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

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]

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]

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]

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, 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]

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, 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]

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, 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, 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]

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, 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, 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]

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, 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]

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]

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]

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, 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]

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]

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]

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, 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. 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]

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]

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).

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]

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

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