OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 42, Iss. 14 — May. 10, 2003
  • pp: 2506–2512

Analysis of illumination coherence properties in small-source systems such as synchrotrons

Chang Chang, Patrick Naulleau, and David Attwood  »View Author Affiliations

Applied Optics, Vol. 42, Issue 14, pp. 2506-2512 (2003)

View Full Text Article

Enhanced HTML    Acrobat PDF (2110 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Modern synchrotron beamlines often take the form of critical illumination systems, where an incoherent source of limited spatial extent is re-imaged to an experimental plane of interest. Unique constraints of synchrotron sources and beamlines, however, may preclude the use of the simple Zernike approximation for calculating the object-image coherence relationship. Here, we perform a rigorous analysis of the object-image coherence relationship valid for synchrotron beamlines. The analysis shows that beamline aberrations have an effect on the coherence properties. Effects of various low-order aberrations on the coherence properties are explicitly studied.

© 2003 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(110.0110) Imaging systems : Imaging systems
(110.4980) Imaging systems : Partial coherence in imaging
(110.7440) Imaging systems : X-ray imaging

Original Manuscript: September 20, 2002
Revised Manuscript: December 11, 2002
Published: May 10, 2003

Chang Chang, Patrick Naulleau, and David Attwood, "Analysis of illumination coherence properties in small-source systems such as synchrotrons," Appl. Opt. 42, 2506-2512 (2003)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Polack, D. Joyeux, J. Svatos, D. Phalippou, “Applications of wavefront division interferometers in soft X-rays,” Rev. Sci. Instrum. 66, 2180–2183 (1995). [CrossRef]
  2. S. Marchesini, R. Coïsson, “Two-dimensional coherence measurements with Fresnel mirrors,” Opt. Eng. 35, 3597–3601 (1996). [CrossRef]
  3. Y. Takayama, T. Hatano, T. Miyahara, W. Okamoto, “Relationship between spatial coherence of synchrotron radiation and emittance,” J. Synchrotron Radiat. 5, 1187–1194 (1998). [CrossRef]
  4. C. Chang, P. Naulleau, E. Anderson, K. Rosfjord, D. Attwood, “Diffractive optical elements based on Fourier optical techniques: A new class of optics for extreme ultraviolet and soft x-ray wavelengths,” Appl. Opt. 41, 7384–7390 (2002). [CrossRef] [PubMed]
  5. R. Coïsson, “Spatial coherence of synchrotron radiation,” Appl. Opt. 34, 904–908 (1995). [CrossRef] [PubMed]
  6. Joseph W. Goodman, Statistical Optics, (Wiley, New York, 1985), critical illumination: Sec. 7.2.1, pp. 306; Zernike approximation: Sec. 7.2.2, pp. 311; Van Cittert-Zernike theorem: Sec. 5.6, pp. 207–211; generalized Van Cittert-Zernike theorem: Sec. 5.6.4, pp. 218–222; Huygens-Fresnel principle: Sec. 5.4.1, pp. 196–198 and Sec. 7.1.4, pp. 296–300.
  7. D. T. Attwood, Soft X-rays and Extreme Ultraviolet Radiation: Principles and Applications, (Cambridge University, Cambridge, UK, 1999). [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, (Cambridge University, Cambridge, UK, 1997), Zernike approximation: Sec. 10.5.2, pp. 522–524; Van Cittert-Zernike theorem: Sec. 10.4.2, pp. 508–512; displacement theorem: Sec. 9.1, pp. 460–464.
  9. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica V, 785–795 (1938). [CrossRef]
  10. D. Attwood, P. Naulleau, K. A. Goldberg, E. Tejnil, C. Chang, R. Beguiristain, P. Batson, J. Bokor, E. M. Gullikson, M. Koike, H. Medecki, J. Underwood, “Tunable coherent radiation in the soft X-ray and extreme ultraviolet spectral regions,” IEEE J. Quantum Electron. 35, 709–720 (1999). [CrossRef]
  11. C. Chang, P. Naulleau, E. Anderson, D. Attwood, “Spatial coherence characterization of undulator radiation,” Opt. Commun. 182, 25–34 (2000). [CrossRef]
  12. Bernard R. A. Nijboer, The Diffraction Theory of Aberrations, (Batavia, Groningen, the Netherlands, 1942). Chap. 4.
  13. A. C. Price, L. B. Sorensen, S. D. Kevan, J. Toner, A. Poniewierski, R. Holyst, “Coherent soft-X-ray dynamic light scattering from smectic-A films,” Phys. Rev. Lett. 82, 755–758 (1999). [CrossRef]
  14. P. Naulleau, K. A. Goldberg, S. H. Lee, C. Chang, C. Bresloff, P. Batson, D. Attwood, J. Bokor, “Characterization of the accuracy of EUV phase-shifting point diffraction interferometry,” Proc. SPIE 3331, 114–123 (1998). [CrossRef]
  15. P. Naulleau, K. A. Goldberg, S. H. Lee, C. Chang, D. Attwood, J. Bokor, “Extreme-ultraviolet phase-shifting point-diffraction interferometer: a wave-front metrology tool with subangstrom reference-wave accuracy,” Appl. Opt. 38, 7252–7263 (1999). [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