V. Oliker, J. Rubinstein, and G. Wolansky, “Ray mapping and illumination control,” J. Photonics Energy3(1), 035599 (2013).

[CrossRef]

R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation,” Opt. Lett.38(2), 229–231 (2013).

[CrossRef]
[PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express21(12), 14728–14735 (2013).

[CrossRef]
[PubMed]

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett.36(6), 918–920 (2011).

[CrossRef]
[PubMed]

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Ration. Mech. Anal.201(3), 1013–1045 (2011).

[CrossRef]

M. M. Sulman, J. F. Williams, and R. D. Russell, “An efficient approach for the numerical solution of Monge-Ampère equation,” Appl. Numer. Math.61(3), 298–307 (2011).

[CrossRef]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express18(5), 5295–5304 (2010).

[CrossRef]
[PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010).

[CrossRef]
[PubMed]

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE6338, 633808 (2006).

[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE5942, 594207 (2005).

[CrossRef]

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE5876, 587607 (2005).

[CrossRef]

T. Glimm and V. Oliker, “Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle,” Indiana Univ. Math. J.53(5), 1255–1277 (2004).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

J. D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,” Numer. Math.84(3), 375–393 (2000).

[CrossRef]

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE3482, 389–396 (1998).

[CrossRef]

R. J. McCann, “Existence and uniqueness of monotone measure-preserving maps,” Duke Math. J.80(2), 309–323 (1995).

[CrossRef]

R. T. Rockafellar, “Characterization of the subdifferentials of convex functions,” Pac. J. Math.17(3), 497–510 (1966).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

J. D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,” Numer. Math.84(3), 375–393 (2000).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

J. D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,” Numer. Math.84(3), 375–393 (2000).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express21(12), 14728–14735 (2013).

[CrossRef]
[PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010).

[CrossRef]
[PubMed]

T. Glimm and V. Oliker, “Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle,” Indiana Univ. Math. J.53(5), 1255–1277 (2004).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation,” Opt. Lett.38(2), 229–231 (2013).

[CrossRef]
[PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010).

[CrossRef]
[PubMed]

R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation,” Opt. Lett.38(2), 229–231 (2013).

[CrossRef]
[PubMed]

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008).

[CrossRef]
[PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010).

[CrossRef]
[PubMed]

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[CrossRef]
[PubMed]

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[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

V. Oliker, J. Rubinstein, and G. Wolansky, “Ray mapping and illumination control,” J. Photonics Energy3(1), 035599 (2013).

[CrossRef]

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Ration. Mech. Anal.201(3), 1013–1045 (2011).

[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE5942, 594207 (2005).

[CrossRef]

T. Glimm and V. Oliker, “Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle,” Indiana Univ. Math. J.53(5), 1255–1277 (2004).

[CrossRef]

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE6338, 633808 (2006).

[CrossRef]

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE3482, 389–396 (1998).

[CrossRef]

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE6338, 633808 (2006).

[CrossRef]

R. T. Rockafellar, “Characterization of the subdifferentials of convex functions,” Pac. J. Math.17(3), 497–510 (1966).

[CrossRef]

M. M. Sulman, J. F. Williams, and R. D. Russell, “An efficient approach for the numerical solution of Monge-Ampère equation,” Appl. Numer. Math.61(3), 298–307 (2011).

[CrossRef]

M. M. Sulman, J. F. Williams, and R. D. Russell, “An efficient approach for the numerical solution of Monge-Ampère equation,” Appl. Numer. Math.61(3), 298–307 (2011).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

M. M. Sulman, J. F. Williams, and R. D. Russell, “An efficient approach for the numerical solution of Monge-Ampère equation,” Appl. Numer. Math.61(3), 298–307 (2011).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

M. M. Sulman, J. F. Williams, and R. D. Russell, “An efficient approach for the numerical solution of Monge-Ampère equation,” Appl. Numer. Math.61(3), 298–307 (2011).

[CrossRef]

V. Oliker, “Designing freeform lenses for intensity and phase control of coherent light with help from geometry and mass transport,” Arch. Ration. Mech. Anal.201(3), 1013–1045 (2011).

[CrossRef]

R. J. McCann, “Existence and uniqueness of monotone measure-preserving maps,” Duke Math. J.80(2), 309–323 (1995).

[CrossRef]

T. Glimm and V. Oliker, “Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat’s principle,” Indiana Univ. Math. J.53(5), 1255–1277 (2004).

[CrossRef]

S. Haker, L. Zhu, A. Tannenbaum, and S. Angenent, “Optimal mass transport for registration and warping,” Int. J. Comput. Vis.60(3), 225–240 (2004).

[CrossRef]

V. Oliker, J. Rubinstein, and G. Wolansky, “Ray mapping and illumination control,” J. Photonics Energy3(1), 035599 (2013).

[CrossRef]

J. D. Benamou and Y. Brenier, “A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem,” Numer. Math.84(3), 375–393 (2000).

[CrossRef]

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004).

[CrossRef]

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008).

[CrossRef]
[PubMed]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express18(5), 5295–5304 (2010).

[CrossRef]
[PubMed]

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010).

[CrossRef]
[PubMed]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express20(13), 14477–14485 (2012).

[CrossRef]
[PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express21(12), 14728–14735 (2013).

[CrossRef]
[PubMed]

R. Wu, L. Xu, P. Liu, Y. Zhang, Z. Zheng, H. Li, and X. Liu, “Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation,” Opt. Lett.38(2), 229–231 (2013).

[CrossRef]
[PubMed]

D. Michaelis, P. Schreiber, and A. Bräuer, “Cartesian oval representation of freeform optics in illumination systems,” Opt. Lett.36(6), 918–920 (2011).

[CrossRef]
[PubMed]

R. T. Rockafellar, “Characterization of the subdifferentials of convex functions,” Pac. J. Math.17(3), 497–510 (1966).

[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE5942, 594207 (2005).

[CrossRef]

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE5876, 587607 (2005).

[CrossRef]

W. A. Parkyn, “Illumination lenses designed by extrinsic differential geometry,” Proc. SPIE3482, 389–396 (1998).

[CrossRef]

B. Parkyn and D. Pelka, “Free form lenses designed by a pseudo-rectangular lawnmower algorithm,” Proc. SPIE6338, 633808 (2006).

[CrossRef]

W. A. Parkyn and D. G. Pelka, “Free-form lenses for rectangular illumination zones,” Anthony, Inc., US Patent 7674019 (2010).

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