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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 32 — Nov. 10, 2009
  • pp: 6355–6364

Radiometric versus geometric, linear, and nonlinear vignetting coefficient

Virgil-Florin Duma  »View Author Affiliations

Applied Optics, Vol. 48, Issue 32, pp. 6355-6364 (2009)

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We analyze the vignetting phenomenon both for optical systems with objects placed at finite distances and for systems with objects at infinity. Four of the possible definitions of the vignetting coefficient k, only two of them existing in the literature, are discussed. We propose two new definitions, i.e., a nonlinear geometric coefficient that is, in part, an analytical model of the vignetting characterization using optical software and a radiometric vignetting coefficient. The object space of each type of optical systems is studied first, defining its characteristic light circles and cones. Several simplifying assumptions are made for each of the two cases considered to derive analytical equations of the vignetting coefficient and thus to determine the best definition to be used. A geometric vignetting coefficient with two expressions, a linear classical and easy-to-use one and a nonlinear, that we propose for both types of systems is obtained. This nonlinear geometric vignetting coefficient proves to be more adequate in modeling the phenomenon, but it does not entirely fit the physical reality. We finally demonstrate that the radiometric vignetting coefficient we define and derive as a view factor for both types of optical systems is the most appropriate one. The half vignetting level, necessary in most optical design procedures to obtain a satisfactory illumination level in the image plane, is also discussed.

© 2009 Optical Society of America

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(120.4570) Instrumentation, measurement, and metrology : Optical design of instruments
(120.5240) Instrumentation, measurement, and metrology : Photometry
(120.5630) Instrumentation, measurement, and metrology : Radiometry
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.2740) Optical design and fabrication : Geometric optical design

Original Manuscript: August 21, 2009
Revised Manuscript: October 19, 2009
Manuscript Accepted: October 19, 2009
Published: November 6, 2009

Virgil-Florin Duma, "Radiometric versus geometric, linear, and nonlinear vignetting coefficient," Appl. Opt. 48, 6355-6364 (2009)

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  1. M. Bass, Handbook of Optics (McGraw-Hill, 1995).
  2. W. J. Smith, Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000).
  3. J. L. Rayces and M. Rosete-Aguilar, “Optics for binocular telescopes,” Proc. SPIE 4441, 1-8 (2001). [CrossRef]
  4. T. H. Tomkinson, J. L. Bentley, M. Kate Crawford, C. J. Harkrider, D. T. Moore, and J. L. Rouke, “Rigid endoscopic relay systems: a comparative study,” Appl. Opt. 35, 6674-6683 (1996). [CrossRef] [PubMed]
  5. A. Litvinov and Y. Y. Schechner, “Radiometric framework for image mosaicking,” J. Opt. Soc. Am. A 22, 839-848 (2005). [CrossRef]
  6. D. W. Berreman, “Multilayer reflecting x-ray optical systems: chromatic vignetting by narrow reflection bands,” Appl. Opt. 30, 1741-1745 (1991). [CrossRef] [PubMed]
  7. O. A. Vinogradova, A. V. Gavrilyuk, V. A. Zverev, and G. V. Karpova, “Illuminating device of a projection system with quasi-uniform light distribution in the image plane,” J. Opt. Technol. 70, 797-801 (2003). [CrossRef]
  8. P. J. Sands, “Prediction of vignetting,” J. Opt. Soc. Am. 63, 803-805 (1973). [CrossRef]
  9. V. F. Duma, “Vignetting of light beams for objects placed at a finite distance from an optical system,” Proc. SPIE 7100, 710005 (2008). [CrossRef]
  10. J. Auerhammer and H. Liu, “Vignetting effects of wiggler bores on empty modes in free-electron laser resonators,” Appl. Opt. 32, 7373-7381 (1993). [CrossRef] [PubMed]
  11. J. E. Greivenkamp and R. O. Gappinger, “Design of a nonnull interferometer for aspheric wave fronts,” Appl. Opt. 43, 5143-5151 (2004). [CrossRef] [PubMed]
  12. S. I. Kliment'ev, “Vignetting in telescope systems with holographic image correction,” J. Opt. Technol. 69, 385-391 (2002). [CrossRef]
  13. V. F. Duma and M. Nicolov, “Neutral density filters with Risley prisms: analysis and design,” Appl. Opt. 48, 2678-2685 (2009). [CrossRef] [PubMed]
  14. D. P. Kelly, J. T. Sheridan, and W. T. Rhodes, “Fundamental diffraction limitations in a paraxial 4f imaging system with coherent and incoherent illumination,” J. Opt. Soc. Am. A 24, 1911-1919 (2007). [CrossRef]
  15. J. E. Greivenkamp, Field Guide to Geometrical Optics (SPIE Press, 2004). [CrossRef]
  16. M. F. Modest, Radiative Heat Transfer (Academic Press, 2003).
  17. www.zemax.com.

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