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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 38, Iss. 10 — Apr. 1, 1999
  • pp: 2028–2039

Differential Equation for Normal Glass Dispersion and Evaluation of the Secondary Spectrum

Juan L. Rayces and Martha Rosete-Aguilar  »View Author Affiliations


Applied Optics, Vol. 38, Issue 10, pp. 2028-2039 (1999)
http://dx.doi.org/10.1364/AO.38.002028


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Abstract

Some of the questions concerning secondary chromatic aberration at both sides of the visible band of the spectrum are the following: (1) What is the bandwidth at different wavelengths, given the permissible chromatic aberration circle and the lens aperture? (2) What is the size of the chromatic aberration circle, given the wavelength, the bandwidth, and the lens aperture? The answers to these and other questions may be found with the new definitions of <i>V</i>-number and relative partial dispersion <i>P</i> based on infinitesimal bandwidths that we propose. In addition, an alignment chart for the secondary color of a normal glass doublet is presented, so fast answers to the questions posed above and to other questions concerned with secondary color can be found. In addition, a continual challenge in computer-aided lens design is the use of optical glasses as design parameters in simultaneous optimization of lens systems over various regions of the spectrum. This problem could be solved if we could find an ideal glass family, not too different from real glasses, such that, given the refractive index <i>n</i> and the <i>V</i>-number at any wavelength, the indices at all wavelengths could be determined. Therefore we derive a differential equation for normal glass dispersion and present a recursive solution.

© 1999 Optical Society of America

OCIS Codes
(220.1010) Optical design and fabrication : Aberrations (global)
(220.2740) Optical design and fabrication : Geometric optical design

Citation
Juan L. Rayces and Martha Rosete-Aguilar, "Differential Equation for Normal Glass Dispersion and Evaluation of the Secondary Spectrum," Appl. Opt. 38, 2028-2039 (1999)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-10-2028


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References

  1. J. Hoogland, “The design of apochromatic lenses,” in Recent Developments in Optical Design, R. A. Ruhloff, ed. (Perkin-Elmer, Norwalk, Conn., 1968), pp. 6–1 and 6–8.
  2. Laurin Publications, ed., The Photonics Design, Book 3 of The Photonics Design and Applications Handbook, 44th international ed. (Laurin Publications, Pittsfield, Mass., 1998), pp. H-384 and H-385.
  3. W. Smith, Modern Lens Design: A Resource Manual (McGraw-Hill, New York, 1992).
  4. W. Besenmatter, “How many glass types does a lens designer really need?” in International Optical Design Conference 1998, L. R. Gardner and K. P. Thompson, eds., Proc. SPIE 3482, 294–305 (1998).
  5. R. Bellman, Introduction to Matrix Analysis McGraw-Hill, New York, 1965), Spanish version, p. 208.

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