OSA's Digital Library

Optics Express

Optics Express

  • Editor: Micha
  • Vol. 13, Iss. 23 — Nov. 14, 2005
  • pp: 9570–9584

Hartmann-Shack test with random masks for modal wavefront reconstruction

Oleg Soloviev and Gleb Vdovin  »View Author Affiliations

Optics Express, Vol. 13, Issue 23, pp. 9570-9584 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (709 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The paper discusses the influence of the geometry of a Hartmann-(Shack) wavefront sensor on the total error of modal wavefront reconstruction. A mathematical model is proposed, which describes the modal wavefront reconstruction in terms of linear operators. The model covers the most general case and is not limited by the orthogonality of decomposition basis or by the method chosen for decomposition. The total reconstruction error is calculated for any given statistics of the wavefront to be measured. Based on this estimate, the total reconstruction error is calculated for regular and randomised Hartmann masks. The calculations demonstrate that random masks with non-regular Fourier spectra provide absolute minimum error and allow to double the number of decomposition modes.

© 2005 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing

ToC Category:
Research Papers

Original Manuscript: September 26, 2005
Revised Manuscript: November 7, 2005
Published: November 14, 2005

Oleg Soloviev and Gleb Vdovin, "Hartmann-Shack test with random masks for modal wavefront reconstruction," Opt. Express 13, 9570-9584 (2005)

Sort:  Journal  |  Reset  


  1. I. Ghozeil, Optical Shop Testing, chap. Hartmann and Other Screen Tests, 2nd ed. (JohnWiley & Sons, Inc., New York, 1992), pp. 367 �?? 396
  2. R. K. Tyson, Principles of adaptive optics, 2nd ed. (Academic Press, Boston, 1998).
  3. D. L. Fried, �??Least-squares fitting a wave-front distortion estimate to an array of phase-difference measurements,�?? J. Opt. Soc. Am. 67, 370 �?? 375 (1977). [CrossRef]
  4. B. R. Hunt, �??Matrix formulation of the reconstruction of phase values from phase differences,�?? J. Opt. Soc. Am. 69, 393 �??399 (1979). [CrossRef]
  5. W. H. Southwell, �??Wave-front estimation from wave-front slope measurements,�?? J. Opt. Soc. Am. 70, 998 �?? 1006 (1980). [CrossRef]
  6. K. R. Freischlad and C. L. Koliopoulos, �??Modal estimation of a wave front from difference measurements using the discrete Fourier transform,�?? J. Opt. Soc. Am. A 3, 1852 �?? 1861 (1986). [CrossRef]
  7. M. C. Roggemann, �??Optical perfomance of fully and partially compensated adaptive optics systems using least-squares and minimum variance phase reconstructors,�?? Computers Elect. Engng 18, 451�??466 (1992). [CrossRef]
  8. R. G. Lane and M. Tallon, �??Wavefront reconstruction using a Shack-Hartmann sensor,�?? Appl. Opt. 31, 6902 �?? 6908 (1992). [CrossRef] [PubMed]
  9. G.-m. Dai, �??Modified Hartmann-Shack Wavefront Sensing and Iterative Wavefront Reconstruction,�?? in Adaptive Optics in Astronomy, vol. 2201 of Proceedings of SPIE, (SPIE, 1994), pp. 562 �?? 573.
  10. G.-m. Dai, �??Modal compensation of atmospheric turbulence with the use of Zernike polynomials and Karhunen-Loève functions,�?? J. Opt. Soc. Am. A 12, 2182 �?? 2193 (1995). [CrossRef]
  11. G.-m. Dai, �??Modal wavefront reconstruction with Zernike polynomials and Karhunen-Loève functions,�?? J. Opt. Soc. Am. A 13, 1218�??1225 (1996). [CrossRef]
  12. M. C. Roggemann and T. J. Schulz, �??Algorithm to increase the largest aberration that can be reconstructed from Hartmann sensor measurements,�?? Appl. Opt. 37, 4321�??4329 (1998). [CrossRef]
  13. W. Zou and Z. Zhang, �??Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann test,�?? Appl. Opt. 39, 250 �?? 268 (2000). [CrossRef]
  14. Y. Carmon and E. N. Ribak, �??Phase retrieval by demodulation of a Hartmann-Shack sensor,�?? Opt. Commun. 215, 285�??288 (2003). [CrossRef]
  15. L. A. Poyneer and J.-P. Véran, �??Optimal modal Fourier-transform wavefront control,�?? J. Opt. Soc. Am. A 22, 1515 �?? 1526 (2005). [CrossRef]
  16. A. Talmi and E. N. Ribak, �??Direct demodulation of Hartmann-Shack patterns,�?? J. Opt. Soc. Am. A 21, 632 �?? 639 (2004). [CrossRef]
  17. J. Herrmann, �??Cross coupling and aliasing in modal wave-front estimation,�?? J. Opt. Soc. Am. A 71, 989�??992 (1981). [CrossRef]
  18. R. J. Noll, �??Zernike polynomials and atmospheric turbulence,�?? J. Opt. Soc. Am. 66, 207 �?? 211 (1976). [CrossRef]
  19. B. Patterson, �??Circular and Annular Zernike Polynomials, Mathematica® Package,�?? <a href="http://library.wolfram.com/infocenter/MathSource/4483/"> http://library.wolfram.com/infocenter/MathSource/4483/</a>(2002). UK Astronomy Technology Centre.
  20. N. Roddier, �??Atmospheric wavefront simulation using Zernike polynomials,�?? Optical Engineering 29, 1174 �?? 1180 (1990). [CrossRef]
  21. D. W. de Lima Monteiro, O. Akhzar-Mehr, P. M. Sarro, and G. Vdovin, �??Single-mask microfabrication of aspherical optics using KOH anisotropic etching of Si,�?? Opt. Express 11, 2244 �?? 2252 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2244">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2244</a> [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited