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Applied Optics

Applied Optics


  • Vol. 43, Iss. 16 — Jun. 1, 2004
  • pp: 3217–3223

Image aberrations in optical three-dimensional measurement systems with fringe projection

Peter Brakhage, Gunther Notni, and Richard Kowarschik  »View Author Affiliations

Applied Optics, Vol. 43, Issue 16, pp. 3217-3223 (2004)

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In optical shape measurement systems, systematic errors appear as a result of imaging aberrations of the lens assemblies in the cameras and projectors. A mathematical description of this effect is intended to correct the whole measurement area with a few independent coefficients. We apply the ideas of photogrammetry to one- and two-dimensional fringe projection techniques. We also introduce some new terms for close-range applications and telecentric objectives. Further, an algorithm for distance-dependent corrections is introduced. Also, we describe a new method with which to determine coefficients of aberration with an optimization-based method.

© 2004 Optical Society of America

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(110.6880) Imaging systems : Three-dimensional image acquisition
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3940) Instrumentation, measurement, and metrology : Metrology
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.1000) Optical design and fabrication : Aberration compensation

Original Manuscript: September 8, 2003
Revised Manuscript: March 1, 2004
Published: June 1, 2004

Peter Brakhage, Gunther Notni, and Richard Kowarschik, "Image aberrations in optical three-dimensional measurement systems with fringe projection," Appl. Opt. 43, 3217-3223 (2004)

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  1. M. A. R. Cooper, S. Robson, “Theory of close range photogrammetry,” in Close Range Photogrammetry and Machine Vision, K. B. Atkinson, ed. (Whittles, Caithness, Scotland, 1996), pp. 9–22.
  2. K. Kraus, Photogrammetrie (de Gruyter, Bonn, Germany, 1982), Vols. 1 and 2.
  3. G. Konecny, G. Lehmann, Photogrammetrie, 4th ed. (de Gruyter, Berlin, 1984).
  4. W. Schreiber, G. Notni, “Theory and arrangements of self-calibrating whole-body three-dimensional measurement systems using fringe projection technique,” Opt. Eng. 39, 159–169 (2000). [CrossRef]
  5. T. Luhmann, Nahbereichsphotogrammetrie (Wichmann, Heidelberg, Germany, 2000).
  6. V. Kirschner, W. Schreiber, R. Kowarschik, G. Notni, “Self-calibrating shape-measuring system based on fringe projection,” in Rapid Prototyping and Flexible Manufacturing, R.-J. Ahlers, G. Reinhart, eds., Proc. SPIE3102, 5–13 (1997). [CrossRef]
  7. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis—Digital Fringe Pattern Measurement Techniques, D. W. Robinson, G. T. Reid, eds. (Institute of Physics Publishing, Bristol, UK, 1993), pp. 95–140.
  8. G. Wiora, R. Malz, U. Laukenmann, “Robustes erweitertes Kalibrier- und Messverfahren für Streifenprojektionssysteme mit metrischem Projektor,” in 6. Symposium Bildverarbeitung 1999, R. Ahlers, ed. (Technische Akademie Esslingen, Esslingen, 1999), Vol. 6, pp. 215–230.
  9. S. A. A. Viana, J. Waldmann, F. de Freitas Caetano, “Non-linear optimization-based batch calibration with accuracy evaluation,” Sociedade Brasileira de Automática Controle Automação 10, 89–99 (1999).
  10. W. Schreiber, G. Notni, P. Kühmstedt, J. Gerber, R. Kowarschik, “Optical 3D-coordinate measuring system using structured light,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 620–627 (1996). [CrossRef]
  11. R. Kowarschik, P. Kühmstedt, J. Gerber, W. Schreiber, G. Notni, “Adaptive optical three-dimensional measurement with structured light,” Opt. Eng. 39, 150–158 (2000). [CrossRef]
  12. J. G. Fryer, “Camera calibration,” in Close Range Photogrammetry and Machine Vision, K. B. Atkinson, ed. (Whittles, Caithness, Scotland, 1996), pp. 156–164.
  13. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999).
  14. F. L. Pedrotti, L. S. Pedrotti, Optics and Vision (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  15. H. Haferkorn, Bewertung Optischer Systeme (VEB Deutscher Verlag, Berlin, 1986).
  16. D. C. Brown, “Close-range camera calibration,” Photogram. Eng. 38, 855–866 (1971).
  17. P. J. Scott, “The pupil in perspective,” Photogrammetric Record 49, 83–92 (1977).
  18. A. A. Magill, “Variation in distortion with magnification,” J. Res. Nat. Bureau Stand. U.S. 54, 135–142 (1955). [CrossRef]
  19. R. Schuhmann, T. Thöniss, “Telezentrische Systeme für die optische Mess- und Prüftechnik,” Technisches Messen 65, 131–136 (1998).
  20. W. Schreiber, V. Kirschner, R. Kowarschik, G. Notni, “Managing some calibration problems in fringe projection shape measurement systems,” in Fringe ’97, W. Jüptner, W. Osten, eds. (Akademie Verlag, Berlin, 1997), pp. 443–450.
  21. W. Wester-Ebbinghaus, “Bündeltriangulation mit gemeinsamer Ausgleichung photogrammetrischer und geodätischer Beobachtungen,” Zeitschrift für Vermessungswesen 3, 101–110 (1985).
  22. J. E. Dennis, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

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