X. Hui, J. Liu, Y. Wan, and H. Lin, “Realization of uniform and collimated light distribution in a single freeform-Fresnel double surface LED lens,” Appl. Opt. 56(15), 4561–4565 (2017).

[Crossref]
[PubMed]

C. Bösel, N. G. Worku, and H. Gross, “Ray-mapping approach in double freeform surface design for collimated beam shaping beyond the paraxial approximation,” Appl. Opt. 56(13), 3679–3688 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, A. A. Mingazov, D. A. Bykov, E. S. Andreev, and E. A. Bezus, “Variational approach to calculation of light field eikonal function for illuminating a prescribed region,” Opt. Express 25(22), 26378–26392 (2017).

[Crossref]
[PubMed]

X. Mao, S. Xu, X. Hu, and Y. Xie, “Design of a smooth freeform illumination system for a point light source based on polar-type optimal transport mapping,” Appl. Opt. 56(22), 6324–6331 (2017).

[Crossref]
[PubMed]

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (SQM),” Opt. Express 25(4), A58–A72 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).

[Crossref]
[PubMed]

L. L. Doskolovich, E. S. Andreev, S. I. Kharitonov, and N. L. Kazansky, “Reconstruction of an optical surface from a given source-target map,” J. Opt. Soc. Am. A 33(8), 1504–1508 (2016).

[Crossref]

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

Z. Feng, B. D. Froese, C.-Y. Huang, D. Ma, and R. Liang, “Creating unconventional geometric beams with large depth of field using double freeform-surface optics,” Appl. Opt. 54(20), 6277–6281 (2015).

[Crossref]
[PubMed]

X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).

[Crossref]
[PubMed]

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

[Crossref]

H. Ma, Z. Liu, P. Jiang, X. Xu, and S. Du, “Improvement of Galilean refractive beam shaping system for accurately generating near diffraction-limited flattop beam with arbitrary beam size,” Opt. Express 19(14), 13105–13117 (2011).

[Crossref]
[PubMed]

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).

[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

D. P. Bertsekas, “The auction algorithm: A distributed relaxation method for the assignment problem,” Ann. Oper. Res. 14(1), 105–123 (1988).

[Crossref]

R. Jonker and A. Volgenant, “A shortest augmenting path algorithm for dense and sparse linear assignment problems,” Computing 38(4), 325–340 (1987).

[Crossref]

J. Munkres, “Algorithms for the assignment and transportation problems,” SIAM J. Appl. Math. 5(1), 32–38 (1957).

[Crossref]

L. L. Doskolovich, A. A. Mingazov, D. A. Bykov, E. S. Andreev, and E. A. Bezus, “Variational approach to calculation of light field eikonal function for illuminating a prescribed region,” Opt. Express 25(22), 26378–26392 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, E. S. Andreev, S. I. Kharitonov, and N. L. Kazansky, “Reconstruction of an optical surface from a given source-target map,” J. Opt. Soc. Am. A 33(8), 1504–1508 (2016).

[Crossref]

D. P. Bertsekas, “The auction algorithm: A distributed relaxation method for the assignment problem,” Ann. Oper. Res. 14(1), 105–123 (1988).

[Crossref]

L. L. Doskolovich, A. A. Mingazov, D. A. Bykov, E. S. Andreev, and E. A. Bezus, “Variational approach to calculation of light field eikonal function for illuminating a prescribed region,” Opt. Express 25(22), 26378–26392 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).

[Crossref]
[PubMed]

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001).

L. L. Doskolovich, A. A. Mingazov, D. A. Bykov, E. S. Andreev, and E. A. Bezus, “Variational approach to calculation of light field eikonal function for illuminating a prescribed region,” Opt. Express 25(22), 26378–26392 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).

[Crossref]
[PubMed]

L. L. Doskolovich, E. S. Andreev, S. I. Kharitonov, and N. L. Kazansky, “Reconstruction of an optical surface from a given source-target map,” J. Opt. Soc. Am. A 33(8), 1504–1508 (2016).

[Crossref]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).

[Crossref]
[PubMed]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

Z. Feng, B. D. Froese, C.-Y. Huang, D. Ma, and R. Liang, “Creating unconventional geometric beams with large depth of field using double freeform-surface optics,” Appl. Opt. 54(20), 6277–6281 (2015).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

R. Jonker and A. Volgenant, “A shortest augmenting path algorithm for dense and sparse linear assignment problems,” Computing 38(4), 325–340 (1987).

[Crossref]

L. L. Doskolovich, E. S. Andreev, S. I. Kharitonov, and N. L. Kazansky, “Reconstruction of an optical surface from a given source-target map,” J. Opt. Soc. Am. A 33(8), 1504–1508 (2016).

[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

L. L. Doskolovich, E. S. Andreev, S. I. Kharitonov, and N. L. Kazansky, “Reconstruction of an optical surface from a given source-target map,” J. Opt. Soc. Am. A 33(8), 1504–1508 (2016).

[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U. S. Patent No. 3,476,463 (4Nov., 1969).

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015).

[Crossref]
[PubMed]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Y. Ding, X. Liu, Z.-R. Zheng, and P.-F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).

[Crossref]
[PubMed]

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

X. Mao, S. Xu, X. Hu, and Y. Xie, “Design of a smooth freeform illumination system for a point light source based on polar-type optimal transport mapping,” Appl. Opt. 56(22), 6324–6331 (2017).

[Crossref]
[PubMed]

X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).

[Crossref]
[PubMed]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).

[Crossref]
[PubMed]

J. Munkres, “Algorithms for the assignment and transportation problems,” SIAM J. Appl. Math. 5(1), 32–38 (1957).

[Crossref]

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (SQM),” Opt. Express 25(4), A58–A72 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

V. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds. (Springer, 2003).

[Crossref]

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

[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

R. Jonker and A. Volgenant, “A shortest augmenting path algorithm for dense and sparse linear assignment problems,” Computing 38(4), 325–340 (1987).

[Crossref]

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

D. P. Bertsekas, “The auction algorithm: A distributed relaxation method for the assignment problem,” Ann. Oper. Res. 14(1), 105–123 (1988).

[Crossref]

B. R. Frieden, “Lossless conversion of a plane laser wave to a plane wave of uniform irradiance,” Appl. Opt. 4(11), 1400–1403 (1965).

[Crossref]

P. W. Rhodes and D. L. Shealy, “Refractive optical systems for irradiance redistribution of collimated radiation: their design and analysis,” Appl. Opt. 19(20), 3545–3553 (1980).

[Crossref]
[PubMed]

J. A. Hoffnagle and C. M. Jefferson, “Design and performance of a refractive optical system that converts a Gaussian to a flattop beam,” Appl. Opt. 39(30), 5488–5499 (2000).

[Crossref]

L. L. Doskolovich, A. Y. Dmitriev, E. A. Bezus, and M. A. Moiseev, “Analytical design of freeform optical elements generating an arbitrary-shape curve,” Appl. Opt. 52(12), 2521–2526 (2013).

[Crossref]
[PubMed]

Z. Feng, B. D. Froese, C.-Y. Huang, D. Ma, and R. Liang, “Creating unconventional geometric beams with large depth of field using double freeform-surface optics,” Appl. Opt. 54(20), 6277–6281 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, K. V. Borisova, M. A. Moiseev, and N. L. Kazanskiy, “Design of mirrors for generating prescribed continuous illuminance distributions on the basis of the supporting quadric method,” Appl. Opt. 55(4), 687–695 (2016).

[Crossref]
[PubMed]

C. Bösel, N. G. Worku, and H. Gross, “Ray-mapping approach in double freeform surface design for collimated beam shaping beyond the paraxial approximation,” Appl. Opt. 56(13), 3679–3688 (2017).

[Crossref]
[PubMed]

X. Hui, J. Liu, Y. Wan, and H. Lin, “Realization of uniform and collimated light distribution in a single freeform-Fresnel double surface LED lens,” Appl. Opt. 56(15), 4561–4565 (2017).

[Crossref]
[PubMed]

X. Mao, S. Xu, X. Hu, and Y. Xie, “Design of a smooth freeform illumination system for a point light source based on polar-type optimal transport mapping,” Appl. Opt. 56(22), 6324–6331 (2017).

[Crossref]
[PubMed]

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

[Crossref]

R. Jonker and A. Volgenant, “A shortest augmenting path algorithm for dense and sparse linear assignment problems,” Computing 38(4), 325–340 (1987).

[Crossref]

L. L. Doskolovich, N. L. Kazansky, S. I. Kharitonov, and V. A. Soifer, “A method of designing diffractive optical elements focusing into plane areas,” J. Mod. Opt. 43(7), 1423–1433 (1996).

[Crossref]

S. Chang, R. Wu, A. Li, and Z. Zheng, “Design beam shapers with double freeform surfaces to form a desired wavefront with prescribed illumination pattern by solving a Monge–Ampère type equation,” J. Opt. 18(12), 125602 (2016).

[Crossref]

Y. Zhang, R. Wu, P. Liu, Z. Zheng, H. Li, and X. Liu, “Double freeform surfaces design for laser beam shaping with Monge–Ampère equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

Y. Ding, X. Liu, Z.-R. Zheng, and P.-F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008).

[Crossref]
[PubMed]

H. Ma, Z. Liu, P. Jiang, X. Xu, and S. Du, “Improvement of Galilean refractive beam shaping system for accurately generating near diffraction-limited flattop beam with arbitrary beam size,” Opt. Express 19(14), 13105–13117 (2011).

[Crossref]
[PubMed]

V. Oliker, “Controlling light with freeform multifocal lens designed with supporting quadric method (SQM),” Opt. Express 25(4), A58–A72 (2017).

[Crossref]
[PubMed]

L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and V. Oliker, “On the use of the supporting quadric method in the problem of the light field eikonal calculation,” Opt. Express 23(15), 19605–19617 (2015).

[Crossref]
[PubMed]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21(12), 14728–14735 (2013).

[Crossref]
[PubMed]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21(23), 28693–28701 (2013).

[Crossref]

X. Mao, H. Li, Y. Han, and Y. Luo, “Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape,” Opt. Express 23(4), 4313–4328 (2015).

[Crossref]
[PubMed]

L. L. Doskolovich, A. A. Mingazov, D. A. Bykov, E. S. Andreev, and E. A. Bezus, “Variational approach to calculation of light field eikonal function for illuminating a prescribed region,” Opt. Express 25(22), 26378–26392 (2017).

[Crossref]
[PubMed]

J. Rubinstein and G. Wolansky, “Reconstruction of optical surfaces from ray data,” Opt. Rev. 8(4), 281–283 (2001).

[Crossref]

J. Munkres, “Algorithms for the assignment and transportation problems,” SIAM J. Appl. Math. 5(1), 32–38 (1957).

[Crossref]

J. L. Kreuzer, “Coherent light optical system yielding an output beam of desired intensity distribution at a desired equiphase surface,” U. S. Patent No. 3,476,463 (4Nov., 1969).

C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001).

V. Oliker, “Mathematical aspects of design of beam shaping surfaces in geometrical optics,” Trends in Nonlinear Analysis, M. Kirkilionis, S. Krömker, R. Rannacher, and F. Tomi, eds. (Springer, 2003).

[Crossref]

R. K. Luneburg, Mathematical Theory of Optics (University of California, 1964).

Fast linear assignment problem using auction algorithm (mex). http://www.mathworks.com/matlabcentral/fileexchange/48448

Opto-mechanical software TracePro. https://www.lambdares.com/tracepro

Computer-aided design software Rhinoceros. http://www.rhino3d.com