T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56, 2405–2411 (2017).

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).

[Crossref]

Y. Jin, A. Hassan, and Y. Jiang, “Freeform microlens array homogenizer for excimer laser beam shaping,” Opt. Express 24, 24846–24858 (2016).

[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (2016).

[Crossref]

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

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-Ampére type equation,” J. Opt. 18, 125602 (2016).

[Crossref]

C. Bösel and H. Gross, “Ray mapping approach in double freeform surface design for collimated beam shaping,” Proc. SPIE 9950, 995004 (2016).

[Crossref]

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

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54, 9364–9369 (2015).

[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31, 2401–2408 (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-Ampére equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

M. Maksimovic, “Design and optimization of compact freeform lens array for laser beam splitting: a case study in optimal surface representation,” Proc. SPIE 9131, 913107 (2014).

[Crossref]

J. D. Benamou, B. D. Froese, and A. M. Oberman, “Numerical solution of the optimal transportation problem using the Monge-Ampére equation,” J. Comput. Phys. 260, 107–126 (2014).

[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, 229–231 (2013).

[Crossref]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

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

[Crossref]

G. Li, Y. Li, K. Liu, X. Ma, and H. Wang, “Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry,” J. Opt. Soc. Am. A 30, 1448–1459 (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, 28693–28701 (2013).

[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

T. Glimm and N. Henscheid, “Iterative scheme for solving optimal transportation problems arising in reflector design,” ISRN Appl. Math. 2013, 1–12 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

T. Li, M. Gong, L. Huang, Y. Qiu, and Q. Xue, “Weighted Fried reconstructor and spatial-frequency response optimization of Shack-Hartmann wavefront sensing,” Appl. Opt. 51, 7115–7123 (2012).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (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, 1013–1045 (2011).

[Crossref]

R. A. Hicks, “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. 22, 323–329 (2005).

[Crossref]

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE 5876, 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, 1255–1278 (2004).

[Crossref]

P. Benítez and J. C. Miñano, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1502 (2004).

[Crossref]

J. Rubinstein and G. Wolansky, “A variational principle in optics,” J. Opt. Soc. Am. A 21, 2164–2172 (2004).

[Crossref]

D. L. Shealy and S. Chao, “Geometric optics-based design of laser beam shapers,” Opt. Eng. 42, 3123–3138 (2003).

[Crossref]

K. Nemoto, T. Fujii, and N. Goto, “Laser beam-forming by deformable mirror,” Proc. SPIE 2119, 155–161 (1994).

[Crossref]

M. Halstead, B. Barsky, S. Klein, and R. Mandell, “Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals,” in 23rd Annual Conference on Computer Graphics and Interactive Techniques (Association of Computing Machinery, 1996), pp. 335–342.

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).

[Crossref]

J. D. Benamou, B. D. Froese, and A. M. Oberman, “Numerical solution of the optimal transportation problem using the Monge-Ampére equation,” J. Comput. Phys. 260, 107–126 (2014).

[Crossref]

P. Benítez and J. C. Miñano, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1502 (2004).

[Crossref]

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

C. Bösel and H. Gross, “Ray mapping approach in double freeform surface design for collimated beam shaping,” Proc. SPIE 9950, 995004 (2016).

[Crossref]

K.-H. Brenner, “General solution of two-dimensional beam-shaping with two surfaces,” in Information Optics and Photonics: Algorithms, Systems, and Applications, B. Javidi, ed. (Springer, 2010), pp. 3–11.

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).

[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-Ampére type equation,” J. Opt. 18, 125602 (2016).

[Crossref]

D. L. Shealy and S. Chao, “Geometric optics-based design of laser beam shapers,” Opt. Eng. 42, 3123–3138 (2003).

[Crossref]

L. A. Romero and F. M. Dickey, “The mathematical and physical theory of lossless beam shaping,” in Laser Beam Shaping: Theory and Techniques, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp. 90–92.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).

[Crossref]

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

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54, 9364–9369 (2015).

[Crossref]

Z. Feng, L. Huang, G. Jin, and M. Gong, “Designing double freeform optical surfaces for controlling both irradiance and wavefront,” Opt. Express 21, 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, 14728–14735 (2013).

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).

[Crossref]

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

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54, 9364–9369 (2015).

[Crossref]

J. D. Benamou, B. D. Froese, and A. M. Oberman, “Numerical solution of the optimal transportation problem using the Monge-Ampére equation,” J. Comput. Phys. 260, 107–126 (2014).

[Crossref]

K. Nemoto, T. Fujii, and N. Goto, “Laser beam-forming by deformable mirror,” Proc. SPIE 2119, 155–161 (1994).

[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (2016).

[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (2016).

[Crossref]

T. Glimm and N. Henscheid, “Iterative scheme for solving optimal transportation problems arising in reflector design,” ISRN Appl. Math. 2013, 1–12 (2013).

[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, 1255–1278 (2004).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21, 14728–14735 (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, 28693–28701 (2013).

[Crossref]

T. Li, M. Gong, L. Huang, Y. Qiu, and Q. Xue, “Weighted Fried reconstructor and spatial-frequency response optimization of Shack-Hartmann wavefront sensing,” Appl. Opt. 51, 7115–7123 (2012).

[Crossref]

K. Nemoto, T. Fujii, and N. Goto, “Laser beam-forming by deformable mirror,” Proc. SPIE 2119, 155–161 (1994).

[Crossref]

C. Bösel and H. Gross, “Ray mapping approach in double freeform surface design for collimated beam shaping,” Proc. SPIE 9950, 995004 (2016).

[Crossref]

R. Swaminathan, S. K. Nayar, and M. D. Grossberg, “Framework to design catadioptric imaging and projection systems,” in IEEE Conference on ICCV-PROCAMS (2003).

M. Halstead, B. Barsky, S. Klein, and R. Mandell, “Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals,” in 23rd Annual Conference on Computer Graphics and Interactive Techniques (Association of Computing Machinery, 1996), pp. 335–342.

T. Glimm and N. Henscheid, “Iterative scheme for solving optimal transportation problems arising in reflector design,” ISRN Appl. Math. 2013, 1–12 (2013).

[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (2016).

[Crossref]

R. A. Hicks, “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. 22, 323–329 (2005).

[Crossref]

R. A. Hicks and R. K. Perline, “Geometric distributions for catadioptric sensor design,” in IEEE Conference on CVPR (2001), pp. 584–589.

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21, 14728–14735 (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, 28693–28701 (2013).

[Crossref]

T. Li, M. Gong, L. Huang, Y. Qiu, and Q. Xue, “Weighted Fried reconstructor and spatial-frequency response optimization of Shack-Hartmann wavefront sensing,” Appl. Opt. 51, 7115–7123 (2012).

[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56, 2405–2411 (2017).

[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31, 2401–2408 (2014).

[Crossref]

Z. Feng, L. Huang, M. Gong, and G. Jin, “Beam shaping system design using double freeform optical surfaces,” Opt. Express 21, 14728–14735 (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, 28693–28701 (2013).

[Crossref]

M. Halstead, B. Barsky, S. Klein, and R. Mandell, “Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals,” in 23rd Annual Conference on Computer Graphics and Interactive Techniques (Association of Computing Machinery, 1996), pp. 335–342.

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-Ampére type equation,” J. Opt. 18, 125602 (2016).

[Crossref]

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

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

[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, 229–231 (2013).

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).

[Crossref]

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

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54, 9364–9369 (2015).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

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

[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, 229–231 (2013).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

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

[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, 229–231 (2013).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).

[Crossref]

M. Maksimovic, “Design and optimization of compact freeform lens array for laser beam splitting: a case study in optimal surface representation,” Proc. SPIE 9131, 913107 (2014).

[Crossref]

M. Halstead, B. Barsky, S. Klein, and R. Mandell, “Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals,” in 23rd Annual Conference on Computer Graphics and Interactive Techniques (Association of Computing Machinery, 1996), pp. 335–342.

P. Benítez and J. C. Miñano, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1502 (2004).

[Crossref]

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

R. Swaminathan, S. K. Nayar, and M. D. Grossberg, “Framework to design catadioptric imaging and projection systems,” in IEEE Conference on ICCV-PROCAMS (2003).

K. Nemoto, T. Fujii, and N. Goto, “Laser beam-forming by deformable mirror,” Proc. SPIE 2119, 155–161 (1994).

[Crossref]

J. D. Benamou, B. D. Froese, and A. M. Oberman, “Numerical solution of the optimal transportation problem using the Monge-Ampére equation,” J. Comput. Phys. 260, 107–126 (2014).

[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, 1013–1045 (2011).

[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, 1255–1278 (2004).

[Crossref]

R. A. Hicks and R. K. Perline, “Geometric distributions for catadioptric sensor design,” in IEEE Conference on CVPR (2001), pp. 584–589.

L. A. Romero and F. M. Dickey, “The mathematical and physical theory of lossless beam shaping,” in Laser Beam Shaping: Theory and Techniques, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp. 90–92.

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

R. Swaminathan, S. K. Nayar, and M. D. Grossberg, “Framework to design catadioptric imaging and projection systems,” in IEEE Conference on ICCV-PROCAMS (2003).

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (2016).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).

[Crossref]

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

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-Ampére type equation,” J. Opt. 18, 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-Ampére equation method,” Opt. Commun. 331, 297–305 (2014).

[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, 229–231 (2013).

[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56, 2405–2411 (2017).

[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31, 2401–2408 (2014).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

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

[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, 229–231 (2013).

[Crossref]

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

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-Ampére type equation,” J. Opt. 18, 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-Ampére equation method,” Opt. Commun. 331, 297–305 (2014).

[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, 229–231 (2013).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56, 2405–2411 (2017).

[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31, 2401–2408 (2014).

[Crossref]

H. Li, N. J. Naples, X. Zhao, and A. Y. Yi, “An integrated approach to design and fabrication of a miniature endoscope using freeform optics,” Adv. Opt. Technol. 5, 335–342 (2016).

N. C. Evans and D. L. Shealy, “Design and optimization of an irradiance profile-shaping system with a genetic algorithm method,” Appl. Opt. 37, 5216–5221 (1998).

[Crossref]

W. Zou and Z. Zhang, “Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann test,” Appl. Opt. 39, 250–268 (2000).

[Crossref]

M. Serkan and H. Kirkici, “Optical beam-shaping design based on aspherical lenses for circularization, collimation, and expansion of elliptical laser beams,” Appl. Opt. 47, 230–241 (2008).

[Crossref]

T. Li, M. Gong, L. Huang, Y. Qiu, and Q. Xue, “Weighted Fried reconstructor and spatial-frequency response optimization of Shack-Hartmann wavefront sensing,” Appl. Opt. 51, 7115–7123 (2012).

[Crossref]

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

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54, 9364–9369 (2015).

[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Freeform illumination optics construction following an optimal transport map,” Appl. Opt. 55, 4301–4306 (2016).

[Crossref]

X. Wu, G. Jin, and J. Zhu, “Freeform illumination design model for multiple light sources simultaneously,” Appl. Opt. 56, 2405–2411 (2017).

[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, 1013–1045 (2011).

[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).

[Crossref]

T. Zhou, X. Liu, Z. Liang, Y. Liu, J. Xie, and X. Wang, “Recent advancements in optical microstructure fabrication through glass molding process,” Front. Mech. Eng. 12, 46–65 (2017).

[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, 1255–1278 (2004).

[Crossref]

T. Glimm and N. Henscheid, “Iterative scheme for solving optimal transportation problems arising in reflector design,” ISRN Appl. Math. 2013, 1–12 (2013).

[Crossref]

J. D. Benamou, B. D. Froese, and A. M. Oberman, “Numerical solution of the optimal transportation problem using the Monge-Ampére equation,” J. Comput. Phys. 260, 107–126 (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-Ampére type equation,” J. Opt. 18, 125602 (2016).

[Crossref]

R. A. Hicks, “Designing a mirror to realize a given projection,” J. Opt. Soc. Am. 22, 323–329 (2005).

[Crossref]

J. S. Schruben, “Formulation of a reflector-design problem for a lighting fixture,” J. Opt. Soc. Am. 62, 1498–1501 (1972).

[Crossref]

O. Bryngdahl, “Geometrical transformations in optics*,” J. Opt. Soc. Am. 64, 1092–1099 (1974).

[Crossref]

J. Hermann, “Least-squares wave front errors of minimum norm,” J. Opt. Soc. Am. 70, 28–35 (1980).

[Crossref]

W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).

[Crossref]

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590–595 (2002).

[Crossref]

J. Rubinstein and G. Wolansky, “A variational principle in optics,” J. Opt. Soc. Am. A 21, 2164–2172 (2004).

[Crossref]

J. Rubinstein and G. Wolansky, “Intensity control with a free-form lens,” J. Opt. Soc. Am. A 24, 463–469 (2007).

[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31, 2401–2408 (2014).

[Crossref]

G. Li, Y. Li, K. Liu, X. Ma, and H. Wang, “Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry,” J. Opt. Soc. Am. A 30, 1448–1459 (2013).

[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Sub-micrometre accurate free-form optics by three-dimensional printing on single-mode fibres,” Nat. Commun. 7, 11763 (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-Ampére equation method,” Opt. Commun. 331, 297–305 (2014).

[Crossref]

D. L. Shealy and S. Chao, “Geometric optics-based design of laser beam shapers,” Opt. Eng. 42, 3123–3138 (2003).

[Crossref]

P. Benítez and J. C. Miñano, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43, 1489–1502 (2004).

[Crossref]

A. Bäuerle, A. Bruneton, R. Wester, J. Stollenwerk, and P. Loosen, “Algorithm for irradiance tailoring using multiple freeform optical surfaces,” Opt. Express 20, 14477–14485 (2012).

[Crossref]

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

[Crossref]

A. Bruneton, A. Bäuerle, R. Wester, J. Stollenwerk, and P. Loosen, “High resolution irradiance tailoring using multiple freeform surfaces,” Opt. Express 21, 10563–10571 (2013).

[Crossref]

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

[Crossref]

Y. Jin, A. Hassan, and Y. Jiang, “Freeform microlens array homogenizer for excimer laser beam shaping,” Opt. Express 24, 24846–24858 (2016).

[Crossref]

A. Bruneton, A. Bäuerle, P. Loosen, and R. Wester, “Freeform lens for an efficient wall washer,” Proc. SPIE 8167, 816707 (2011).

[Crossref]

M. Maksimovic, “Design and optimization of compact freeform lens array for laser beam splitting: a case study in optimal surface representation,” Proc. SPIE 9131, 913107 (2014).

[Crossref]

K. Nemoto, T. Fujii, and N. Goto, “Laser beam-forming by deformable mirror,” Proc. SPIE 2119, 155–161 (1994).

[Crossref]

H. Ries, “Laser beam shaping by double tailoring,” Proc. SPIE 5876, 587607 (2005).

[Crossref]

C. Bösel and H. Gross, “Ray mapping approach in double freeform surface design for collimated beam shaping,” Proc. SPIE 9950, 995004 (2016).

[Crossref]

M. Halstead, B. Barsky, S. Klein, and R. Mandell, “Reconstructing curved surfaces from specular reflection patterns using spline surface fitting of normals,” in 23rd Annual Conference on Computer Graphics and Interactive Techniques (Association of Computing Machinery, 1996), pp. 335–342.

R. A. Hicks and R. K. Perline, “Geometric distributions for catadioptric sensor design,” in IEEE Conference on CVPR (2001), pp. 584–589.

R. Swaminathan, S. K. Nayar, and M. D. Grossberg, “Framework to design catadioptric imaging and projection systems,” in IEEE Conference on ICCV-PROCAMS (2003).

R. Winston, J. C. Miñano, P. Benítez, N. Shatz, and J. C. Bortz, “Concentrators for prescribed irradiance optics,” in Nonimaging Optics (Elsevier, 2005), pp. 159–180.

K.-H. Brenner, “General solution of two-dimensional beam-shaping with two surfaces,” in Information Optics and Photonics: Algorithms, Systems, and Applications, B. Javidi, ed. (Springer, 2010), pp. 3–11.

L. A. Romero and F. M. Dickey, “The mathematical and physical theory of lossless beam shaping,” in Laser Beam Shaping: Theory and Techniques, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp. 90–92.