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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 44, Iss. 19 — Jul. 1, 2005
  • pp: 3893–3897

Blind-spot problem for motor vehicles

R. Andrew Hicks and Ronald K. Perline  »View Author Affiliations


Applied Optics, Vol. 44, Issue 19, pp. 3893-3897 (2005)
http://dx.doi.org/10.1364/AO.44.003893


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Abstract

We consider the problem of designing a passenger side mirror for an automobile that does not have a blind spot and that does not distort the image. Our model consists of a coupled pair of partial differential equations that do not have a common solution. Using a best mean-square-error functional, we find approximate solutions using nonlinear optimization. In one case a local minimum provides a mirror that solves the problem, but it does not reverse the image.

© 2005 Optical Society of America

OCIS Codes
(080.2720) Geometric optics : Mathematical methods (general)
(080.2740) Geometric optics : Geometric optical design

History
Original Manuscript: September 17, 2004
Revised Manuscript: February 16, 2005
Manuscript Accepted: February 18, 2005
Published: July 1, 2005

Citation
R. Andrew Hicks and Ronald K. Perline, "Blind-spot problem for motor vehicles," Appl. Opt. 44, 3893-3897 (2005)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-19-3893


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References

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  2. R. A. Hicks, “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. A 22, 323–330 (2005). [CrossRef]
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  9. R. A. Hicks, R. Bajcsy, “Reflective surfaces as computational sensors,” in Proceedings of the Second Workshop on Perception for Mobile Agents, CVPR 99 (IEEE Press, 1999), pp. 82–86.
  10. M. Ollis, H. Herman, S. Singh, “Analysis and design of panoramic stereo vision using equi-angular pixel cameras,” Tech. Rep. (Robotics Institute, Carnegie Mellon University, 1999).
  11. R. A. Hicks, R. Perline, “Geometric distributions and catadioptric sensor design,” in Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision Pattern Recognition (IEEE Press, 2001), pp. 584–589.
  12. M. Srinivasan, “A new class of mirrors for wide-angle imaging,” in Proceedings of the IEEE Workshop on Omnidirectional Vision (IEEE Press, 2003).
  13. R. Swaminathan, S. Nayar, M. Grossberg, “Framework for designing catadioptric projection and imaging systems,” in IEEE International Workshop on Projector-Camera Systems (IEEE Press, 2003).
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  15. F. John, Partial Differential Equations (Springer-Verlag, 1975).
  16. I. Gelfand, S. Fomin, Calculus of Variations (Prentice-Hall, 1963).
  17. W. Cheney, Analysis for Applied Mathematics (Springer-Verlag, 2001). [CrossRef]

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