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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 26, Iss. 12 — Dec. 1, 2009
  • pp: 2538–2549

Perturbation methods in optics: application to the interferometric measurement of surfaces

Eugenio Garbusi and Wolfgang Osten  »View Author Affiliations

JOSA A, Vol. 26, Issue 12, pp. 2538-2549 (2009)

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Manufacturing and misalignment errors are present in every optical system. Usually these errors lead to intolerable wavefront deviations and system inaccuracies if they are not characterized and taken into consideration. In the interferometric measurement of surfaces, the characterization of the interferometer aberrations plays a central role, since unknown phase contributions lead to an erroneous assessment of the test surface and therefore an incorrect estimation of the performance of an optical system. In this work, we present a method for the interferometric characterization of surfaces based on the principles of Hamilton’s characteristic functions and perturbation theory. The application of the proposed method to an interferometer for the measurement of aspherical surfaces is shown.

© 2009 Optical Society of America

OCIS Codes
(120.3940) Instrumentation, measurement, and metrology : Metrology
(220.1250) Optical design and fabrication : Aspherics
(220.3620) Optical design and fabrication : Lens system design

ToC Category:
Optical Design and Fabrication

Original Manuscript: June 5, 2009
Manuscript Accepted: September 3, 2009
Published: November 9, 2009

Eugenio Garbusi and Wolfgang Osten, "Perturbation methods in optics: application to the interferometric measurement of surfaces," J. Opt. Soc. Am. A 26, 2538-2549 (2009)

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  1. H. J. Tiziani, “Optical methods for precision measurements,” Opt. Quantum Electron. 21, 253-282 (1989). [CrossRef]
  2. B. Braunecker, R. Hentschel, and H. J. Tiziani, “Advanced Optics Using Aspherical Elements,” SPIE Press Monograph, Vol. PM173 (2008).
  3. E. J. Hinch, Perturbation Methods, Cambridge Texts in Applied Mathematics (Cambridge Univ. Press, 2002).
  4. J. L. Synge, Geometrical Optics: An Introduction to Hamilton's Method (Cambridge Univ. Press, 1937).
  5. R. K. Luneburg, Mathematical Theory of Optics (U. California Press, 1964), Chap. 2.
  6. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, 1993), Chap. 2 and 3.
  7. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press, 1999), Chap. 3.
  8. H. H. Hopkins and H. J. Tiziani, “A theoretical and experimental study of lens centering errors and their influence on optical image quality,” Br. J. Appl. Phys. 17, 33-54 (1966). [CrossRef]
  9. M. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533-537 (1970). [CrossRef] [PubMed]
  10. B. D. Stone, “Perturbations of optical systems,” J. Opt. Soc. Am. A 14, 2837-2849 (1997). [CrossRef]
  11. R. N. Youngworth and B. D. Stone, “Simple estimates for the effects of mid-spatial-frequency surface errors on image quality,” Appl. Opt. 39, 2198-2209 (2000). [CrossRef]
  12. W. Osten, “Messung von Verschiebungsfeldern und Objektkoordinaten mit optimierten holografischen Interferometern,” Ph.D. dissertation (Martin-Luther-Universitaet, Halle, Germany, 1983).
  13. W. Osten, “Some considerations on the statistical error analysis in holographic interferometry,” J. Mod. Opt. 32, 827-838 (1985). [CrossRef]
  14. J. Liesener, E. Garbusi, C. Pruss, and W. Osten, “Verfahren und Messvorrichtung zur Vermessung einer optisch glatten Oberflaeche,” Deutsches Patent und Markenamt: 10 2006 057 606.3.
  15. E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33, 2973-2975 (2008). [CrossRef] [PubMed]
  16. C. J. Evans and J. B. Bryan, “Compensation for errors introduced by nonzero fringe densities in phase-measuring interferometers,” CIRP Annals Manufacturing Technology , 42, 577-580 (1993). [CrossRef]
  17. G. Schulz, “Aspheric surfaces,” in Progress in Optics, Vol. XXV, E.Wolf, ed. (North-Holland, 1988), pp. 349-415. [CrossRef]
  18. J. E. Greivenkamp and R. O. Gappinger, “Design of a nonnull interferometer for aspheric wave fronts,” Appl. Opt. 43, 5143-5151 (2004). [CrossRef] [PubMed]
  19. M. Andrews, “Concatenation of characteristic functions in Hamiltonian optics,” J. Opt. Soc. Am. 72, 1493-1497 (1982). [CrossRef]
  20. D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (Taylor & Francis, 2005), Chap. 4. [CrossRef]
  21. A. W. Lohmann and D. P. Paris, “Space-variant image formation,” J. Opt. Soc. Am. 55, 1007-1013 (1965). [CrossRef]
  22. ZEMAX Development Corporation, www.zemax.com.
  23. G. N. Lawrence and W. W. Chow, “Wave-front tomography by Zernike polynomial decomposition,” Opt. Lett. 9, 267-269 (1984). [CrossRef] [PubMed]
  24. C. Progler and A. Wong, “Zernike coefficients: are they really enough?” Proc. SPIE 4000, 40-52 (2000). [CrossRef]
  25. H. A. Buchdahl, “Perturbations of the point characteristic,” J. Opt. Soc. Am. A 7, 2260-2263 (1990). [CrossRef]
  26. H. A. Buchdahl, “Perturbed characteristic functions II,” Int. J. Theor. Phys. 24, 457-465 (1985). [CrossRef]
  27. H. A. Buchdahl, “Perturbed characteristic functions III,” Int. J. Theor. Phys. 29, 209-213 (1990). [CrossRef]
  28. W. S. S. Blaschke, “A procedure for the differential correction of optical systems allowing large parameter changes,” J. Mod. Opt. 3, 10-23 (1956). [CrossRef]
  29. B. R. A. Nijboer, “The diffraction theory of aberrations,” Ph.D. dissertation (University of Groningen, Groningen, The Netherlands, 1942).

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