Abstract

The theory developed in Part I of this study [Y. Li, “Differential geometry of the ruled surfaces optically generated by mirror-scanning devices. I. Intrinsic and extrinsic properties of the scan field,” J. Opt. Soc. Am. A28, 667 (2011)] for the ruled surfaces optically generated by single-mirror scanning devices is extended to multimirror scanning systems for an investigation of optical generation of the well-known ruled surfaces, such as helicoid, Plücker’s conoid, and hyperbolic paraboloid.

© 2011 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Li, “Differential geometry of the ruled surfaces optically generated by mirror scanning devices: I. Intrinsic and extrinsic properties of the scan field,” J. Opt. Soc. Am. A 28, 667–674(2011).
    [CrossRef]
  2. E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, 2003).
  3. URL: http://en.wikipedia.org/wiki/Line_(geometry).
  4. URL: http://www.mathopenref.com/ray.html.
  5. A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC, 2006), Chap. 14.
  6. URL: http://mathworld.wolfram.com/PlueckersConoid.html.
  7. D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, 1956), pp. 16, pp. 307–315.
  8. URL: http://en.wikipedia.org/wiki/Helicoid.
  9. URL: http://en.wikipedia.org/wiki/Ruled_surface.
  10. URL: http://mathworld.wolfram.com/HyperbolicParaboloid.html.

2011 (1)

Abbena, E.

A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC, 2006), Chap. 14.

Cohn-Vossen, S.

D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, 1956), pp. 16, pp. 307–315.

Gray, A.

A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC, 2006), Chap. 14.

Hilbert, D.

D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, 1956), pp. 16, pp. 307–315.

Li, Y.

Salamon, S.

A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC, 2006), Chap. 14.

Weisstein, E. W.

E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, 2003).

J. Opt. Soc. Am. A (1)

Other (9)

E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, 2003).

URL: http://en.wikipedia.org/wiki/Line_(geometry).

URL: http://www.mathopenref.com/ray.html.

A. Gray, E. Abbena, and S. Salamon, Modern Differential Geometry of Curves and Surfaces with Mathematica, 3rd ed. (Chapman & Hall/CRC, 2006), Chap. 14.

URL: http://mathworld.wolfram.com/PlueckersConoid.html.

D. Hilbert and S. Cohn-Vossen, Geometry and the Imagination (Chelsea, 1956), pp. 16, pp. 307–315.

URL: http://en.wikipedia.org/wiki/Helicoid.

URL: http://en.wikipedia.org/wiki/Ruled_surface.

URL: http://mathworld.wolfram.com/HyperbolicParaboloid.html.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics