Abstract

Snell’s law describes the relationship between the incidence angle and reflection (or refraction) angle of a light ray impinging on the interface between two different isotropic media. In this paper, Snell’s law is used to derive the unit normal vectors of an aspherical surface given a knowledge of the unit directional vectors of the incoming and outgoing rays. The proposed method has important applications in the design and fabrication of aspherical surfaces since the surface normal vectors determine not only the optical performance of the surface but also the cutting tool angles required to machine the surfaces.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2007 (1)

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

2006 (1)

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

2002 (1)

1979 (2)

1976 (1)

H. Howden and J. A. Clarke, “Refracting replica aspheric optics,” Opt. Eng. 15, 197–201 (1976).

1965 (1)

1957 (1)

Awatsuji, Y.

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

Babolat, C.

Biddut, A. Q.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Boothroyd, G.

G. Boothroyd, Fundamentals of Metal Machining and Machine Tools (McGraw-Hill, 1975), Chap. 7.

Braat, J. J. M.

Burge, J. H.

Clarke, J. A.

H. Howden and J. A. Clarke, “Refracting replica aspheric optics,” Opt. Eng. 15, 197–201 (1976).

Frieden, B. R.

Greve, P. F.

Haisma, J.

Howden, H.

H. Howden and J. A. Clarke, “Refracting replica aspheric optics,” Opt. Eng. 15, 197–201 (1976).

Hugues, E.

Kawano, N.

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

Kubota, T.

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

Maeda, Y.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Neo, K. S.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Paul, R. P.

R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control (MIT, 1982).

Rahman, M.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Rezaur, K. M.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Sawa, M.

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

Takaoka, T.

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

Vaskas, E. M.

Zhao, C.

Appl. Opt. (3)

Int. J. Adv. Manuf. Technol. (1)

A. Q. Biddut, M. Rahman, K. S. Neo, K. M. Rezaur, M. Sawa, and Y. Maeda, “Performance of single crystal diamond tools with different rake angles during micro-grooving on electroless nickel plated die materials,” Int. J. Adv. Manuf. Technol. 33, 891–899 (2007).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

H. Howden and J. A. Clarke, “Refracting replica aspheric optics,” Opt. Eng. 15, 197–201 (1976).

Opt. Lett. (1)

Opt. Rev. (1)

T. Takaoka, N. Kawano, Y. Awatsuji, and T. Kubota, “Design of a reflective aspherical surface of a compact beam-shaping device,” Opt. Rev. 13, 77–86 (2006).
[CrossRef]

Other (2)

G. Boothroyd, Fundamentals of Metal Machining and Machine Tools (McGraw-Hill, 1975), Chap. 7.

R. P. Paul, Robot Manipulators: Mathematics, Programming, and Control (MIT, 1982).

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