## Differential geometry of the ruled surfaces optically generated by mirror scanning devices: II. Generation of helicoids and hyperbolic paraboloids |

JOSA A, Vol. 28, Issue 6, pp. 1239-1242 (2011)

http://dx.doi.org/10.1364/JOSAA.28.001239

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### 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. A 28, 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

**OCIS Codes**

(080.0080) Geometric optics : Geometric optics

(080.2720) Geometric optics : Mathematical methods (general)

(120.5800) Instrumentation, measurement, and metrology : Scanners

(220.2740) Optical design and fabrication : Geometric optical design

**History**

Original Manuscript: November 23, 2010

Revised Manuscript: February 22, 2011

Manuscript Accepted: March 21, 2011

Published: May 25, 2011

**Citation**

Yajun Li, "Differential geometry of the ruled surfaces optically generated by mirror
scanning devices: II. Generation of helicoids and hyperbolic paraboloids," J. Opt. Soc. Am. A **28**, 1239-1242 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-6-1239

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### References

- 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]
- 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.

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