for freeform aspheric," Optical Manufacturing and Testing X, Proc. SPIE 8838, 88380B1-9 (2013).
2 W. H. Southwell, "Wavefront estimation from wave-front slope measurements," JOSA 70, 998-1006 (1980).   DOI   ScienceOn
3 P. Thomsen-Schmidt, M. Schulz, and I. Weingartner, "A facility for the curvature-based measurement of the nanotopography of complex surfaces," in Optical Devices and Diagnostics in Materials Science, D. L. Andrew, T. Asakura, S. Jutamulia, W. P. Kirk, M. G. Lagally, R. B. Lal, and J. D. Trolinger eds., Proc. SPIE 4098, 94-101 (2000).
4 C. Elster, J. Gerhardt, P. Thomsen-Schmidt, M. Schulz, and I. Weingartner, "Reconstructing surface profiles from curvature measurements," Optik 113, 154-158 (2002).   DOI   ScienceOn
5 I. Weingartner, M. Schulz, P. Thomsen-Schmidt, and C. Elster, "Measurement of steep aspheres: A step forward to nanometer accuracy," in Optical Metrology for the Semiconductor, Optical, and Data Storage Industries II, A. Duparre and B. Singh, eds., Proc. SPIE 4449, 195-204 (2001).
6 M. Schulz, "Topography measurement by a reliable large-area curvature sensor," Optik 112, 86-90 (2001).   DOI
7 M. Schulz and I. Weingartner, "Measurement of steep aspheres by curvature scanning: An uncertainty budget," Proc. 2nd Euspen International Conference, 478-481 (2001).
8 M. Schulz, R. D. Geckeler, and J. Illemann, "High accuracy form measurement of large optical surfaces," in Recent Developments in Traceable Dimensional Measurements II, J. E. Decker and N. Brown, eds., Proc. SPIE 5190, 211-219 (2003).
9 B. C. Kim, T. Saiag, Q. Wang, J. Soons, R. S. Polvani, and U. Griesmann, "The geometry measuring machine (GEMM) project at NIST," in Free-Form Optics: Design, Fabrication, Metrology, Assembly, ASPE 2004 Winter Topical Meeting (North Carolina, USA, 2004), pp. 108-111.
10 Y. K. Kwon, B. C. Kim, D. H. Wang, Y. W. Lee, H. S. Yang, and H. G. Rhee, "Aspheric measurement based on the curvature sensing method," Proc. SPIE 6671, 667119-667126 (2007).
11 U. Griesmann, N. Machkour-Deshayes, J. Soons, B. C. Kim, Q. Wang, J. R. Stoup, and L. Assoufld, "Uncertainties in aspheric profile measurements with the geometry measuring machine at NIST," in Advanced Characterization Techniques for Optics, Semiconductors, and Nanotechnologies II, A. Duparre, B. Singh, Z. Gu, eds., Proc. SPIE 5878, 112-124 (2005).
12 B. C. Kim, M. C. Kwon, B. U. Choo, and I. J. Yoon, "3-D shape measurement using curvature data," Proc. SPIE 7389, 73892H-8 (2009).
13 P. E. Glenn, "Angstrom level profilometry for submillimeter to meter scale surface errors," in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, and L. R. Baker, eds., Proc. SPIE 1333, 326-336 (1990).
14 P. E. Glenn, "Lambda-over-one-thousand metrology results for steep aspheres using a curvature profiling technique," in Advanced Optical Manufacturing and Testing II, V. J. D. D. V. M. ed., Proc. SPIE 1531, 61-64 (1992).