OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Jospeh N. Mait
  • Vol. 48, Iss. 3 — Jan. 20, 2009
  • pp: 436–441

Angle spread function degradation by surface roughness in imaging optics

Fabio E. Zocchi  »View Author Affiliations


Applied Optics, Vol. 48, Issue 3, pp. 436-441 (2009)
http://dx.doi.org/10.1364/AO.48.000436


View Full Text Article

Enhanced HTML    Acrobat PDF (449 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A formula is derived for the total width of the angle spread function in an imaging optical system, the performance of which is degraded by surface roughness. The derivation is done in the framework of the scalar theory of diffraction, but it does not rely on the small roughness approximation. The contribution of scattering from surface roughness to the total width of the angle spread function is found to depend only on the variance of the roughness slope. It is also shown that the common rule of obtaining the total width of the angle spread function as a square sum of the pure scattering component and the pure specular component is actually incorrect and does not fully account for the contribution of the specular component.

© 2009 Optical Society of America

OCIS Codes
(110.4850) Imaging systems : Optical transfer functions
(260.1960) Physical optics : Diffraction theory
(290.5880) Scattering : Scattering, rough surfaces
(290.5825) Scattering : Scattering theory

ToC Category:
Optics at Surfaces

History
Original Manuscript: September 24, 2008
Revised Manuscript: November 14, 2008
Manuscript Accepted: December 11, 2008
Published: January 12, 2009

Citation
Fabio E. Zocchi, "Angle spread function degradation by surface roughness in imaging optics," Appl. Opt. 48, 436-441 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-3-436


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Wolter, “Mirror systems with glancing incidence as image-producing optics for X-rays,” Ann. Phys. 445, 94-114 (1952). [CrossRef]
  2. R. C. Chase and L. P. Van Speybroeck, “Wolter-Schwarzshild telescopes for X-ray astronomy,” Appl. Opt. 12, 1042-1044(1973). [CrossRef]
  3. R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, and T. Zehnpfennig, “Grazing incidence telescopes for X-ray astronomy,” Space Sci. Rev. 9, 3-57 (1969). [CrossRef]
  4. M. J. L. Turner and K. A. Flanagan, eds., Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray, Proc. SPIE 7011 (2008).
  5. F. M. Schellenberg, ed., Emerging Lithographic Technologies XII, Proc. SPIE 6921 (2008).
  6. V.Bakshi ed., EUV Lithography (SPIE, 2008).
  7. F. E. Zocchi, “High efficiency collector design for extreme ultra-violet and X-ray applications,” Appl. Opt. 45 (35), 8882-8888 (2006). [CrossRef]
  8. J. K. Silk, “A grazing incident microscope for X-ray imaging applications,” Ann. N.Y. Acad. Sci. 342, 116-129 (1980). [CrossRef]
  9. R. B. Hoover and B. C. Walker, eds., X-ray/EUV Optics for Astronomy, Microscopy, Polarimetry, and Projection Lithography, Proc. SPIE 1343 (1991).
  10. T. Foltyn, K. Bergmann, S. Braun, P. Gawlitza, A. Leson, W. Neff, and K. Walter, “Design and development of an optical system for EUV microscopy,” Proc. SPIE 5533, 37-46 (2004). [CrossRef]
  11. D. Schäfer, T. Nisius, R. Früke, S. Rausch, M. Wieland, U. Vogt, and T. Wilhein, “Compact X-ray microscopes for EUV- and soft X-radiation with spectral imaging capabilities,” Proc. SPIE 6317, 631704 (2006). [CrossRef]
  12. T. W. Barbee, “Multilayer for X-ray optics,” Opt. Eng. 25, 898-915 (1986).
  13. K. D. Joensen, P. Voutov, A. Szentgyorgyi, J. Roll, P. Gorenstein, P. Hoghoj, and F. E. Christensen, “Design of grazing-incidence multilayer supermirrors for hard X-ray reflectors,” Appl. Opt. 34, 7935-7944 (1995).
  14. K. Yamashita, H. Kuneida, Y. Tawara, K. Tamura, Y. Ogasaka, K. Haga, T. Okajima, Y. Hidaka, S. Ichimaru, S. TakaHashi, A. Goto, H. Kito, Y. Tsusaka, K. Yokoyama, and S. Takeda, “New design concept of multilayer supermirrors for hard X-ray optics,” Proc. SPIE 3766, 327-335 (1999). [CrossRef]
  15. E. Spiller, “High performance multilayer coatings for EUV lithography,” Proc. SPIE 5193, 89-97 (2004). [CrossRef]
  16. E. Spiller, Soft X-Ray Optics (SPIE, 1994).
  17. E. L. Church and P. Z. Takacs, “Specification of glancing- and normal-incidence X-ray mirrors,” Opt. Eng. 34, 353-360(1995). [CrossRef]
  18. E. L. Church and P. Z. Takacs, “Specification of surface figure and finish in terms of system performance,” Appl. Opt. 32, 3344-3353 (1993).
  19. J. E. Harvey, “Modeling the image quality of enhanced reflectance X-ray multilayers as a surface power spectral density filter function,” Appl. Opt. 34, 3715-3726 (1995).
  20. J. E. Harvey, K. L. Lewotsky, and A. K. Thompson, “Performance predictions of a Schwarzschild imaging microscope for soft X-ray applications,” Opt. Eng. 35, 2423-2436 (1996). [CrossRef]
  21. D. G. Stearns, D. P. Gaines, D. W. Sweeney, and E. M. Gullikson, “Nonspecular X-ray scattering in a multiplayer-coated imaging system,” J. Appl. Phys. 84, 1003-1028 (1998). [CrossRef]
  22. J. E. Harvey, “Scattering effects in X-ray imaging systems,” Proc. SPIE 2515, 246-272 (1995). [CrossRef]
  23. F. E. Christensen, A. Hornstrup, and H. W. Schnopper, “Surface correlation function analysis of high resolution scattering data from mirrored surfaces obtained using a triple-axis x-ray diffractometer,” Appl. Opt. 27, 1548-1557 (1988).
  24. T. Karabacak, Y. Zhao, M. Stowe, B. Quayle, G. C. Wang, and T. M. Lu, “Large in-plane light scattering from rough surfaces,” Appl. Opt. 39, 4658-4668 (2000). [CrossRef]
  25. P. Zhao and L. P. Van Spreybroeck, “New method to model X-ray scattering from random rough surfaces,” Proc. SPIE 4851, 124-139 (2003). [CrossRef]
  26. D. Spiga, “Analytical evaluation of the X-ray scattering contribution to imaging degradation in grazing-incidence X-ray telescopes,” Astron. Astrophys. 468, 775-784 (2007). [CrossRef]
  27. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  28. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978).
  29. J. E. Harvey, “Fourier treatment of near field scalar diffraction theory,” Proc. SPIE 2515, 246-272 (1995). [CrossRef]
  30. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  31. F. D. Smith, “Optical image evaluation and the transfer function,” Appl. Opt. 2, 335-350 (1963). [CrossRef]
  32. J. E. Harvey, E. C. Moran, and W. P. Zmek, “Transfer function characterization of grazing incidence optical systems,” Appl. Opt. 27, 1527-1533 (1988).
  33. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1965).
  34. E. L. Church, “Fractal surface finish,” Appl. Opt. 27, 1518-1526 (1988).

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited