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Differential geometry of the ruled surfaces optically generated by mirror-scanning devices. I. Intrinsic and extrinsic properties of the scan field |
JOSA A, Vol. 28, Issue 4, pp. 667-674 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000667
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Abstract
Rectilinear propagation of light rays in homogeneous isotropic media makes it possible for optical generation of ruled surfaces as the ray is deflected by a rotatable mirror. Scan patterns on a plane or curved surface are merely curves on the ruled surface. Based on this understanding, structures of the scan fields produced by mirror- scanning devices of different configurations are investigated in terms of differential geometry. Expressions of the first and second fundamental coefficients and the first and second Gauss differential forms are given for an investigation of the intrinsic properties of the optically generated ruled surfaces. The Plücker ruled conoid is then generalized for mathematical modeling of the scan fields produced by single-mirror scanning devices of different configurations. Part II will be devoted to a study of multi-mirror scanning systems for optical generation of well-known ruled surfaces such as helicoids and hyperbolic paraboloids.
© 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
ToC Category:
Geometric Optics
History
Original Manuscript: November 23, 2010
Manuscript Accepted: January 12, 2011
Published: March 30, 2011
Citation
Yajun 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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-4-667
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