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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 4 — Feb. 13, 2012
  • pp: 4050–4055

Observations on the linear programming formulation of the single reflector design problem

Cristina Canavesi, William J. Cassarly, and Jannick P. Rolland  »View Author Affiliations

Optics Express, Vol. 20, Issue 4, pp. 4050-4055 (2012)

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We implemented the linear programming approach proposed by Oliker and by Wang to solve the single reflector problem for a point source and a far-field target. The algorithm was shown to produce solutions that aim the input rays at the intersections between neighboring reflectors. This feature makes it possible to obtain the same reflector with a low number of rays – of the order of the number of targets – as with a high number of rays, greatly reducing the computation complexity of the problem.

© 2012 OSA

OCIS Codes
(080.1753) Geometric optics : Computation methods
(220.2945) Optical design and fabrication : Illumination design
(080.4228) Geometric optics : Nonspherical mirror surfaces
(080.4298) Geometric optics : Nonimaging optics

Original Manuscript: December 19, 2011
Revised Manuscript: January 30, 2012
Manuscript Accepted: January 30, 2012
Published: February 2, 2012

Cristina Canavesi, William J. Cassarly, and Jannick P. Rolland, "Observations on the linear programming formulation of the single reflector design problem," Opt. Express 20, 4050-4055 (2012)

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  1. W. B. Elmer, The Optical Design of Reflectors, 2nd ed. (Wiley, 1980).
  2. W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE3482, 389–396 (1998). [CrossRef]
  3. L. Wang, K. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt.46(18), 3716–3723 (2007). [CrossRef] [PubMed]
  4. H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19(3), 590–595 (2002). [CrossRef] [PubMed]
  5. L. A. Caffarelli, S. A. Kochengin, and V. I. Oliker, “On the numerical solution of the problem of reflector design with given far-field scattering data,” Contemp. Math.226, 13–32 (1999). [CrossRef]
  6. V. I. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” in Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds. (Springer, 2003), Chap. 4, pp. 193–222.
  7. X.-J. Wang, “On the design of a reflector antenna II,” Calculus Var. Partial Differ. Eq.20(3), 329–341 (2004). [CrossRef]
  8. T. Glimm and V. Oliker, “Optical design of single reflector systems and the Monge-Kantorovich mass transfer problem,” J. Math. Sci.117(3), 4096–4108 (2003). [CrossRef]
  9. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5942, 594207, 594207-12 (2005). [CrossRef]
  10. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE7423, 742302, 742302-12 (2009). [CrossRef]
  11. D. Michaelis, S. Kudaev, R. Steinkopf, A. Gebhardt, P. Schreiber, and A. Bräuer, “Incoherent beam shaping with freeform mirror,” Proc. SPIE7059, 705905, 705905-6 (2008). [CrossRef]
  12. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express18(5), 5295–5304 (2010). [CrossRef] [PubMed]

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