Abstract

Hybrid micro-optics of infrared (IR) materials are of great advantage in realizing the function integration and minimization of advanced IR optical systems. However, due to the hard-and-brittle nature of IR materials, it is still challenging for both non-mechanical and mechanical technologies to achieve one-step generation of hybrid infrared micro-optics with high form accuracy. In the present study, a flexible method, namely ultra-precision side milling (UPSM), is first introduced to achieve one-step generation of infrared hybrid micro-optics in ductile mode, and the corresponding reflective diffraction characteristics are analyzed. In UPSM, the reflective/refractive primary surface of the hybrid micro-optics is formed via the removal of workpiece material, and the high-frequent secondary diffractive micro/nanostructures are simultaneously generated by the tool residual marks of cutting trajectories. With the consideration of the changing curvature of the primary surface, the optimal toolpath generation strategy is introduced to acquire the desired shapes of the secondary micro/nanostructures, and the selecting criteria of the machining parameters is discussed to avoid the brittle fractures of IR materials. In practice, two types of hybrid micro-optic components, namely hybrid micro-aspheric arrays and sinusoid grid surface with high-frequent secondary unidirectional phase gratings, are successfully fabricated on single-crystal silicon to validate the proposed method. The method adopted in this study is very promising for the deterministic fabrication of hybrid micro-optics on infrared materials.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2018 (5)

2017 (8)

A. R. A. Manaf, T. Sugiyama, and J. Yan, “Design and fabrication of Si-HDPE hybrid Fresnel lenses for infrared imaging systems,” Opt. Express 25(2), 1202–1220 (2017).
[Crossref] [PubMed]

Z. Li, F. Fang, J. Chen, and X. Zhang, “Machining approach of freeform optics on infrared materials via ultra-precision turning,” Opt. Express 25(3), 2051–2062 (2017).
[Crossref] [PubMed]

H. Zuo, D.-Y. Choi, X. Gai, B. Luther-Davies, and B. Zhang, “CMOS compatible fabrication of micro, nano convex silicon lens arrays by conformal chemical vapor deposition,” Opt. Express 25(4), 3069–3076 (2017).
[Crossref] [PubMed]

J. M. Ramirez, V. Vakarin, J. Frigerio, P. Chaisakul, D. Chrastina, X. Le Roux, A. Ballabio, L. Vivien, G. Isella, and D. Marris-Morini, “Ge-rich graded-index Si 1-xGex waveguides with broadband tight mode confinement and flat anomalous dispersion for nonlinear mid-infrared photonics,” Opt. Express 25(6), 6561–6567 (2017).
[Crossref] [PubMed]

Z. Dong and H. Cheng, “Ductile mode grinding of reaction-bonded silicon carbide mirrors,” Appl. Opt. 56(26), 7404–7412 (2017).
[Crossref] [PubMed]

Z. Li, F. Fang, X. Zhang, X. Liu, and H. Gao, “Highly efficient machining of non-circular freeform optics using fast tool servo assisted ultra-precision turning,” Opt. Express 25(21), 25243–25256 (2017).
[Crossref] [PubMed]

J. Zhang, J. Zhang, T. Cui, Z. Hao, and A. Al Zahrani, “Sculpturing of single crystal silicon microstructures by elliptical vibration cutting,” J. Manuf. Process. 29, 389–398 (2017).
[Crossref]

M. Mukaida and J. Yan, “Ductile machining of single-crystal silicon for microlens arrays by ultraprecision diamond turning using a slow tool servo,” Int. J. Mach. Tools Manuf. 115, 2–14 (2017).
[Crossref]

2016 (2)

J. Zhang, T. Cui, C. Ge, Y. Sui, and H. Yang, “Review of micro/nano machining by utilizing elliptical vibration cutting,” Int. J. Mach. Tools Manuf. 106, 109–126 (2016).
[Crossref]

S. Zhang, S. To, Z. Zhu, and G. Zhang, “A review of fly cutting applied to surface generation in ultra-precision machining,” Int. J. Mach. Tools Manuf. 103, 13–27 (2016).
[Crossref]

2015 (4)

S. Goel, X. Luo, A. Agrawal, and R. L. Reuben, “Diamond machining of silicon: a review of advances in molecular dynamics simulation,” Int. J. Mach. Tools Manuf. 88, 131–164 (2015).
[Crossref]

Y. Chen, “Nanofabrication by electron beam lithography and its applications: a review,” Microelectron. Eng. 135, 57–72 (2015).
[Crossref]

Z. Deng, Q. Yang, F. Chen, X. Meng, H. Bian, J. Yong, C. Shan, and X. Hou, “Fabrication of large-area concave microlens array on silicon by femtosecond laser micromachining,” Opt. Lett. 40(9), 1928–1931 (2015).
[Crossref] [PubMed]

G. Xiao, S. To, and E. Jelenković, “Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon,” J. Mater. Process. Technol. 225, 439–450 (2015).
[Crossref]

2014 (3)

T. Ando, T. Korenaga, M. A. Suzuki, and J. Tanida, “Diffraction light analysis method for a diffraction grating imaging lens,” Appl. Opt. 53(11), 2532–2538 (2014).
[Crossref] [PubMed]

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

J. Zhang, N. Suzuki, Y. Wang, and E. Shamoto, “Fundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamond,” J. Mater. Process. Technol. 214(11), 2644–2659 (2014).
[Crossref]

2013 (4)

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

2012 (2)

J. E. Harvey, N. Choi, S. Schroeder, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

M. Wang, W. Wang, and Z. Lu, “Anisotropy of machined surfaces involved in the ultra-precision turning of single-crystal silicon—a simulation and experimental study,” Int. J. Adv. Manuf. Technol. 60(5-8), 473–485 (2012).
[Crossref]

2011 (3)

D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]

R. Kleindienst, R. Kampmann, S. Stoebenau, and S. Sinzinger, “Hybrid optical (freeform) components--functionalization of nonplanar optical surfaces by direct picosecond laser ablation,” Appl. Opt. 50(19), 3221–3228 (2011).
[Crossref] [PubMed]

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

2010 (1)

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

2009 (2)

J. Kim, N. Takama, B. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

J. Yan, T. Asami, H. Harada, and T. Kuriyagawa, “Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining,” Precis. Eng. 33(4), 378–386 (2009).
[Crossref]

2006 (1)

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

2004 (1)

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11-12), 816–820 (2004).
[Crossref]

2002 (1)

C. M. Waits, A. Modafe, and R. Ghodssi, “Investigation of gray-scale technology for large area 3D silicon MEMS structures,” J. Micromech. Microeng. 13(2), 170–177 (2002).
[Crossref]

1991 (1)

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113(2), 184–189 (1991).
[Crossref]

Adie, S. G.

Agrawal, A.

S. Goel, X. Luo, A. Agrawal, and R. L. Reuben, “Diamond machining of silicon: a review of advances in molecular dynamics simulation,” Int. J. Mach. Tools Manuf. 88, 131–164 (2015).
[Crossref]

Al Zahrani, A.

J. Zhang, J. Zhang, T. Cui, Z. Hao, and A. Al Zahrani, “Sculpturing of single crystal silicon microstructures by elliptical vibration cutting,” J. Manuf. Process. 29, 389–398 (2017).
[Crossref]

Allen, Y. Y.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Ando, T.

Asami, T.

J. Yan, T. Asami, H. Harada, and T. Kuriyagawa, “Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining,” Precis. Eng. 33(4), 378–386 (2009).
[Crossref]

Ballabio, A.

Beausoleil, R. G.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Belazaras, K.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Bian, H.

Bifano, T. G.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113(2), 184–189 (1991).
[Crossref]

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Chaisakul, P.

Chen, F.

Chen, J.

Chen, Y.

Y. Chen, “Nanofabrication by electron beam lithography and its applications: a review,” Microelectron. Eng. 135, 57–72 (2015).
[Crossref]

Cheng, H.

Choi, D.-Y.

Choi, N.

J. E. Harvey, N. Choi, S. Schroeder, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Chrastina, D.

Cole, G. D.

Comley, P.

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

Cox, A.

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

Cox, R.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Cui, T.

J. Zhang, J. Zhang, T. Cui, Z. Hao, and A. Al Zahrani, “Sculpturing of single crystal silicon microstructures by elliptical vibration cutting,” J. Manuf. Process. 29, 389–398 (2017).
[Crossref]

J. Zhang, T. Cui, C. Ge, Y. Sui, and H. Yang, “Review of micro/nano machining by utilizing elliptical vibration cutting,” Int. J. Mach. Tools Manuf. 106, 109–126 (2016).
[Crossref]

Davies, M. A.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Deng, Z.

DeSimone, J. M.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Dong, Z.

Dow, T. A.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113(2), 184–189 (1991).
[Crossref]

Dummer, M. M.

Duparré, A.

J. E. Harvey, N. Choi, S. Schroeder, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Dutterer, B. S.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Eberhardt, R.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Euliss, L. E.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Evans, C.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Fang, F.

L. Zhu, Z. Li, F. Fang, S. Huang, and X. Zhang, “Review on fast tool servo machining of optical freeform surfaces,” Int. J. Adv. Manuf. Technol. 95(5-8), 2071–2092 (2018).
[Crossref]

Z. Li, F. Fang, X. Zhang, X. Liu, and H. Gao, “Highly efficient machining of non-circular freeform optics using fast tool servo assisted ultra-precision turning,” Opt. Express 25(21), 25243–25256 (2017).
[Crossref] [PubMed]

Z. Li, F. Fang, J. Chen, and X. Zhang, “Machining approach of freeform optics on infrared materials via ultra-precision turning,” Opt. Express 25(3), 2051–2062 (2017).
[Crossref] [PubMed]

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Farsari, M.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Frigerio, J.

Fujita, H.

J. Kim, N. Takama, B. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Gadonas, R.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Gai, X.

Gaidukeviciute, A.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Gao, H.

Ge, C.

J. Zhang, T. Cui, C. Ge, Y. Sui, and H. Yang, “Review of micro/nano machining by utilizing elliptical vibration cutting,” Int. J. Mach. Tools Manuf. 106, 109–126 (2016).
[Crossref]

Gebhardt, A.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Ghodssi, R.

C. M. Waits, A. Modafe, and R. Ghodssi, “Investigation of gray-scale technology for large area 3D silicon MEMS structures,” J. Micromech. Microeng. 13(2), 170–177 (2002).
[Crossref]

Gilbergs, H.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Goel, S.

S. Goel, X. Luo, A. Agrawal, and R. L. Reuben, “Diamond machining of silicon: a review of advances in molecular dynamics simulation,” Int. J. Mach. Tools Manuf. 88, 131–164 (2015).
[Crossref]

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

Gopal, A. V.

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11-12), 816–820 (2004).
[Crossref]

Hao, Z.

J. Zhang, J. Zhang, T. Cui, Z. Hao, and A. Al Zahrani, “Sculpturing of single crystal silicon microstructures by elliptical vibration cutting,” J. Manuf. Process. 29, 389–398 (2017).
[Crossref]

Harada, H.

J. Yan, T. Asami, H. Harada, and T. Kuriyagawa, “Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining,” Precis. Eng. 33(4), 378–386 (2009).
[Crossref]

Harriman, T. A.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Harvey, J. E.

J. E. Harvey, N. Choi, S. Schroeder, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Henderson, K. J.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Herzig, H.-P.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Hildebrand, D. S.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Hong, G.

D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]

Hou, X.

Huang, S.

L. Zhu, Z. Li, F. Fang, S. Huang, and X. Zhang, “Review on fast tool servo machining of optical freeform surfaces,” Int. J. Adv. Manuf. Technol. 95(5-8), 2071–2092 (2018).
[Crossref]

Isella, G.

Jelenkovic, E.

G. Xiao, S. To, and E. Jelenković, “Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon,” J. Mater. Process. Technol. 225, 439–450 (2015).
[Crossref]

Johnson, K.

Juodkazis, S.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Kampmann, R.

Kim, B.

J. Kim, N. Takama, B. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Kim, J.

J. Kim, N. Takama, B. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Kitsmiller, V. J.

Kleindienst, R.

Ko, D.-H.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Korenaga, T.

Kuriyagawa, T.

J. Yan, T. Asami, H. Harada, and T. Kuriyagawa, “Fundamental investigation of subsurface damage in single crystalline silicon caused by diamond machining,” Precis. Eng. 33(4), 378–386 (2009).
[Crossref]

Le Roux, X.

Li, L.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Li, Y.

Li, Z.

Lineberger, J. L.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Liu, D.

Liu, S.

Liu, X.

Lopez, R.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Lu, Z.

M. Wang, W. Wang, and Z. Lu, “Anisotropy of machined surfaces involved in the ultra-precision turning of single-crystal silicon—a simulation and experimental study,” Int. J. Adv. Manuf. Technol. 60(5-8), 473–485 (2012).
[Crossref]

Lucca, D. A.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Luo, X.

S. Goel, X. Luo, A. Agrawal, and R. L. Reuben, “Diamond machining of silicon: a review of advances in molecular dynamics simulation,” Int. J. Mach. Tools Manuf. 88, 131–164 (2015).
[Crossref]

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

Luther-Davies, B.

Malinauskas, M.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Manaf, A. R. A.

Marris-Morini, D.

Meng, X.

Miyashita, T.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Modafe, A.

C. M. Waits, A. Modafe, and R. Ghodssi, “Investigation of gray-scale technology for large area 3D silicon MEMS structures,” J. Micromech. Microeng. 13(2), 170–177 (2002).
[Crossref]

Momot, A.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Mukaida, M.

M. Mukaida and J. Yan, “Ductile machining of single-crystal silicon for microlens arrays by ultraprecision diamond turning using a slow tool servo,” Int. J. Mach. Tools Manuf. 115, 2–14 (2017).
[Crossref]

Mulligan, J. A.

Naessens, K.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

O’Sullivan, T. D.

Ottevaere, H.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Paipulas, D.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Pang, Y.

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Piskarskas, A.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Purlys, V.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Qu, S.

Ramirez, J. M.

Rao, P. V.

A. V. Gopal and P. V. Rao, “A new chip-thickness model for performance assessment of silicon carbide grinding,” Int. J. Adv. Manuf. Technol. 24(11-12), 816–820 (2004).
[Crossref]

Reuben, R. L.

S. Goel, X. Luo, A. Agrawal, and R. L. Reuben, “Diamond machining of silicon: a review of advances in molecular dynamics simulation,” Int. J. Mach. Tools Manuf. 88, 131–164 (2015).
[Crossref]

S. Goel, X. Luo, P. Comley, R. L. Reuben, and A. Cox, “Brittle–ductile transition during diamond turning of single crystal silicon carbide,” Int. J. Mach. Tools Manuf. 65, 15–21 (2013).
[Crossref]

Risse, S.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Sakellari, I.

M. Malinauskas, A. Žukauskas, V. Purlys, K. Belazaras, A. Momot, D. Paipulas, R. Gadonas, A. Piskarskas, H. Gilbergs, A. Gaidukevičiūtė, I. Sakellari, M. Farsari, and S. Juodkazis, “Femtosecond laser polymerization of hybrid/integrated micro-optical elements and their characterization,” J. Opt. 12(12), 124010 (2010).
[Crossref]

Samulski, E. T.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Scattergood, R. O.

T. G. Bifano, T. A. Dow, and R. O. Scattergood, “Ductile-regime grinding: a new technology for machining brittle materials,” J. Eng. Ind. 113(2), 184–189 (1991).
[Crossref]

Scheiding, S.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Schroeder, S.

J. E. Harvey, N. Choi, S. Schroeder, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012).
[Crossref]

Shamoto, E.

J. Zhang, N. Suzuki, Y. Wang, and E. Shamoto, “Fundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamond,” J. Mater. Process. Technol. 214(11), 2644–2659 (2014).
[Crossref]

Shan, C.

Sinzinger, S.

Smilie, P. J.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Stoebenau, S.

Sugiyama, T.

Sui, Y.

J. Zhang, T. Cui, C. Ge, Y. Sui, and H. Yang, “Review of micro/nano machining by utilizing elliptical vibration cutting,” Int. J. Mach. Tools Manuf. 106, 109–126 (2016).
[Crossref]

Suleski, T. J.

B. S. Dutterer, J. L. Lineberger, P. J. Smilie, D. S. Hildebrand, T. A. Harriman, M. A. Davies, T. J. Suleski, and D. A. Lucca, “Diamond milling of an Alvarez lens in germanium,” Precis. Eng. 38(2), 398–408 (2014).
[Crossref]

Sun, Z.

Z. Sun, S. To, and S. Zhang, “A novel ductile machining model of single-crystal silicon for freeform surfaces with large azimuthal height variation by ultra-precision fly cutting,” Int. J. Mach. Tools Manuf. 135, 1–11 (2018).
[Crossref]

Suzuki, M. A.

Suzuki, N.

J. Zhang, N. Suzuki, Y. Wang, and E. Shamoto, “Fundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamond,” J. Mater. Process. Technol. 214(11), 2644–2659 (2014).
[Crossref]

Taghizadeh, M.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Takama, N.

J. Kim, N. Takama, B. Kim, and H. Fujita, “Optical-softlithographic technology for patterning on curved surfaces,” J. Micromech. Microeng. 19(5), 055017 (2009).
[Crossref]

Tanida, J.

Thienpont, H.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

To, S.

Z. Sun, S. To, and S. Zhang, “A novel ductile machining model of single-crystal silicon for freeform surfaces with large azimuthal height variation by ultra-precision fly cutting,” Int. J. Mach. Tools Manuf. 135, 1–11 (2018).
[Crossref]

S. Zhang, S. To, Z. Zhu, and G. Zhang, “A review of fly cutting applied to surface generation in ultra-precision machining,” Int. J. Mach. Tools Manuf. 103, 13–27 (2016).
[Crossref]

G. Xiao, S. To, and E. Jelenković, “Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon,” J. Mater. Process. Technol. 225, 439–450 (2015).
[Crossref]

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Tumbleston, J. R.

D.-H. Ko, J. R. Tumbleston, K. J. Henderson, L. E. Euliss, J. M. DeSimone, R. Lopez, and E. T. Samulski, “Biomimetic microlens array with antireflective “moth-eye” surface,” Soft Matter 7(14), 6404–6407 (2011).
[Crossref]

Tünnermann, A.

H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
[Crossref]

Vakarin, V.

Vivien, L.

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Völkel, R.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Waits, C. M.

C. M. Waits, A. Modafe, and R. Ghodssi, “Investigation of gray-scale technology for large area 3D silicon MEMS structures,” J. Micromech. Microeng. 13(2), 170–177 (2002).
[Crossref]

Wang, J.

Wang, M.

M. Wang, W. Wang, and Z. Lu, “Anisotropy of machined surfaces involved in the ultra-precision turning of single-crystal silicon—a simulation and experimental study,” Int. J. Adv. Manuf. Technol. 60(5-8), 473–485 (2012).
[Crossref]

Wang, W.

M. Wang, W. Wang, and Z. Lu, “Anisotropy of machined surfaces involved in the ultra-precision turning of single-crystal silicon—a simulation and experimental study,” Int. J. Adv. Manuf. Technol. 60(5-8), 473–485 (2012).
[Crossref]

Wang, Y.

J. Zhang, N. Suzuki, Y. Wang, and E. Shamoto, “Fundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamond,” J. Mater. Process. Technol. 214(11), 2644–2659 (2014).
[Crossref]

Weckenmann, A.

F. Fang, X. Zhang, A. Weckenmann, G. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62(2), 823–846 (2013).
[Crossref]

Wong, Y.

D. Yu, Y. Wong, and G. Hong, “Ultraprecision machining of micro-structured functional surfaces on brittle materials,” J. Micromech. Microeng. 21(9), 095011 (2011).
[Crossref]

Woo, H.

H. Ottevaere, R. Cox, H.-P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Xiao, G.

G. Xiao, S. To, and E. Jelenković, “Effects of non-amorphizing hydrogen ion implantation on anisotropy in micro cutting of silicon,” J. Mater. Process. Technol. 225, 439–450 (2015).
[Crossref]

Xu, Z.

Yan, J.

A. R. A. Manaf, T. Sugiyama, and J. Yan, “Design and fabrication of Si-HDPE hybrid Fresnel lenses for infrared imaging systems,” Opt. Express 25(2), 1202–1220 (2017).
[Crossref] [PubMed]

M. Mukaida and J. Yan, “Ductile machining of single-crystal silicon for microlens arrays by ultraprecision diamond turning using a slow tool servo,” Int. J. Mach. Tools Manuf. 115, 2–14 (2017).
[Crossref]

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S. Zhang, S. To, Z. Zhu, and G. Zhang, “A review of fly cutting applied to surface generation in ultra-precision machining,” Int. J. Mach. Tools Manuf. 103, 13–27 (2016).
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Z. Sun, S. To, and S. Zhang, “A novel ductile machining model of single-crystal silicon for freeform surfaces with large azimuthal height variation by ultra-precision fly cutting,” Int. J. Mach. Tools Manuf. 135, 1–11 (2018).
[Crossref]

M. Mukaida and J. Yan, “Ductile machining of single-crystal silicon for microlens arrays by ultraprecision diamond turning using a slow tool servo,” Int. J. Mach. Tools Manuf. 115, 2–14 (2017).
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H. Zhang, L. Li, S. Scheiding, A. Gebhardt, S. Risse, R. Eberhardt, A. Tünnermann, D. Yao, and Y. Y. Allen, “Fabrication of three-dimensional functional microstructures on curved substrates using three-dimensional microlens projection,” J. Micro Nano-Manuf. 1(3), 031006 (2013).
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Figures (15)

Fig. 1
Fig. 1 Schematic of the machining approach for hybrid surfaces with secondary micro/nanostructures.
Fig. 2
Fig. 2 Strategy of UPSM for hybrid micro-optics.
Fig. 3
Fig. 3 Geometrical relation between the diamond tool and the workpiece surface.
Fig. 4
Fig. 4 Geometrical relation between the residual tool height and the step distance.
Fig. 5
Fig. 5 Schematic of UPSM viewed along the y direction.
Fig. 6
Fig. 6 Cross-sectional profile of the taper groove in <100> direction.
Fig. 7
Fig. 7 Schematic of (a) the toolpath and (b) the SCPs in x-y plane.
Fig. 8
Fig. 8 Picture of the milling system.
Fig. 9
Fig. 9 Characteristics of the machined hybrid micro-aspheric arrays, (a) a large area view, (b) for an individual structure and (c) cross-sectional profile.
Fig. 10
Fig. 10 3D topographies of (a) generated hierarchical micro-aspheric surface, (b) the filter primary aspheric surface, (c) the extracted secondary nano-grooves and (d) 2D profile in cross-sectional direction after removing the primary profile.
Fig. 11
Fig. 11 Micro-topography of the generated surface.
Fig. 12
Fig. 12 (a) 3D topography of the generated hybrid sinusoid freeform surface and its cross-sectional profiles in (b) feed direction and (c) raster direction.
Fig. 13
Fig. 13 Microscope image of the generated sinusoid freeform surface in a small zone.
Fig. 14
Fig. 14 2D profiles in cross-sectional direction after removing the primary profile by (a) ordinary algorithm and (b) optimized algorithm.
Fig. 15
Fig. 15 Reflective diffraction characteristics of the hybrid sinusoid freeform surface.

Tables (2)

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Table 1 Structure parameters used for the primary micro-aspheric surface.

Tables Icon

Table 2 Machining parameters used for the hybrid micro-aspheric and sinusoid surfaces.

Equations (11)

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{ x c (m,n) = n N s L y c (m,n) =m S r z c (m,n) =F( x c (m,n) , y c (m,n) )
{ x t (m,n) = x c (m,n) +Rsin θ (m,n) y t (m,n) = y c (m,n) +Rcos θ (m,n) sin φ (m,n) z t (m,n) = z c (m,n) +Rcos θ (m,n) cos φ (m,n)
{ α (m,n) =arctan F( x c (m,n) , y c (m,n) ) x c (m,n) θ (m,n) =arctan F( x c (m,n) , y c (m,n) ) y c (m,n) φ (m,n) =arctan(cos θ (m,n) tan α (m,n) )
{ x s (m,n) = x c (m,n) +Rsin θ (m,n) +( S w R)sin α (m,n) y s (m,n) = y c (m,n) +Rcos θ (m,n) sin φ (m,n) z s (m,n) = z c (m,n) +Rcos θ (m,n) cos φ (m,n) +( S w R)cos α (m,n)
S w <min[| (1+ ( F x ) 2 ) 3 2 2 F x 2 |]
S r (m,n) =2cos[| arctan( F y ) |]× h(2Rh)
{ x b = f e + S w 2 y b 2 y b = F x × x b + S w d 0 cos(| arctan( F x ) |)
h max = S w ( x b 2 + y b 2 )
z(x,y)= sC R 0 2 4+4 1(1+k) C 2 R 0 2 sC ρ 2 (x,y) 4+4 1(1+k) C 2 ρ 2 (x,y)
z(x,y)= A x sin(2π f x x)+ A y sin(2π f y y)
TIS ( 4πδ λ ) 2

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