Abstract

Recent energy efficient illumination advancements have capitalized on using light-emitting diodes (LEDs) in combination with freeform lenses. However, the available freeform lens design methods are application specific. In addition, manufacturing of this class of optics is challenging. In this work, considering manufacturing constraints, we apply a customized algorithm to design freeform lenses for (1) transforming LED radiation into a uniform rectangular illumination pattern and (2) shaping collimated LED light beams into complex image target irradiance distributions. The algorithm is based on a numerical solution of the elliptic Monge–Ampère equation. Then, we proposed manufacturing these lenses using a modified ink-jet 3D printing technology called Printoptical technology. The demonstrated optical performance of printed lenses, exhibiting surface roughness of $\textrm {RMS} = 10\pm 2$ nm, is in good agreement with the simulation. We also explored an industrial application of the 3D-printed lens matrix for low-cost illumination of a paper milling machine.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]

2018 (2)

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

2017 (5)

2016 (2)

F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,” Adv. Opt. Technol. 5(4), 303–324 (2016).
[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

2015 (2)

P. Maillard and A. Heinrich, “3D printed freeform optical sensors for metrology application,” Proc. SPIE 9628, 96281J (2015).
[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54 (31), 9364–9369 (2015).
[Crossref]

2014 (1)

2013 (2)

2012 (2)

2011 (1)

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

2010 (2)

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18(5), 5295–5304 (2010).
[Crossref]

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

2009 (3)

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE 7423, 742302 (2009).
[Crossref]

J. C. Minano, P. Benìtez, and A. Santamarìa, “Free-Form Optics for Illumination,” Opt. Rev. 16(2), 99–102 (2009).
[Crossref]

I. Moreno, C.-C. Sun, and R. Ivanov, “Far-field condition for light emitting diode arrays,” Appl. Opt. 48(6), 1190–1197 (2009).
[Crossref]

2004 (1)

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

2002 (2)

J.-D. Benamou, Y. Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,” Int. J. Numer. Meth. Fluids 40(1–2), 21–30 (2002).
[Crossref]

H. Ries and J. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
[Crossref]

2001 (1)

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Abate, M.

E. Ham, R. Dyke, and M. Abate, “3D lens,” www.princeton.edu/ssp/joseph-henry-project/3d-lens/ , (Princeton University, 2014).

Angenent, S.

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

Assefa, B. G.

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Bauer, A.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light: Sci. Appl. 6(7), e17026 (2017).
[Crossref]

Bäuerle, A.

Benamou, J.-D.

J.-D. Benamou, Y. Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,” Int. J. Numer. Meth. Fluids 40(1–2), 21–30 (2002).
[Crossref]

Benìtez, P.

J. C. Minano, P. Benìtez, and A. Santamarìa, “Free-Form Optics for Illumination,” Opt. Rev. 16(2), 99–102 (2009).
[Crossref]

Berens, M.

Biskop, J.

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

R. V. de Vrie, R. Blomaard, and J. Biskop, “Method of printing an optical element,” U.S. Patent Application No. 14/758,826 (2016).

Blomaard, R.

R. V. de Vrie, R. Blomaard, and J. Biskop, “Method of printing an optical element,” U.S. Patent Application No. 14/758,826 (2016).

Bosel, C.

Bösel, C.

Brenier, Y.

J.-D. Benamou, Y. Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,” Int. J. Numer. Meth. Fluids 40(1–2), 21–30 (2002).
[Crossref]

Brockmeyer, E.

K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive devices,” ACM symposium on user interface software and technology (ACM UIST 12), (Disney Research, 2012).

Bruneton, A.

Cakmakci, O.

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

Cassarly, W. J.

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18(5), 5295–5304 (2010).
[Crossref]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE 7423, 742302 (2009).
[Crossref]

Cheng, Y.

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2(5–6), 445–453 (2013).
[Crossref]

Cote, J.

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

Cui, Z.

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

de Vrie, R. V.

R. V. de Vrie, R. Blomaard, and J. Biskop, “Method of printing an optical element,” U.S. Patent Application No. 14/758,826 (2016).

Dyke, R.

E. Ham, R. Dyke, and M. Abate, “3D lens,” www.princeton.edu/ssp/joseph-henry-project/3d-lens/ , (Princeton University, 2014).

Fang, F.

F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,” Adv. Opt. Technol. 5(4), 303–324 (2016).
[Crossref]

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2(5–6), 445–453 (2013).
[Crossref]

Feng, Z.

Feßler, R.

Fournier, F. R.

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18(5), 5295–5304 (2010).
[Crossref]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE 7423, 742302 (2009).
[Crossref]

Froese, B. D.

Giessen, H.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Gissibl, T.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Gross, H.

Guittet, K.

J.-D. Benamou, Y. Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,” Int. J. Numer. Meth. Fluids 40(1–2), 21–30 (2002).
[Crossref]

Haker, S.

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

Ham, E.

E. Ham, R. Dyke, and M. Abate, “3D lens,” www.princeton.edu/ssp/joseph-henry-project/3d-lens/ , (Princeton University, 2014).

Heinrich, A.

P. Maillard and A. Heinrich, “3D printed freeform optical sensors for metrology application,” Proc. SPIE 9628, 96281J (2015).
[Crossref]

Herkommer, A.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Hong, Z.

Z. Hong and R. Liang, “IR-laser assisted additive freeform optics manufacturing,” Sci. Rep. 7(1), 7145 (2017).
[Crossref]

Hudson, S. E.

K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive devices,” ACM symposium on user interface software and technology (ACM UIST 12), (Disney Research, 2012).

Ivanov, R.

Jegorov, J.

Kuittinen, M.

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Liang, R.

Z. Hong and R. Liang, “IR-laser assisted additive freeform optics manufacturing,” Sci. Rep. 7(1), 7145 (2017).
[Crossref]

Z. Feng, B. D. Froese, and R. Liang, “Composite method for precise freeform optical beam shaping,” Appl. Opt. 54 (31), 9364–9369 (2015).
[Crossref]

Loosen, P.

Lu, C.

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Maillard, P.

P. Maillard and A. Heinrich, “3D printed freeform optical sensors for metrology application,” Proc. SPIE 9628, 96281J (2015).
[Crossref]

Meuret, Y.

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Minano, J. C.

J. C. Minano, P. Benìtez, and A. Santamarìa, “Free-Form Optics for Illumination,” Opt. Rev. 16(2), 99–102 (2009).
[Crossref]

Moreno, I.

Müller, G.

Muschaweck, J.

Notni, G.

Oliker, V.

Pekkarinen, M.

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

Poupyrev, I.

K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive devices,” ACM symposium on user interface software and technology (ACM UIST 12), (Disney Research, 2012).

Reimers, J.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light: Sci. Appl. 6(7), e17026 (2017).
[Crossref]

Ries, H.

Rolland, J. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light: Sci. Appl. 6(7), e17026 (2017).
[Crossref]

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation using source-target maps,” Opt. Express 18(5), 5295–5304 (2010).
[Crossref]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE 7423, 742302 (2009).
[Crossref]

Russel, R. D.

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

Saarinen, J.

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Saastamoinen, T.

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Santamarìa, A.

J. C. Minano, P. Benìtez, and A. Santamarìa, “Free-Form Optics for Illumination,” Opt. Rev. 16(2), 99–102 (2009).
[Crossref]

Shen, J.

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Stollenwerk, J.

Su, X.

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Sulman, M. M.

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

Sun, C.-C.

Tannenbaum, A.

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

Tervo, J.

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

Thiele, S.

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Thompson, K. P.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light: Sci. Appl. 6(7), e17026 (2017).
[Crossref]

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

Turunen, J.

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

Vallee, P.

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

Völl, A.

Wester, R.

Williams, J. F.

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

Willis, K. D.

K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive devices,” ACM symposium on user interface software and technology (ACM UIST 12), (Disney Research, 2012).

Worku, N. G.

Yang, B.

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

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Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Zhang, N.

F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,” Adv. Opt. Technol. 5(4), 303–324 (2016).
[Crossref]

Zhang, X.

F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,” Adv. Opt. Technol. 5(4), 303–324 (2016).
[Crossref]

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2(5–6), 445–453 (2013).
[Crossref]

Zhu, L.

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

Zwick, S.

Adv. Opt. Technol. (2)

F. Fang, Y. Cheng, and X. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2(5–6), 445–453 (2013).
[Crossref]

F. Fang, N. Zhang, and X. Zhang, “Precision injection molding of freeform optics,” Adv. Opt. Technol. 5(4), 303–324 (2016).
[Crossref]

Appl. Numer. Math. (1)

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

Appl. Opt. (3)

Int. J. Comp. Vis. (1)

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

Int. J. Numer. Meth. Fluids (1)

J.-D. Benamou, Y. Brenier, and K. Guittet, “The Monge-Kantorovich mass transfer and its computational fluid mechanics formulation,” Int. J. Numer. Meth. Fluids 40(1–2), 21–30 (2002).
[Crossref]

J. Opt. Soc. Am. A (2)

Light: Sci. Appl. (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light: Sci. Appl. 6(7), e17026 (2017).
[Crossref]

Nat. Photonics (1)

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10(8), 554–560 (2016).
[Crossref]

Opt. Express (6)

Opt. Rev. (2)

J. C. Minano, P. Benìtez, and A. Santamarìa, “Free-Form Optics for Illumination,” Opt. Rev. 16(2), 99–102 (2009).
[Crossref]

B. G. Assefa, T. Saastamoinen, J. Biskop, M. Kuittinen, J. Turunen, and J. saarinen, “3D printed plano-freeform optics for non-coherent discontinuous beam shaping,” Opt. Rev. 25(3), 456–462 (2018).
[Crossref]

Polymer (1)

Z. Cui, C. Lu, B. Yang, J. Shen, X. Su, and H. Yang, “The research on syntheses and properties of novel epoxy/polymercaptan curing optical resins with high refractive indices,” Polymer 42(26), 10095–10100 (2001).
[Crossref]

Proc. SPIE (4)

B. G. Assefa, T. Saastamoinen, M. Pekkarinen, J. Biskop, M. Kuittinen, J. Turunen, and J. Saarinen, “Design and characterization of 3D-printed freeform lenses for random illuminations,” Proc. SPIE 10554, 105541J (2018).
[Crossref]

P. Maillard and A. Heinrich, “3D printed freeform optical sensors for metrology application,” Proc. SPIE 9628, 96281J (2015).
[Crossref]

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Designing freeform reflectors for extended sources,” Proc. SPIE 7423, 742302 (2009).
[Crossref]

O. Cakmakci, K. P. Thompson, P. Vallee, J. Cote, and J. P. Rolland, “Design of a free-form single-element head-worn display,” Proc. SPIE 7618, 761803 (2010).
[Crossref]

Sci. Rep. (1)

Z. Hong and R. Liang, “IR-laser assisted additive freeform optics manufacturing,” Sci. Rep. 7(1), 7145 (2017).
[Crossref]

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K. D. Willis, E. Brockmeyer, S. E. Hudson, and I. Poupyrev, “Printed Optics: 3D Printing of embedded optical elements for interactive devices,” ACM symposium on user interface software and technology (ACM UIST 12), (Disney Research, 2012).

B. G. Assefa, Y. Meuret, J. Tervo, T. Saastamoinen, M. Kuittinen, and J. Saarinen, “Evaluation of freeform lens designs for specific target distributions and fabrication using 3D printing,” In: The 11th Japan-Finland Joint Symposium on Optics in Engineering (OIE2015) proceedings, (University of Eastern Finland Press, 2015).

E. Ham, R. Dyke, and M. Abate, “3D lens,” www.princeton.edu/ssp/joseph-henry-project/3d-lens/ , (Princeton University, 2014).

R. V. de Vrie, R. Blomaard, and J. Biskop, “Method of printing an optical element,” U.S. Patent Application No. 14/758,826 (2016).

Supplementary Material (1)

NameDescription
» Visualization 1       The video show the simulated irradiance pattern as the source size increases from $1 \times1~{\rm mm}^2$ to $10 \times 10~{\rm mm}^2$

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Figures (12)

Fig. 1.
Fig. 1. Sketch of ray-mapping using a freeform surface.
Fig. 2.
Fig. 2. Freeform lens designs. (a) 3D-CAD format and (b) top-view contour of the freeform lens for an ideal uniform rectangular illumination; (c) 3D-CAD format and (d) top-view contour of the freeform lens for paper web illumination.
Fig. 3.
Fig. 3. Simulation results: relative irradiance distribution for (a) the ideal rectangular and (b) the paper web illumination case studies at the target plane; cross sections in $x$ and $y$ direction for (c) the ideal rectangular and (d) the paper mill machine illumination cases.
Fig. 4.
Fig. 4. LED size effect on the target illumination (See Visualization 1, MP4, 378 KB). The video show the simulated irradiance pattern as the source size increases from $1 \times 1~\textrm {mm}^2$ to $10 \times 10~\textrm {mm}^2$.
Fig. 5.
Fig. 5. Freeform lens design for complex target irradiance distributions: (a) 3D-CAD format and (b) sub-microns features of freeform lens design for Plato and Aristotle target image; (c) 3D-CAD format and (d) sub-microns features of freeform lens design for Lenna target image.
Fig. 6.
Fig. 6. Numerical simulation of the freeform lens designs for complex target images : (a) & (d) ideal prescribed target irradiance distribution of Plato and Aristotle and Lenna images, respectively; (b) & (e) ray-traced target image irradiance distributions and (c) & (f) the absolute difference between the ideal and simulated target image irradiance distributions of the freeform lenses designed for Plato and Aristotle and Lenna images, respectively.
Fig. 7.
Fig. 7. Numerical simulation of the freeform lens design with randomly generated surface profile deviation for Lenna target images case study: optical performance of the design for additional surface profile error of (a) $\pm$ 100 nm, (b) $\pm$ 250 nm and (c) $\pm$ 500 nm.
Fig. 8.
Fig. 8. The custom-designed 3D-printer for optics manufacturing.
Fig. 9.
Fig. 9. Surface measurement of 3D-printed freeform lens. (a) 3D-printed freeform lens top view; the surface profile deviation between the design and printed lens (b) top-view and (c) 3D-view; cross-section surface profile thickness at the center of printed lens in (d) horizontal-direction and (e) vertical-direction relative to the design.
Fig. 10.
Fig. 10. 3D-printed freeform lens matrix for paper web illumination. (a) 3D-printed freeform lens array, (b) layout of paper web illumination, and (c) actual illumination of the paper web.
Fig. 11.
Fig. 11. LED based 3D printed freeform lens array for paper web illumination. (a) Illumination device using 3D printed lens arrays and (b) the experimentally demonstrated target distribution.
Fig. 12.
Fig. 12. Freeform lens matrices. (a) 3D-printed freeform lenses with high UV-curing dosage and (b) silicon molded and epoxy resin casted freeform lenses.

Tables (1)

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Table 1. Design specifications of free-form lenses for rectangular and paper web uniform illumination

Equations (7)

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S ( x s , y s ) d x s d y s = T ( x t , y t ) d x t d y t ,
det ( Φ ( x s , y s ) ) T ( Φ ( x s , y s ) ) = S ( x s , y s ) ,
C ( Φ ) = Φ ( x s , y s ) ( x s , y s ) 2 S ( x s , y s ) d x s d y s .
det ( 2 Ψ ( x s , y s ) ) T ( Ψ ( x s , y s ) ) = S ( x s , y s ) .
Ψ t = log [ T ( Ψ ( x s , y s ) ) det ( 2 Ψ ( x s , y s ) ) S ( x s , y s ) ]
r ( i ) = r 0 ( i ) + λ ( i ) s ( i ) ,
L M ( λ ) = i { [ x T ( i ) x t ( i ) ] 2 + [ y T ( i ) x t ( i ) ] 2 } ,

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