Cylindrical coordinate machining of optical
freeform surfaces

doi:10.1364/OE.16.007323

Cylindrical coordinate machining of optical freeform surfaces

F. Z. Fang, X. D. Zhang, and X. T. Hu »View Author Affiliations

Optics Express, Vol. 16, Issue 10, pp. 7323-7329 (2008)
http://dx.doi.org/10.1364/OE.16.007323

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Abstract
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References (12)
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Abstract

The cylindrical coordinate machining method (CCM) is systematically studied in generating optical freeform surfaces, in which the feature points are fitted to typical Non-Uniform Rational B-Splines (NURBS). The given points have the mapping coordinates in the variable space using the point inversion technique, while the other points have their NURBS coordinates due to the interpolation technique. The derivation and mathematical features are obtained using the fitting formula. The compensation and optimized values for tool geometry are studied using a proposed sectional curve method for fabricating designed surfaces. Typical freeform surfaces fabricated by the CCM method are presented.

OCIS Codes
(220.1250) Optical design and fabrication : Aspherics
(220.1920) Optical design and fabrication : Diamond machining

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: February 14, 2008
Revised Manuscript: April 8, 2008
Manuscript Accepted: May 3, 2008
Published: May 6, 2008

Citation
F. Z. Fang, X. D. Zhang, and X. T. Hu, "Cylindrical coordinate machining of optical freeform surfaces," Opt. Express 16, 7323-7329 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7323

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References

X. Jiang, P. Scott, and D. Whitehouse, "Freeform surface characterisation - A fresh strategy," Ann. CIRP 56, 553-556 (2007). [CrossRef]
H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, "Dimensional micro and nano metrology," Ann. CIRP 55, 721-743 (2006). [CrossRef]
L. De Chiffre, H. Kunzmann, G. N. Peggs, and D. A. Lucca, "Surfaces in precision engineering, microengineering and nanotechnology," Ann. CIRP 52, 561-578 (2003). [CrossRef]
Y. Takeuchia, S. Maedaa, T. Kawaib, K. Sawadab, "Manufacture of multiple-focus micro Fresnel lenses by means of nonrotational diamond grooving," Ann. CIRP 51, 343-346 (2002). [CrossRef]
C. C. Chen, C. M. Chen, and J. R. Chen, "Toolpath generation of diamond shaping of aspheric lens array," J. Mater. Proc. Technol. 192-193, 194-199 (2007). [CrossRef]
H. B. Wu, Z. Q. Wang, R. L. Fu, and J. Liu, "Design of a hybrid diffractive/refractive achromatized telecentric f-θ lens," Optik 117, 271-276 (2006). [CrossRef]
L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, "Designing reflectors to generate a line-shaped directivity diagram," J. Mod. Opt. 52, 1529-1536 (2005). [CrossRef]
C. F. Cheung, L. B. Kong, and W. B. Lee, "Modelling and simulation of freeform surface generation in ultra-precision raster milling," J. Eng. Manuf. 220, 1787-1801 (2006). [CrossRef]
L. Piegl and W. Tiller, "The NURBS Book," (New York: Springer-Verlag, 1997).
Q8. W. Ma, J. P. Kruth, "NURBS curve and surface fitting for reverse engineering," J. Adv. Manuf. Technol. 14, 918-927 (2005). [CrossRef]
Y. L. Ma, W. T. Hewitt, "Point inversion and projection for NURBS curve and surface: control polygon approach," Comput. Aided Geom. Des. 20, 79-99 (2003). [CrossRef]
K. H. Jeong, J. Kim, L. P. Lee, "Biological inspired artificial compound eyes," Science 312, 557-561 (2006). [CrossRef] [PubMed]

Bernard, S.
Carneiro, K.
Chen, C. C.
Chen, C. M.
Chen, J. R.
Cheung, C. F.
De Chiffre, L.
Doskolovich, L. L.
Fu, R. L.
Haitjema, H.
Hansen, H. N.
Hewitt, W. T.
Jeong, K. H.
Jiang, X.
Kawaib, T.
Kazanskiy, N. L.
Kharitonov, S. I.
Kim, J.
Kong, L. B.
Kruth, J. P.
Kunzmann, H.
Lee, L. P.
Lee, W. B.
Liu, J.
Lucca, D. A.
Ma, W.
Ma, Y. L.
Maedaa, S.
Peggs, G. N.
Perlo, P.
Sawadab, K.
Scott, P.
Takeuchia, Y.
Wang, Z. Q.
Whitehouse, D.
Wu, H. B.

Ann. CIRP

X. Jiang, P. Scott, and D. Whitehouse, "Freeform surface characterisation - A fresh strategy," Ann. CIRP 56, 553-556 (2007). [CrossRef]
H. N. Hansen, K. Carneiro, H. Haitjema, and L. De Chiffre, "Dimensional micro and nano metrology," Ann. CIRP 55, 721-743 (2006). [CrossRef]
L. De Chiffre, H. Kunzmann, G. N. Peggs, and D. A. Lucca, "Surfaces in precision engineering, microengineering and nanotechnology," Ann. CIRP 52, 561-578 (2003). [CrossRef]
Y. Takeuchia, S. Maedaa, T. Kawaib, K. Sawadab, "Manufacture of multiple-focus micro Fresnel lenses by means of nonrotational diamond grooving," Ann. CIRP 51, 343-346 (2002). [CrossRef]

Comput. Aided Geom. Des.

Y. L. Ma, W. T. Hewitt, "Point inversion and projection for NURBS curve and surface: control polygon approach," Comput. Aided Geom. Des. 20, 79-99 (2003). [CrossRef]

J. Adv. Manuf. Technol.

Q8. W. Ma, J. P. Kruth, "NURBS curve and surface fitting for reverse engineering," J. Adv. Manuf. Technol. 14, 918-927 (2005). [CrossRef]

J. Eng. Manuf.

C. F. Cheung, L. B. Kong, and W. B. Lee, "Modelling and simulation of freeform surface generation in ultra-precision raster milling," J. Eng. Manuf. 220, 1787-1801 (2006). [CrossRef]

J. Mater. Proc. Technol.

C. C. Chen, C. M. Chen, and J. R. Chen, "Toolpath generation of diamond shaping of aspheric lens array," J. Mater. Proc. Technol. 192-193, 194-199 (2007). [CrossRef]

J. Mod. Opt.

L. L. Doskolovich, N. L. Kazanskiy, S. I. Kharitonov, P. Perlo, and S. Bernard, "Designing reflectors to generate a line-shaped directivity diagram," J. Mod. Opt. 52, 1529-1536 (2005). [CrossRef]

Optik

H. B. Wu, Z. Q. Wang, R. L. Fu, and J. Liu, "Design of a hybrid diffractive/refractive achromatized telecentric f-θ lens," Optik 117, 271-276 (2006). [CrossRef]

Science

K. H. Jeong, J. Kim, L. P. Lee, "Biological inspired artificial compound eyes," Science 312, 557-561 (2006). [CrossRef] [PubMed]

Other

L. Piegl and W. Tiller, "The NURBS Book," (New York: Springer-Verlag, 1997).

2007, Jiang, Ann. CIRP
2007, Chen, J. Mater. Proc. Technol.
2006, Wu, Optik
2006, Cheung, J. Eng. Manuf.
2006, Hansen, Ann. CIRP
2006, Jeong, Science
2005, Ma, J. Adv. Manuf. Technol.
2005, Doskolovich, J. Mod. Opt.
2003, Ma, Comput. Aided Geom. Des.
2003, De Chiffre, Ann. CIRP
2002, Takeuchia, Ann. CIRP

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