Abstract

A general equation of high-order surfaces is given. If its second term is equal to zero, this equation will automatically reduce to the conic surfaces. By adding two parameters g and k into the conic equation, we are able to use only one euqation to describe the planar, cylindrical, and conic surfaces. A set of skew ray tracing formulas for these surfaces, including tilted and decentered elements, is derived. The formulas analytical and easy to use. Based on the tracing of skew rays, a merit function of the optical system is defined and an analytical formula for determining the narrowest cross-sectional position of skew rays is given. A program of skew ray tracing is edited for the Sharp-1500 pocket computer. An example for a 2-D infrared scanner is given. Based on the skew ray tracing formulas and by using the damped least-squares method, some examples for automatic design of optical systems are also shown on the IBM PC/XT personal computer.

© 1988 Optical Society of America

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References

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  1. T. H. Jamieson, Optimization Techniques in Lens Design (American Elsevier, New York, 1971).
  2. W. T. Welford, Aberrations of the Symmetrical System (Academic, London, 1974).
  3. D. P. Feder, “Optical Calculations with Automatic Computing Machinery,” J. Opt. Soc. Am. 41, 630 (1951).
    [CrossRef]
  4. A. B. Meinel, M. P. Meinel, “Zero Coma Condition for Decentered and Tilted Secondary Mirror in Cassegrain/Nasmyth Configuration,” Opt. Eng. 23, 801 (1984).
    [CrossRef]
  5. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  6. M. Herzberger, “Geometrical Optics,” in Handbook of Physics, Second Edition, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1967).
  7. B. J. Howell, M. E. Wilson, “Automatic Ray–Surface Intersection Method,” Appl. Opt. 21, 2184 (1982).
    [CrossRef] [PubMed]
  8. G. Pinto, “A Program for Ray Tracing Through Tilted and Decentered Optical Surfaces,” Opt. Acta 26, 1321 (1979).
    [CrossRef]
  9. J. S. Hanssen, “Ray–Tracing Programs for Spherical and Aspherical Surfaces,” Electro Opt. Syst. Des. 27 (Oct.1980).
  10. L. H. J. F. Beckmann, “Programmable Calculators: Their Use in Lens Design and Analysis,” Opt. Eng. 24, 713 (1986).
  11. R. Willey et al., “Minimized Cost Through Optimized Tolerance Distribution in Optical Assemblies,” Proc. Soc. Photo-Opt. Instrum. Eng. 389, 12 (1983).
  12. D. Heshmaty-Manesh, G. Y. Haig, “Lens Tolerancing by Desk-Top Computer,” 25, 1268 (1986).
  13. Y. Zhang et al., “Automatic Design of Non-Coaxial and Aspherical Infrared Optical System,” Acta Phys. Sin. 28, 492 (1979).
  14. Y. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, China, 1983), Chaps. 4 and 5.
  15. Wang Lan-Juan, Su Ding-Qiang, “The Studies of Two Types of Catadioptric Telescope,” Acta Opt. Sin. 3, 132 (1983).
  16. T. B. Andersen, “Evaluating rms Spot Radii by Ray Tracing,” Appl. Opt. 21, 1241 (1982).
    [CrossRef] [PubMed]

1986 (2)

L. H. J. F. Beckmann, “Programmable Calculators: Their Use in Lens Design and Analysis,” Opt. Eng. 24, 713 (1986).

D. Heshmaty-Manesh, G. Y. Haig, “Lens Tolerancing by Desk-Top Computer,” 25, 1268 (1986).

1984 (1)

A. B. Meinel, M. P. Meinel, “Zero Coma Condition for Decentered and Tilted Secondary Mirror in Cassegrain/Nasmyth Configuration,” Opt. Eng. 23, 801 (1984).
[CrossRef]

1983 (2)

R. Willey et al., “Minimized Cost Through Optimized Tolerance Distribution in Optical Assemblies,” Proc. Soc. Photo-Opt. Instrum. Eng. 389, 12 (1983).

Wang Lan-Juan, Su Ding-Qiang, “The Studies of Two Types of Catadioptric Telescope,” Acta Opt. Sin. 3, 132 (1983).

1982 (2)

1980 (1)

J. S. Hanssen, “Ray–Tracing Programs for Spherical and Aspherical Surfaces,” Electro Opt. Syst. Des. 27 (Oct.1980).

1979 (2)

G. Pinto, “A Program for Ray Tracing Through Tilted and Decentered Optical Surfaces,” Opt. Acta 26, 1321 (1979).
[CrossRef]

Y. Zhang et al., “Automatic Design of Non-Coaxial and Aspherical Infrared Optical System,” Acta Phys. Sin. 28, 492 (1979).

1951 (1)

Andersen, T. B.

Beckmann, L. H. J. F.

L. H. J. F. Beckmann, “Programmable Calculators: Their Use in Lens Design and Analysis,” Opt. Eng. 24, 713 (1986).

Ding-Qiang, Su

Wang Lan-Juan, Su Ding-Qiang, “The Studies of Two Types of Catadioptric Telescope,” Acta Opt. Sin. 3, 132 (1983).

Feder, D. P.

Haig, G. Y.

D. Heshmaty-Manesh, G. Y. Haig, “Lens Tolerancing by Desk-Top Computer,” 25, 1268 (1986).

Hanssen, J. S.

J. S. Hanssen, “Ray–Tracing Programs for Spherical and Aspherical Surfaces,” Electro Opt. Syst. Des. 27 (Oct.1980).

Herzberger, M.

M. Herzberger, “Geometrical Optics,” in Handbook of Physics, Second Edition, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1967).

Heshmaty-Manesh, D.

D. Heshmaty-Manesh, G. Y. Haig, “Lens Tolerancing by Desk-Top Computer,” 25, 1268 (1986).

Howell, B. J.

Jamieson, T. H.

T. H. Jamieson, Optimization Techniques in Lens Design (American Elsevier, New York, 1971).

Lan-Juan, Wang

Wang Lan-Juan, Su Ding-Qiang, “The Studies of Two Types of Catadioptric Telescope,” Acta Opt. Sin. 3, 132 (1983).

Meinel, A. B.

A. B. Meinel, M. P. Meinel, “Zero Coma Condition for Decentered and Tilted Secondary Mirror in Cassegrain/Nasmyth Configuration,” Opt. Eng. 23, 801 (1984).
[CrossRef]

Meinel, M. P.

A. B. Meinel, M. P. Meinel, “Zero Coma Condition for Decentered and Tilted Secondary Mirror in Cassegrain/Nasmyth Configuration,” Opt. Eng. 23, 801 (1984).
[CrossRef]

Pinto, G.

G. Pinto, “A Program for Ray Tracing Through Tilted and Decentered Optical Surfaces,” Opt. Acta 26, 1321 (1979).
[CrossRef]

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical System (Academic, London, 1974).

Willey, R.

R. Willey et al., “Minimized Cost Through Optimized Tolerance Distribution in Optical Assemblies,” Proc. Soc. Photo-Opt. Instrum. Eng. 389, 12 (1983).

Wilson, M. E.

Zhang, Y.

Y. Zhang et al., “Automatic Design of Non-Coaxial and Aspherical Infrared Optical System,” Acta Phys. Sin. 28, 492 (1979).

Y. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, China, 1983), Chaps. 4 and 5.

Acta Opt. Sin. (1)

Wang Lan-Juan, Su Ding-Qiang, “The Studies of Two Types of Catadioptric Telescope,” Acta Opt. Sin. 3, 132 (1983).

Acta Phys. Sin. (1)

Y. Zhang et al., “Automatic Design of Non-Coaxial and Aspherical Infrared Optical System,” Acta Phys. Sin. 28, 492 (1979).

Appl. Opt. (2)

Electro Opt. Syst. Des. (1)

J. S. Hanssen, “Ray–Tracing Programs for Spherical and Aspherical Surfaces,” Electro Opt. Syst. Des. 27 (Oct.1980).

J. Opt. Soc. Am. (1)

Lens Tolerancing by Desk-Top Computer (1)

D. Heshmaty-Manesh, G. Y. Haig, “Lens Tolerancing by Desk-Top Computer,” 25, 1268 (1986).

Opt. Acta (1)

G. Pinto, “A Program for Ray Tracing Through Tilted and Decentered Optical Surfaces,” Opt. Acta 26, 1321 (1979).
[CrossRef]

Opt. Eng. (2)

L. H. J. F. Beckmann, “Programmable Calculators: Their Use in Lens Design and Analysis,” Opt. Eng. 24, 713 (1986).

A. B. Meinel, M. P. Meinel, “Zero Coma Condition for Decentered and Tilted Secondary Mirror in Cassegrain/Nasmyth Configuration,” Opt. Eng. 23, 801 (1984).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. Willey et al., “Minimized Cost Through Optimized Tolerance Distribution in Optical Assemblies,” Proc. Soc. Photo-Opt. Instrum. Eng. 389, 12 (1983).

Other (5)

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

M. Herzberger, “Geometrical Optics,” in Handbook of Physics, Second Edition, E. U. Condon, H. Odishaw, Eds. (McGraw-Hill, New York, 1967).

T. H. Jamieson, Optimization Techniques in Lens Design (American Elsevier, New York, 1971).

W. T. Welford, Aberrations of the Symmetrical System (Academic, London, 1974).

Y. Zhang, Infrared Optical Engineering (Shanghai Scientific Press, China, 1983), Chaps. 4 and 5.

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