OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 5 — Mar. 2, 2009
  • pp: 3707–3715

Frequency analysis of wavefront curvature sensing: optimum propagation distance and multi-z wavefront curvature sensing

Xi Fengjie, Jiang Zongfu, Xu Xiaojun, Hou Jing, and Liu Zejin  »View Author Affiliations

Optics Express, Vol. 17, Issue 5, pp. 3707-3715 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (275 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In this paper we determine the optimum propagation distance between measurement planes and the plane of the lens in a wavefront curvature sensor with the diffraction optics approach. From the diffraction viewpoint, the measured wavefront aberration can be decomposed into Fourier harmonics at various frequencies. The curvature signal produced by a single harmonic is analyzed with the wave propagation transfer function approach, which is the frequency analysis of wavefront curvature sensing. The intensity of the curvature signal is a sine function of the product of the propagation distance and the squared frequency. To maximize the curvature signal, the optimum propagation distance is proposed as one quarter of the Talbot length at the critical frequency (average power point at which the power spectrum density is the average power spectrum density). Following the determination of the propagation distance, the intensity of the curvature signal varies sinusoidally with the squared frequencies, vanishing at some higher frequency bands just like a comb filter. To cover these insensitive bands, wavefront curvature sensing with dual propagation distances or with multi-propagation distances is proposed.

© 2009 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects

ToC Category:
Physical Optics

Original Manuscript: September 9, 2008
Revised Manuscript: December 16, 2008
Manuscript Accepted: December 19, 2008
Published: February 24, 2009

Xi Fengjie, Jiang Zongfu, Xu Xiaojun, Hou Jing, and Liu Zejin, "Frequency analysis of wavefront curvature sensing: optimum propagation distance and multi-z wavefront curvature sensing," Opt. Express 17, 3707-3715 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics," Appl. Opt. 27, 1223-1225 (1988). [CrossRef] [PubMed]
  2. M. Soto, E. Acosta, and S. Ríos, "Performance analysis of curvature sensors: optimum positioning of the measurement planes," Opt. Express 11, 2577-2588 (2003). [CrossRef] [PubMed]
  3. O. Guyon, "High-performance curvature wavefront sensing for extreme AO," SPIE 6691, 66910G (2007). [CrossRef]
  4. O. Guyon, C. Blain, H. Takami, Y. Hayano, M. Hattori, M. Watanabe, "Improving the Sensitivity of Astronomical Curvature Wavefront Sensor Using Dual-Stroke Curvature," PASP.  120, 655-664 (2008). [CrossRef]
  5. D. Johnston, B. Ellerbroek, and S. Pompeat, "Curvature sensing analysis," SPIE 2201, 528-538 (1994). [CrossRef]
  6. J. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996), Chap. 2.
  7. F. Roddier, Adaptive Optics in Astronomy (Cambridge University Press, 1999), Chap. 5. [CrossRef]
  8. G. Yang, B. Gu, and B. Dong, "Theory of the amplitude-phase retrieval in an any linear transform system and its applications," SPIE 1767, 457-478 (1992). [CrossRef]
  9. M. Teague, "Deterministic phase retrieval: a Green’s function solution," J. Opt. Soc. Am. 73, 1434-1441 (1983). [CrossRef]
  10. F. Roddier, "Wavefront sensing and equation the irradiance transport," Appl. Opt. 29, 1402-1403 (1990). [CrossRef] [PubMed]
  11. T. Gureyev and K. Nugent, "Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination," J. Opt. Soc. Am. A. 13, 1670-1682 (1996). [CrossRef]
  12. J. Cowley and A. Moodie, "Fourier images IV: the phase grating," Proc. Phys. Soc. London Sect. B 76, 378-384 (1960).
  13. V. Arrizόn and J. Ojeda-Castaňeda, "Irradiance at Fresnel planes of a phase grating," J. Opt. Soc. Am. A 9, 1801-1806 (1992). [CrossRef]
  14. M. van Dam and R. Lane, "Extended analysis of curvature sensing," J. Opt. Soc. Am. A 19, 1390-1397 (2002). [CrossRef]
  15. R. Gerchberg and W. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik 35, 237-246 (1972).
  16. S. Woods and A. Greenaway, "Wavefront sensing by use of a Green’s function solution to the intensity transport equation," J. Opt. Soc. Am. A. 20, 508-512 (2003). [CrossRef]
  17. J. Graves and D. McKenna, "University of Hawaii adaptive optics system: III. Wavefront curvature sensor," SPIE 1542, 262-272 (1991). [CrossRef]
  18. P. Blanchard and A. Greenaway, "Simultaneous multiplane imaging with a distorted diffraction grating," Appl. Opt. 38, 6692-6699 (1999). [CrossRef]
  19. P. Blanchard, D. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wavefront sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000). [CrossRef]
  20. R. W. Lambert, R. Cortés-Martínez, A. J. Waddie, J. D. Shephard, M. R. Taghizadeh, A. H. Greenaway, and D. P. Hand, "Compact optical system for pulse-to-pulse laser beam quality measurement and applications in laser machining," Appl. Opt. 43, 5037-5046 (2004). [CrossRef] [PubMed]
  21. F. Xi, Z. Jiang, X. Xu, and Y. Geng, "High-diffractive-efficiency defocus grating for wavefront curvature sensing," J. Opt. Soc. Am. A 24, 3444-3448 (2007). [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited