Abstract

Freeform optics has been regarded as the next generation of the optical components, especially those with non-circular apertures are playing an increasingly significant role in scanning field and specialized optical system. However, there still exist challenges to machine non-circular optical freeform surface. This paper is focused on highly efficiently generating freeform surfaces with optical surface quality by ultra-precision turning using a fast tool servo (FTS). A systematic strategy of machining smooth freeform surfaces with rectangular aperture is proposed in this paper. The contour of freeform optics is decomposed and assigned to the motions of slide and FTS back-and-forth. An optimized model is established for deriving the profile of the rotational component to cater for the capacity of FTS. Tool path reconstruction is carried out to generate a smooth tool trajectory and modified the contour to cater for the stroke of FTS. Simulation is adopted to analyze the machining property of a typical rectangular freeform surface. A rectangular freeform surface is efficiently machined via the proposed method, where a micron level profile error and nanometric finish in Ra are realized. Characteristics of reflection are analyzed via experiment and simulation. Prospects of such machining approach are discussed to provide guidance to future study.

© 2017 Optical Society of America

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2017 (2)

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

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

2015 (4)

F. Tian, Z. Yin, and S. Li, “Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors,” Int. J. Adv. Manuf. Technol. 80(9), 1759–1765 (2015).

Z. Zhu, S. To, and S. Zhang, “Active control of residual tool marks for freeform optics functionalization by novel biaxial servo assisted fly cutting,” Appl. Opt. 54(25), 7656–7662 (2015).
[PubMed]

Y. Wen and H. Cheng, “Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications,” Opt. Eng. 54(1), 014103 (2015).

Z. Zhu, S. To, and S. Zhang, “Large-scale fabrication of micro-lens array by novel end-fly-cutting-servo diamond machining,” Opt. Express 23(16), 20593–20604 (2015).
[PubMed]

2014 (4)

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).

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
[PubMed]

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” P. I. Mech. Eng. B-J. Eng. 228(12), 1721–1726 (2014).

2013 (3)

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

F. Duerr, Y. Meuret, and H. Thienpont, “Potential benefits of free-form optics in on-axis imaging applications with high aspect ratio,” Opt. Express 21(25), 31072–31081 (2013).
[PubMed]

2012 (4)

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

K. P. Thompson and J. P. Rolland, “Freeform Optical Surfaces: A Revolution in Imaging Optical Design,” Opt. Photonics News 23(6), 30–35 (2012).

L. Kong and C. Cheung, “Modeling and characterization of surface generation in fast tool servo machining of microlens arrays,” Comput. Ind. Eng. 63(4), 957–970 (2012).

D. P. Yu, G. S. Hong, and Y. San Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).

2011 (2)

2010 (1)

2009 (3)

D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009).
[PubMed]

L. Kong, C. Cheung, S. To, and W. Lee, “An investigation into surface generation in ultra-precision raster milling,” J. Mater. Process. Technol. 209(8), 4178–4185 (2009).

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

2008 (1)

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

2003 (1)

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

1999 (1)

C. J. Evans and J. B. Bryan, ““Structured”,“textured” or “engineered” surfaces,” Cirp. Ann-Manuf. Techn. 48(2), 541–556 (1999).

1997 (1)

M. S. Karpman and B. A. Wells, “Virtual displays for entertainment applications: hitting cost/performance with LED arrays,” Proc. SPIE 3000, 161–168 (1997).

1991 (1)

T. A. Dow, M. H. Miller, and P. J. Falter, “Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces,” Precis. Eng. 13(4), 243–250 (1991).

Ahn, J.-H.

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

Araki, T.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

Bryan, J. B.

C. J. Evans and J. B. Bryan, ““Structured”,“textured” or “engineered” surfaces,” Cirp. Ann-Manuf. Techn. 48(2), 541–556 (1999).

Chen, H.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Chen, J.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Chen, J. J.

Chen, S.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Chen, S. J.

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

Cheng, D.

Cheng, H.

Y. Wen and H. Cheng, “Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications,” Opt. Eng. 54(1), 014103 (2015).

Cheung, C.

L. Kong and C. Cheung, “Modeling and characterization of surface generation in fast tool servo machining of microlens arrays,” Comput. Ind. Eng. 63(4), 957–970 (2012).

L. Kong, C. Cheung, S. To, and W. Lee, “An investigation into surface generation in ultra-precision raster milling,” J. Mater. Process. Technol. 209(8), 4178–4185 (2009).

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).

Dow, T. A.

T. A. Dow, M. H. Miller, and P. J. Falter, “Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces,” Precis. Eng. 13(4), 243–250 (1991).

Duerr, F.

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).

Eberhardt, R.

Evans, C. J.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

C. J. Evans and J. B. Bryan, ““Structured”,“textured” or “engineered” surfaces,” Cirp. Ann-Manuf. Techn. 48(2), 541–556 (1999).

Falter, P. J.

T. A. Dow, M. H. Miller, and P. J. Falter, “Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces,” Precis. Eng. 13(4), 243–250 (1991).

Fang, F. Z.

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

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

Feng, H.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Gao, H. M.

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

Gao, W.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

Gebhardt, A.

Guo, Y. W.

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

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).

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).

Hong, G. S.

D. P. Yu, G. S. Hong, and Y. San Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).

Hou, W.

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
[PubMed]

Hua, H.

Jianjun, Y.

J. Yiqun, S. Weimin, and Y. Jianjun, “Design of F-τheta Lenses Used in Laser Marking Machines,” in International Optical Design Conference, (Optical Society of America, 2006), ME21.

Jin, G.

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
[PubMed]

Karpman, M. S.

M. S. Karpman and B. A. Wells, “Virtual displays for entertainment applications: hitting cost/performance with LED arrays,” Proc. SPIE 3000, 161–168 (1997).

Kim, H.-J.

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

Kim, J.-H.

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

Kim, S.-S.

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

Kiyono, S.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

Kong, L.

L. Kong and C. Cheung, “Modeling and characterization of surface generation in fast tool servo machining of microlens arrays,” Comput. Ind. Eng. 63(4), 957–970 (2012).

L. Kong, C. Cheung, S. To, and W. Lee, “An investigation into surface generation in ultra-precision raster milling,” J. Mater. Process. Technol. 209(8), 4178–4185 (2009).

Kuhn, M.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011).

Lee, D.-K.

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

Lee, W.

L. Kong, C. Cheung, S. To, and W. Lee, “An investigation into surface generation in ultra-precision raster milling,” J. Mater. Process. Technol. 209(8), 4178–4185 (2009).

Li, L.

Li, S.

F. Tian, Z. Yin, and S. Li, “Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors,” Int. J. Adv. Manuf. Technol. 80(9), 1759–1765 (2015).

Li, Y.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Li, Z. X.

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).

Liu, Q.

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” P. I. Mech. Eng. B-J. Eng. 228(12), 1721–1726 (2014).

Liu, X. L.

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

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).

Meuret, Y.

Miller, M. H.

T. A. Dow, M. H. Miller, and P. J. Falter, “Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces,” Precis. Eng. 13(4), 243–250 (1991).

Okazaki, Y.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

Risse, S.

Rolland, J. P.

K. P. Thompson and J. P. Rolland, “Freeform Optical Surfaces: A Revolution in Imaging Optical Design,” Opt. Photonics News 23(6), 30–35 (2012).

San Wong, Y.

D. P. Yu, G. S. Hong, and Y. San Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).

Scheiding, 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).

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).

Talha, M. M.

Thienpont, H.

Thompson, K. P.

K. P. Thompson and J. P. Rolland, “Freeform Optical Surfaces: A Revolution in Imaging Optical Design,” Opt. Photonics News 23(6), 30–35 (2012).

Tian, F.

F. Tian, Z. Yin, and S. Li, “Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors,” Int. J. Adv. Manuf. Technol. 80(9), 1759–1765 (2015).

To, S.

Tünnermann, A.

Wang, Y.

Weckenmann, A.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

Weimin, S.

J. Yiqun, S. Weimin, and Y. Jianjun, “Design of F-τheta Lenses Used in Laser Marking Machines,” in International Optical Design Conference, (Optical Society of America, 2006), ME21.

Wells, B. A.

M. S. Karpman and B. A. Wells, “Virtual displays for entertainment applications: hitting cost/performance with LED arrays,” Proc. SPIE 3000, 161–168 (1997).

Wen, Y.

Y. Wen and H. Cheng, “Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications,” Opt. Eng. 54(1), 014103 (2015).

Wu, Q. Q.

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

Wyrowski, F.

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011).

Xia, R.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Xu, P.

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” P. I. Mech. Eng. B-J. Eng. 228(12), 1721–1726 (2014).

Yamanaka, M.

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

Yang, T.

Yang, Y. H.

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

Yang, Y.-S.

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

Yi, A. Y.

Yin, Z.

F. Tian, Z. Yin, and S. Li, “Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors,” Int. J. Adv. Manuf. Technol. 80(9), 1759–1765 (2015).

Yiqun, J.

J. Yiqun, S. Weimin, and Y. Jianjun, “Design of F-τheta Lenses Used in Laser Marking Machines,” in International Optical Design Conference, (Optical Society of America, 2006), ME21.

Yu, D. P.

D. P. Yu, G. S. Hong, and Y. San Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).

Yuan, Y.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Zhang, G. X.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

Zhang, H. J.

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

Zhang, S.

Zhang, X. D.

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

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

Zhou, M.

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

Zhou, X.

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” P. I. Mech. Eng. B-J. Eng. 228(12), 1721–1726 (2014).

Zhu, D.

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

Zhu, J.

T. Yang, J. Zhu, W. Hou, and G. Jin, “Design method of freeform off-axis reflective imaging systems with a direct construction process,” Opt. Express 22(8), 9193–9205 (2014).
[PubMed]

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

Zhu, Z.

Appl. Opt. (2)

Cirp. Ann-manuf. Techn. (1)

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. J. Evans, “Manufacturing and measurement of freeform optics,” Cirp. Ann-manuf. Techn. 62(2), 823–846 (2013).

C. J. Evans and J. B. Bryan, ““Structured”,“textured” or “engineered” surfaces,” Cirp. Ann-Manuf. Techn. 48(2), 541–556 (1999).

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” Cirp. Ann-Manuf. Techn. 61(1), 519–522 (2012).

Comput. Ind. Eng. (1)

L. Kong and C. Cheung, “Modeling and characterization of surface generation in fast tool servo machining of microlens arrays,” Comput. Ind. Eng. 63(4), 957–970 (2012).

Int. J. Adv. Manuf. Technol. (3)

H. Feng, R. Xia, Y. Li, J. Chen, Y. Yuan, D. Zhu, S. Chen, and H. Chen, “Fabrication of freeform progressive addition lenses using a self-developed long stroke fast tool servo,” Int. J. Adv. Manuf. Technol. 91(9), 3799–3806 (2017).

F. Tian, Z. Yin, and S. Li, “Fast tool servo diamond turning of optical freeform surfaces for rear-view mirrors,” Int. J. Adv. Manuf. Technol. 80(9), 1759–1765 (2015).

X. D. Zhang, F. Z. Fang, Q. Q. Wu, X. L. Liu, and H. M. Gao, “Coordinate transformation machining of off-axis aspheric mirrors,” Int. J. Adv. Manuf. Technol. 67, 2217 (2013).

Int. J. Mach. Tools Manuf. (1)

D. P. Yu, G. S. Hong, and Y. San Wong, “Profile error compensation in fast tool servo diamond turning of micro-structured surfaces,” Int. J. Mach. Tools Manuf. 52(1), 13–23 (2012).

J. Korean Phys. Soc. (1)

D.-K. Lee, Y.-S. Yang, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Development of a F-theta Lens for a Laser Scanning Unit,” J. Korean Phys. Soc. 53(5), 2527–2530 (2008).

J. Mater. Process. Technol. (1)

L. Kong, C. Cheung, S. To, and W. Lee, “An investigation into surface generation in ultra-precision raster milling,” J. Mater. Process. Technol. 209(8), 4178–4185 (2009).

J. Mod. Opt. (1)

F. Wyrowski and M. Kuhn, “Introduction to field tracing,” J. Mod. Opt. 58(5–6), 449–466 (2011).

J. Opt. (1)

J. Zhu, W. Hou, X. D. Zhang, and G. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17(1), 015605 (2014).

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (1)

H. J. Zhang, S. J. Chen, M. Zhou, and Y. H. Yang, “Fast tool servo control for diamond-cutting microstructured optical components,” J. Vac. Sci. Technol. B 27(3), 1226–1229 (2009).

Opt. Eng. (1)

Y. Wen and H. Cheng, “Measurement for off-axis aspheric mirror using off-axis annular subaperture stitching interferometry: theory and applications,” Opt. Eng. 54(1), 014103 (2015).

Opt. Express (5)

Opt. Photonics News (1)

K. P. Thompson and J. P. Rolland, “Freeform Optical Surfaces: A Revolution in Imaging Optical Design,” Opt. Photonics News 23(6), 30–35 (2012).

P. I. Mech. Eng. B-J. Eng. (1)

Q. Liu, X. Zhou, and P. Xu, “A new tool path for optical freeform surface fast tool servo diamond turning,” P. I. Mech. Eng. B-J. Eng. 228(12), 1721–1726 (2014).

Precis. Eng. (3)

W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precis. Eng. 27(3), 289–298 (2003).

T. A. Dow, M. H. Miller, and P. J. Falter, “Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces,” Precis. Eng. 13(4), 243–250 (1991).

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).

Proc. SPIE (1)

M. S. Karpman and B. A. Wells, “Virtual displays for entertainment applications: hitting cost/performance with LED arrays,” Proc. SPIE 3000, 161–168 (1997).

Other (5)

D.-K. Lee, J.-H. Ahn, S.-S. Kim, H.-J. Kim, and J.-H. Kim, “Optical performance of F-Theta lens for laser scanning Unit,” in International Symposium on Optomechatronic Technologies, (International Society for Optics and Photonics, 2007), 67170E.

V. Yurevich, V. Grimm, A. Afonyushkin, K. Yudin, and S. Gorny, “Optical design and performance of F-Theta lenses for high-power and high-precision applications,” in SPIE Optical Systems Design, (International Society for Optics and Photonics, 2015), 96261S–96216.

J. Yiqun, S. Weimin, and Y. Jianjun, “Design of F-τheta Lenses Used in Laser Marking Machines,” in International Optical Design Conference, (Optical Society of America, 2006), ME21.

S. To, T. C. Kwok, C. F. Cheung, and W. B. Lee, “Study of ultra-precision diamond turning of a microlens array with a fast tool servo system.” in 2nd international Symposium on Advanced Optical Manufacturing and Testing Technologies (International Society for Optics and Photonics, 2006), 61490S–61496.

X. H. Wang, Z. Ding, and Y. Z. Ma, “Turning of Micro-Structured Surfaces Based on a Fast Tool Servo System,” in Applied Mechanics and Materials, (Trans Tech Publ, 2014), 308–312.

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Figures (12)

Fig. 1
Fig. 1 Flowchart of FTS-assisted diamond turning non-circular freeform surface.
Fig. 2
Fig. 2 (a) Original surface with rectangular aperture, (b) extended surface in circular aperture with the generatrix of rotational component, (c) rotational surface and (d) NRS zooming on x-y plane.
Fig. 3
Fig. 3 Variation of surface contour before and after Hermite interpolation.
Fig. 4
Fig. 4 Illustration of sampled data on an NRS.
Fig. 5
Fig. 5 (a) The extended original surface, (b) NRD and (c) variation of the objective function.
Fig. 6
Fig. 6 (a) Original NRS and (b) NRS after Hermite interpolation.
Fig. 7
Fig. 7 Amplitude-frequency characteristics of the NRS before and after delivered.
Fig. 8
Fig. 8 Illustration of FTS-assisted diamond turning F-theta lens.
Fig. 9
Fig. 9 (a) Surface topography measured by optical tracking profiler and (b) central profile and the profile error.
Fig. 10
Fig. 10 Surface roughness at different areas, where Area (a) and (e) are at the edge of the aperture, Area (b) and (d) are at the middle field, and Area (c) is at the center.
Fig. 11
Fig. 11 Reflection characteristics of machined surface: (a) Reflection behaviors include diffraction ring and image of tool mark when lighting at the center and (b) Tool mark-induced high order diffraction with high order diffraction spot spreading along circumferential direction when lighting at the edge.
Fig. 12
Fig. 12 Simulation of the tool mark-induced diffraction effect at different machining parameters: The coordinate units on axes are millimeter and the color bar represents the normalized intensity.

Tables (3)

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Table 1 Impact level of preparing process.

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Table 2 Surface parameters.

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Table 3 Machining parameters.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

z r ( r ) = z ( r cos θ , r sin θ ) ,
z r = z ( r cos θ , r sin θ ) = z ( r , θ ) .
min S ( θ ) = w 1 ( z n max z n min ) 2 + w 2 ( z n max + z n min ) 2 subject to: z n ( r , φ ) = z ( r , φ ) z r ( r ) z ( r , φ ) = f ( r cos φ , r sin φ ) z r ( r ) = f ( r cos θ , r sin θ ) , ( r , φ ) Ω θ [ 0 , 2 π )
H 2 n + 1 ( ξ ) = i = 0 m j = 0 n φ i j ( ξ ) z j ( i ) ,
H 2 n + 1 ( ξ ) = j = 0 n α j ( ξ ) z j + j = 0 n β j ( ξ ) z j ( 1 ) ,
{ r = R f t φ = 2 π S t z n = z n ( R f t , 2 π S t ) = z n ( t ) .

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