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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.48.006355


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Abstract

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

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

Citation
Virgil-Florin Duma, "Radiometric versus geometric, linear, and nonlinear vignetting coefficient," Appl. Opt. 48, 6355-6364 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-32-6355

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