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Applied Optics

Applied Optics


  • Vol. 39, Iss. 10 — Apr. 1, 2000
  • pp: 1511–1520

Position and displacement sensing with Shack–Hartmann wave-front sensors

Jorge Ares, Teresa Mancebo, and Salvador Bará  »View Author Affiliations

Applied Optics, Vol. 39, Issue 10, pp. 1511-1520 (2000)

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The use of a Shack–Hartmann wave-front sensor as a position-sensing device is proposed and demonstrated. The coordinates of a pointlike object are determined from the modal Zernike coefficients of the wave fronts emitted by the object and detected by the sensor. The position of the luminous centroid of a moderately extended incoherent flat object can also be measured with this device. Experimental results with off-the-shelf CCD cameras and conventional relay optics as well as inexpensive diffractive microlens arrays show that axial positioning accuracies of 74 µm rms at 300 mm and angular accuracies of 4.3 µrad rms can easily be achieved.

© 2000 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(220.4840) Optical design and fabrication : Testing

Original Manuscript: October 5, 1999
Revised Manuscript: January 14, 2000
Published: April 1, 2000

Jorge Ares, Teresa Mancebo, and Salvador Bará, "Position and displacement sensing with Shack–Hartmann wave-front sensors," Appl. Opt. 39, 1511-1520 (2000)

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  1. R. K. Tyson, Principles of Adaptive Optics (Academic, Boston, Mass., 1991).
  2. F. Merkle, “Adaptive optics,” in International Trends in Optics, J. W. Goodman, ed. (Academic, New York, 1991), Chap. 26, pp. 375–390. [CrossRef]
  3. J. Primot, G. Rousset, J. C. Fontanella, “Deconvolution from wave-front sensing: a new technique for compensating turbulence-degraded images,” J. Opt. Soc. Am. A. 7, 1589–1608 (1990). [CrossRef]
  4. H. J. Tiziani, J. H. Chen, “Shack–Hartmann sensor for fast infrared wave-front testing,” J. Mod. Opt. 44, 535–541 (1997). [CrossRef]
  5. G. Artzner, “Aspherical wavefront measurements: Shack–Hartmann numerical and practical experiments,” Pure Appl. Opt. 7, 435–448 (1998). [CrossRef]
  6. J. Pfund, N. Lindlein, J. Schwider, R. Burow, Th. Blümel, K.-E. Elssner, “Absolute sphericity measurement: a comparative study of the use of interferometry and a Shack–Hartmann sensor,” Opt. Lett. 23, 742–744 (1998). [CrossRef]
  7. T. Kohno, S. Tanaka, “Figure measurement of concave mirror by fiber-grating Hartmann test,” Opt. Rev. 1, 118–120 (1994). [CrossRef]
  8. N. S. Prasad, S. M. Doyle, M. K. Giles, “Collimation and beam alignment: testing and estimation using liquid-crystal televisions,” Opt. Eng. 35, 1815–1819 (1996). [CrossRef]
  9. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wavefront sensor,” J. Opt. Soc. Am. A. 11, 1949–1957 (1994). [CrossRef]
  10. L. Diaz, J. C. Dainty, “Single-pass measurements of the wave-front aberrations of the human eye by use of retinal lipofuscin autofluorescence,” Opt. Lett. 24, 61–63 (1999). [CrossRef]
  11. M. P. Rimmer, J. C. Wyant, “Evaluation of large aberrations using a lateral-shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975). [CrossRef] [PubMed]
  12. G. Häusler, J. Hutfless, M. Maul, H. Weissmann, “Range sensing based on shearing interferometry,” Appl. Opt. 27, 4638–4644 (1988). [CrossRef] [PubMed]
  13. G. Harbers, P. J. Kunst, G. W. R. Leibbrandt, “Analysis of lateral shearing interferograms by use of Zernike polynomials,” Appl. Opt. 35, 6162–6172 (1996). [CrossRef] [PubMed]
  14. R. Navarro, E. Moreno-Barriuso, “A laser ray tracing method for optical testing,” Opt. Lett. 24, 951–953 (1999). [CrossRef]
  15. C. Castellini, F. Francini, B. Tiribilli, “Hartmann test modification for measuring ophtalmic progressive lenses,” Appl. Opt. 33, 4120–4124 (1994). [CrossRef] [PubMed]
  16. G. Häusler, G. Schneider, “Testing optics by experimental ray tracing with a lateral effect photodiode,” Appl. Opt. 27, 5160–5164 (1988). [CrossRef] [PubMed]
  17. M. R. Teague, “Irradiance moments: their propagation and use for unique retrieval of phase,” J. Opt. Soc. Am. 72, 1199–1209 (1982). [CrossRef]
  18. J. Hartmann, “Objectivuntersuchungen,” Z. Instrum. XXIV, 1–21, 3–47, 98–117 (1904).
  19. G. Y. Yoon, T. Jitsuno, M. Nakatsuka, S. Nakai, “Shack Hartmann wave-front measurement with a large F-number plastic microlens array,” Appl. Opt. 35, 188–192 (1996). [CrossRef] [PubMed]
  20. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1993), pp. 464–466, 767–772.
  21. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynomials,” Appl. Opt. 19, 1510–1518 (1980). [CrossRef] [PubMed]
  22. D. Malacara, S. L. DeVore, “Interferogram evaluation and wavefront fitting,” in Optical Shop Testing, 2nd ed, D. Malacara, ed. (Wiley, New York, 1992), Chap. 13, pp. 455–499.
  23. P. B. Liebelt, An Introduction to Optimal Estimation (Addison-Wesley, Reading, Mass., 1967), pp. 135–172.
  24. E. P. Wallner, “Optimal wave-front correction using slope measurements,” J. Opt. Soc. Am. 73, 1771–1776 (1983). [CrossRef]
  25. M. C. Roggemann, “Optical performance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,” Comput. Electr. Eng. 18, 451–466 (1992). [CrossRef]
  26. D. P. Petersen, K. H. Cho, “Sampling and reconstruction of a turbulence-distorted wave front,” J. Opt. Soc. Am. A 3, 818–825 (1986). [CrossRef]
  27. V. V. Voitsekhovich, S. Bará, S. Ríos, E. Acosta, “Minimum-variance phase reconstruction from Hartmann sensors with circular subpupils,” Opt. Commun. 148, 225–229 (1998). [CrossRef]
  28. P. A. Bakut, V. E. Kirakoshyants, V. A. Loginov, C. J. Solomon, J. C. Dainty, “Optimal wavefront reconstruction from a Shack–Hartmann sensor by use of a Bayesian algorithm,” Opt. Commun. 109, 10–15 (1994). [CrossRef]
  29. C. J. Solomon, J. C. Dainty, N. Wooder, “Bayesian estimation of atmospherically distorted wavefronts using Shack–Hartmann sensors,” Opt. Rev. 2, 217–220 (1995). [CrossRef]
  30. J. Herrmann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980). [CrossRef]
  31. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  32. J. Pfund, N. Lindlein, J. Schwider, “Misalignment effects of the Shack–Hartmann sensor,” Appl. Opt. 37, 22–27 (1998). [CrossRef]
  33. G. Roblin, D. Horville, “Study of the aberration induced by a microlens array,” J. Opt. 24, 77–87 (1993). [CrossRef]
  34. Ref. 20, p. 757.

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