Abstract

Generalized ray tracing equations are derived to include special cases in optics such as uncentered spherical interfaces, prisms, mirrors, and centered aspheric surfaces. These equations were constructed for use with the IBM Card Programmed Electronic Calculator. The method has been applied to complicated optical systems involving uncentered lenses in addition to reflecting and refracting prisms. A method is given for the design of an aspheric surface, and a design curve of an aspheric optical system is given as an example.

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  1. W. A. Allen and R. H. Stark, J. Opt. Soc. Am. 41, 636 (1951).
  2. A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), first edition, Part 1, p. 413.
  3. L. Silberstein, Simplified Method of Tracing Rays Through AnyOptical System of Lenses, Prisms, and Mirrors (Longmans, Green and Company, New York, 1918).
  4. D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).
  5. R. Glazebrook, Dictionary of Applied Physics (Macmillan and Company, Ltd., London, 1923), Vol. IV, p. 287.
  6. R. K. Luneburg, Mathcmatical Theory of Optics (Brown University lecture notes, 1944), p. 410.
  7. W. Wallin, Theory of Optical Image Formation (University of California at Los Angeles lecture notes, U. S. Naval Ordnance Test Station, 1951), p. 17.
  8. D. P. Feder, J. Research Natl. Bur. Standards 45, 61 (1950).
  9. Henry Margenau and George Moseley Murphy, Te Matheimatics of Physics and Chemistry (D. Van Nostrand Company, Inc., New York, 1947), first edition, p. 475.
  10. A. Bouwers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), second edition, p. 40.
  11. D. D. Maksutov, J. Opt. Soc. Am. 34, 270 (1944).
  12. F. A. Lucy, J. Opt. Soc. Am. 30, 251 (1940).
  13. H. S. Friedman, J. Opt. Soc. Am. 37, 480 (1947).
  14. William Edmund Milne, Numerical Calculus (Princeton University Press, Princeton, New Jersey, 1949), p. 242.

Allen, W. A.

W. A. Allen and R. H. Stark, J. Opt. Soc. Am. 41, 636 (1951).

Bouwers, A.

A. Bouwers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), second edition, p. 40.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), first edition, Part 1, p. 413.

Feder, D. P.

D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).

D. P. Feder, J. Research Natl. Bur. Standards 45, 61 (1950).

Friedman, H. S.

H. S. Friedman, J. Opt. Soc. Am. 37, 480 (1947).

Glazebrook, R.

R. Glazebrook, Dictionary of Applied Physics (Macmillan and Company, Ltd., London, 1923), Vol. IV, p. 287.

Lucy, F. A.

F. A. Lucy, J. Opt. Soc. Am. 30, 251 (1940).

Luneburg, R. K.

R. K. Luneburg, Mathcmatical Theory of Optics (Brown University lecture notes, 1944), p. 410.

Maksutov, D. D.

D. D. Maksutov, J. Opt. Soc. Am. 34, 270 (1944).

Margenau, Henry

Henry Margenau and George Moseley Murphy, Te Matheimatics of Physics and Chemistry (D. Van Nostrand Company, Inc., New York, 1947), first edition, p. 475.

Milne, William Edmund

William Edmund Milne, Numerical Calculus (Princeton University Press, Princeton, New Jersey, 1949), p. 242.

Murphy, George Moseley

Henry Margenau and George Moseley Murphy, Te Matheimatics of Physics and Chemistry (D. Van Nostrand Company, Inc., New York, 1947), first edition, p. 475.

Silberstein, L.

L. Silberstein, Simplified Method of Tracing Rays Through AnyOptical System of Lenses, Prisms, and Mirrors (Longmans, Green and Company, New York, 1918).

Stark, R. H.

W. A. Allen and R. H. Stark, J. Opt. Soc. Am. 41, 636 (1951).

Wallin, W.

W. Wallin, Theory of Optical Image Formation (University of California at Los Angeles lecture notes, U. S. Naval Ordnance Test Station, 1951), p. 17.

Other (14)

W. A. Allen and R. H. Stark, J. Opt. Soc. Am. 41, 636 (1951).

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), first edition, Part 1, p. 413.

L. Silberstein, Simplified Method of Tracing Rays Through AnyOptical System of Lenses, Prisms, and Mirrors (Longmans, Green and Company, New York, 1918).

D. P. Feder, J. Opt. Soc. Am. 41, 630 (1951).

R. Glazebrook, Dictionary of Applied Physics (Macmillan and Company, Ltd., London, 1923), Vol. IV, p. 287.

R. K. Luneburg, Mathcmatical Theory of Optics (Brown University lecture notes, 1944), p. 410.

W. Wallin, Theory of Optical Image Formation (University of California at Los Angeles lecture notes, U. S. Naval Ordnance Test Station, 1951), p. 17.

D. P. Feder, J. Research Natl. Bur. Standards 45, 61 (1950).

Henry Margenau and George Moseley Murphy, Te Matheimatics of Physics and Chemistry (D. Van Nostrand Company, Inc., New York, 1947), first edition, p. 475.

A. Bouwers, Achievements in Optics (Elsevier Publishing Company, Inc., New York, 1950), second edition, p. 40.

D. D. Maksutov, J. Opt. Soc. Am. 34, 270 (1944).

F. A. Lucy, J. Opt. Soc. Am. 30, 251 (1940).

H. S. Friedman, J. Opt. Soc. Am. 37, 480 (1947).

William Edmund Milne, Numerical Calculus (Princeton University Press, Princeton, New Jersey, 1949), p. 242.

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