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Generalized conic concentrators.

W L Eichhorn1

  • 1NASA Goddard Space Flight Center, Greenbelt, Maryland 20770, USA.

Applied Optics
|April 17, 2010
PubMed
Summary
This summary is machine-generated.

This study derives explicit formulas for generalized quadric surfaces using tilted elliptical or hyperbolic parent surfaces. These parameters are then linked to physical conic concentrators, aperture sizes, and limiting ray angles.

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Area of Science:

  • Mathematics
  • Optical Engineering

Background:

  • Generalized quadric surfaces are essential in optics and engineering.
  • Understanding their parameters is key for designing optical systems.

Purpose of the Study:

  • To derive explicit forms for the coefficients of generalized quadric surfaces.
  • To relate these coefficients to the parameters of parent elliptical or hyperbolic surfaces, including tilt and displacement.

Main Methods:

  • Derivation of explicit coefficient forms.
  • Relating parent conic parameters to physical conic concentrators.
  • Connecting parent conic parameters to aperture sizes and limiting ray angles.

Main Results:

  • Explicit formulas for six coefficients of generalized quadric surfaces are presented.
  • The relationship between parent surface parameters (tilt, displacement) and conic concentrators is established.
  • Parent conic parameters are linked to concentrator aperture sizes and limiting ray angles.

Conclusions:

  • The derived formulas provide a direct method for defining generalized quadric surfaces.
  • This work facilitates the design and analysis of conic concentrators.
  • The findings are applicable to optical systems requiring precise surface definitions.