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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 9 — Sep. 1, 2008
  • pp: 2331–2337

Differential Shack–Hartmann curvature sensor: local principal curvature measurements

Weiyao Zou, Kevin P. Thompson, and Jannick P. Rolland  »View Author Affiliations


JOSA A, Vol. 25, Issue 9, pp. 2331-2337 (2008)
http://dx.doi.org/10.1364/JOSAA.25.002331


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Abstract

The concept of a differential Shack–Hartmann (DSH) curvature sensor was recently proposed, which yields wavefront curvatures by measuring wavefront slope differentials. As an important feature of the DSH curvature sensor, the wavefront twist curvature terms can be efficiently obtained from slope differential measurements, thus providing a means to measure the Monge-equivalent patch. Specifically, the principal curvatures and principal directions, four key parameters in differential geometry, can be computed from the wavefront Laplacian and twist curvature terms. The principal curvatures and directions provide a “complete” definition of wavefront local shape. Given adequate sampling, these measurements can be useful in quantifying the mid-spatial-frequency wavefront errors, yielding a complete characterization of the surface being measured.

© 2008 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(120.6650) Instrumentation, measurement, and metrology : Surface measurements, figure
(220.4840) Optical design and fabrication : Testing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: January 14, 2008
Revised Manuscript: June 20, 2008
Manuscript Accepted: July 15, 2008
Published: August 21, 2008

Citation
Weiyao Zou, Kevin P. Thompson, and Jannick P. Rolland, "Differential Shack-Hartmann curvature sensor: local principal curvature measurements," J. Opt. Soc. Am. A 25, 2331-2337 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-9-2331


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References

  1. P. E. Glenn, “Robust, sub-angstrom level mid-spatial frequency profilometry,” Proc. SPIE 1333, 230-238 (1990). [CrossRef]
  2. I. Weingaertner, M. Schulz, and C. Elster, “Novel scanning technique for ultra-precise measurement of topography,” Proc. SPIE 3782, 306-317 (1999). [CrossRef]
  3. M. Schulz, “Topography measurement by a reliable large-area curvature sensor,” Optik (Stuttgart) 112, 86-90 (2001). [CrossRef]
  4. I. Weingaertner, M. Schulz, P. Thomsen-Schmidt, and C. Elster, “Measurement of steep aspheres: a step toward nanometer accuracy,” Proc. SPIE 4449, 195-204 (2001). [CrossRef]
  5. P. Glenn, “Angstrom level profilometry for sub-millimeter to meter scale surface errors,” Proc. SPIE 1333, 326-336 (1990). [CrossRef]
  6. F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223-1225 (1988). [CrossRef] [PubMed]
  7. C. Paterson and J. C. Dainty, “Hybrid curvature and gradient wave-front sensor,” Opt. Lett. 25, 1687-1689 (2000). [CrossRef]
  8. H. V. Tippur, “Coherent gradient sensing: a Fourier optics analysis and applications to fracture,” Appl. Opt. 31, 4428-4439 (1992). [CrossRef] [PubMed]
  9. J. J. Koenderink, Solid Shape (MIT, 1990), pp. 210, 214, 212, 228, 232.
  10. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).
  11. R. Ragazzoni, “Pupil plane wavefront sensing with an oscillating prism,” J. Mod. Opt. 43, 289-293 (1996). [CrossRef]
  12. W. Zou and J. Rolland, “Differential wavefront curvature sensor,” Proc. SPIE 5869, 5869171 (2005).
  13. W. Zou and J. Rolland, “Differential Shack-Hartmann curvature sensor,” U.S. patent 7,390,999 (24 June 2008).
  14. M. Sarazin and F. Roddier, “The ESO differential image motion monitor,” Astron. Astrophys. 227, 294-300 (1990).
  15. A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac. 114, 1156-1166 (2002). [CrossRef]
  16. V. Interrante, H. Fuchs, and S. M. Pizer, “Conveying the 3D shape of smoothly curving transparent surface via texture,” IEEE Trans. Vis. Comput. Graph. 3, 98-117 (1997). [CrossRef]
  17. W. Zou, “Optimization of zonal wavefront estimation and curvature measurements,” Ph.D. dissertation (University of Central Florida, 2007).
  18. Adaptive Optics Associates Inc., part no. 1790-90-s, http://www.aoainc.com/index.html.
  19. O. Guyon, “Limits of adaptive optics for high-contrast imaging,” Astrophys. J. 629, 592-614 (2005). [CrossRef]
  20. J. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).
  21. C. Roddier and F. Roddier, “Wave-front reconstruction from defocused images and the testing of ground-based optical telescopes,” J. Opt. Soc. Am. A 10, 2277-2287 (1993). [CrossRef]

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