OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 12 — Apr. 20, 2010
  • pp: 2334–2338

Interferometric Shack–Hartmann wavefront sensor with an array of four-hole apertures

David López and Susana Ríos  »View Author Affiliations

Applied Optics, Vol. 49, Issue 12, pp. 2334-2338 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (387 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A modified Hartmann test based on the interference produced by a four-hole mask can be used to measure an unknown wavefront. To scan the wavefront, the interference pattern is measured for different positions of the mask. The position of the central fringe of the diamond-shaped interference pattern gives a measure of the local wavefront slopes. Using a set of four-hole apertures located behind an array of lenslets in such a way that each four-hole window is inside one lenslet area, a set of four-hole interference patterns can be obtained in the back focal plane of the lenslets without having to scan the wavefront. The central fringe area of each interference pattern is narrower than the area of the central maximum of the diffraction pattern of the lenslet, increasing the accuracy in the estimate of the lobe position as compared with the Shack–Hartmann wavefront sensor.

© 2010 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(050.1220) Diffraction and gratings : Apertures
(100.2960) Image processing : Image analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: October 22, 2009
Revised Manuscript: January 27, 2010
Manuscript Accepted: March 19, 2010
Published: April 14, 2010

David López and Susana Ríos, "Interferometric Shack–Hartmann wavefront sensor with an array of four-hole apertures," Appl. Opt. 49, 2334-2338 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. I. Ghozeil, “Hartmann and other screen tests,” in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 367–396.
  2. J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkd.  24, 1–119 (1904).
  3. I. C. Gardner and A. H. Bennett, “A modified Hartmann test based on interference,” J. Opt. Soc. Am.  11, 441–452 (1925). [CrossRef]
  4. W. Vaidya and K. S. Gupta, “Measurement of axial and off-axis geometrical aberrations of microscope objectives,” J. Opt. Soc. Am.  50, 467–477 (1960). [CrossRef]
  5. X. H. M. Lew, X. Cui, and C. Yang, “Interference of a four-hole aperture for on-chip quantitative two-dimensional differential phase imaging,” Opt. Lett.  32, 2963–2965 (2007). [CrossRef] [PubMed]
  6. S. Thomas, T. Fusco, A. Tokovinin, M. Nicolle, V. Michau, and G. Rousset, “Comparison of centroid computation algorithms in a Shack-Hartmann sensor,” Mon. Not. R. Astron. Soc.  371, 323–336 (2006). [CrossRef]
  7. G. Cao and X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng.  33, 2331–2335 (1994). [CrossRef]
  8. J. Ares and J. Arines, “Influence of thresholding on centroid statistics: full analytical description,” Appl. Opt.  43, 5796–5805 (2004). [CrossRef] [PubMed]
  9. J. Ares and J. Arines, “Effective noise in thresholded intensity distribution: influence on centroid statistics,” Opt. Lett.  26, 1831–1833 (2001). [CrossRef]
  10. Z. Jiang, S. Gong, and Y. Dai, “Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor,” Opt. Laser Technol.  38, 614–619 (2006). [CrossRef]
  11. X. Ma, C. Rao, and H. Zheng, “Error analysis of CCD-based point source centroid computation under the background light,” Opt. Express  17, 8525–8541 (2009). [CrossRef] [PubMed]
  12. R. Irwan and R. G. Lane, “Analysis of optimal centroid estimation applied to Shack-Hartmann sensing,” Appl. Opt.  38, 6737–6743 (1999). [CrossRef]
  13. J. Arines and J. Ares, “Minimum variance centroid thresholding,” Opt. Lett.  27, 497–499 (2002). [CrossRef]
  14. S. Ríos and D. López, “Modified Shack-Hartmann wavefront sensor using an array of superresolution pupil filters,” Opt. Express  17, 9669–9679 (2009). [CrossRef] [PubMed]
  15. M. De and M. K. S. Gupta, “Measurement of wave aberrations of microscope and other objectives,” J. Opt. Soc. Am.  51, 158–164 (1961). [CrossRef]
  16. C. Lorant, “Variance of a product of independent random variables with small deviations from their means,” Proc. IEEE  53, 1760–1761 (1965). [CrossRef]
  17. H. Chen and C. Rao, “Accuracy analysis on centroid estimation algorithm limited by photon noise for point object,” Opt. Commun.  282, 1526–1530 (2009). [CrossRef]
  18. Hamamatsu Photonics, “ieee 1394-based digital camera orca-285 data sheet,” http://sales.hamamatsu.com/assets/pdf/hpspdf/C4742-95-12G04.pdf.
  19. A. Tokovinin, “From differential image motion to seeing,” Publ. Astron. Soc. Pac.  114, 1156–1166 (2002). [CrossRef]

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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited