Abstract

The IBM Card Programmed Electronic Calculator has been applied to the problem of lens design. Optical design is an inverse process consisting of a provisional choice of optical parameters, an exhaustive mathematical study of such a tentative prescription, and subsequent refinement of the lens system.

The standard ray tracing equations can be adapted easily for machine use. The mathematical treatment is algebraic rather than trigonometric. Examples of meridional and skew ray tracing are given. A satisfactory lens has been calculated and tested entirely by machine methods.

The machine is expected to be of value in the refining of optical systems, in the determination of optical shop tolerances, and in the investigation of existing prescriptions.

© 1951 Optical Society of America

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References

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  1. H. R. Grosch, J. Opt. Soc. Am. 39, 1059(A) (1949).
  2. D. P. Feder, J. Opt. Soc. Am. 41, 289(A) (1951).
  3. The Thomas J. Watson Astronomical Computing Bureau, Columbia University, New York, 1940.
  4. A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), Part 1, p. 4.
  5. See reference 4, Part 1, p. 413.
  6. L. Silberstein, Simplified Method of Tracing Rays Through Any Optical System of Lenses, Prisms and Mirrors (Longmans, Green and Company, New York, 1918).
  7. See reference 4, Part 1, p. 409.

1951 (1)

D. P. Feder, J. Opt. Soc. Am. 41, 289(A) (1951).

1949 (1)

H. R. Grosch, J. Opt. Soc. Am. 39, 1059(A) (1949).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), Part 1, p. 4.

Feder, D. P.

D. P. Feder, J. Opt. Soc. Am. 41, 289(A) (1951).

Grosch, H. R.

H. R. Grosch, J. Opt. Soc. Am. 39, 1059(A) (1949).

Silberstein, L.

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

J. Opt. Soc. Am. (2)

H. R. Grosch, J. Opt. Soc. Am. 39, 1059(A) (1949).

D. P. Feder, J. Opt. Soc. Am. 41, 289(A) (1951).

Other (5)

The Thomas J. Watson Astronomical Computing Bureau, Columbia University, New York, 1940.

A. E. Conrady, Applied Optics and Optical Design (Oxford University Press, New York, 1929), Part 1, p. 4.

See reference 4, Part 1, p. 413.

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

See reference 4, Part 1, p. 409.

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Figures (4)

Fig. 1
Fig. 1

Meridional ray.

Fig. 2
Fig. 2

Skew ray.

Fig. 3
Fig. 3

Variable-focus collimator.

Fig. 4
Fig. 4

Plot of sinu′ for last interface of variable-focus collimator.

Equations (54)

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N sin I = N sin I ,
L U } initial data ,             r N / N d } interface data ,
sin I = ( L - r ) ( sin U ) / r ,
sin I = ( N / N ) sin I ,
U = U + I - I ,
L = r sin I / sin U + r ,
U 2 U L 2 L - d } transfer equations.
L s k H s k U z U y } initial data ,             r N / N d } interface data ,
tan U c = - H s k / ( L s k - r ) ,
tan θ = tan U z / sin ( U y - U c ) ,
sin U = sin U z / sin θ ,
C B = - H s k / sin U c ,
sin I = C B ( sin U ) / r ,
sin I = ( N / N ) sin I ,
U = U + I - I ,
C B = r sin I / sin U ,
L s k = r + C B cos U c ,
H s k = C B sin U c ,
sin U z = sin θ sin U ,
sin ( U y - U c ) = tan U z / tan θ ,
L s k 1 L s k - d H s k 1 H s k U z 1 U z U y 1 U y } transfer equations.
L sin U } initial data ,             r N / N d } interface data ,
sin I = ( L - r ) ( sin U ) / r ,
sin I = ( N / N ) sin I ,
cos U = ( 1 - sin 2 U ) 1 2 ,
cos I = ( 1 - sin 2 I ) 1 2 ,
cos I = ( 1 - sin 2 I ) 1 2 ,
sin U = cos I ( sin U cos I + cos U sin I ) - sin I ( cos U cos I - sin U sin I ) ,
L = r sin I / sin U + r ,
L 2 L - d sin U 2 sin U } transfer equations.
L s k H s k sin U y sin U z tan U z } initial data ,             r N / N d } interface data,
cos U y = ( 1 - sin 2 U y ) 1 2 ,
tan U c = - H s k / ( L s k - r ) ,
sec U c = ( 1 + tan 2 U c ) 1 2 ,
sin U c = tan U c / sec U c ,
tan θ = tan U z / [ ( sin U y / sec U c ) - cos U y sin U c ] ,
sin θ = tan θ ( 1 + tan 2 θ ) - 1 2 ,
sin U = sin U z / sin θ ,
C B = - H s k / sin U c ,
sin I = C B ( sin U ) / r ,
sin I = ( N / N ) sin I ,
cos U = ( 1 - sin 2 U ) 1 2 ,
cos I = ( 1 - sin 2 I ) 1 2 ,
cos I = ( 1 - sin 2 I ) 1 2 ,
sin U = cos I ( sin U cos I + cos U sin I ) - sin I ( cos U cos I - sin U sin I ) ,
C B = r sin I / sin U ,
L s k = r + C B / sec U c ,
H s k = - C B sin U c ,
sin U z = sin θ sin U ,
tan U z = sin U z ( 1 - sin 2 U z ) - 1 2 ,
sin U y = sin U c [ 1 - ( tan U z tan θ ) 2 ] 1 2 - ( tan U z / tan θ ) / sec U c ,
L s k 2 = L s k - d H s k 2 = H s k sin U y 2 = sin U y sin U z 2 = sin U z tan U z 2 = tan U z } transfer equations.
L = - 1096.426 sin U = - 0.003648200 } initial data , r = + 75.39700 N / N = + 0.6567626 d = + 0.8000000 } interface data , sin I = + 0.05670046 , sin I = + 0.03723874 , cos U = + 0.9999933 , cos I = + 0.9976987 , cos I = + 0.9998102 , sin U = + 0.01583466 , L = + 252.7099 , L 2 = + 251.9099 sin U 2 = + 0.01583466 } transfer equations.
L s k = - 6.161100 H s k = - 5.681400 sin U y = - 0.6180900 sin U z = - 0.008800000 tan U z = - 0.008800347 } initial data , r = + 4.000000 N / N = + 0.6100202 d = + 0.1500000 } interface data , cos U y = + 0.7861072 , cos U = + 0.9877432 , tan U c = + 0.5591324 , cos I = + 0.8908611 , sec U c = + 1.145700 , cos I = + 0.9608360 , sin U c = + 0.4880269 , sin U = + 0.03403151 , tan θ = + 0.05646848 , C B = + 32.57187 , sin θ = + 0.05637867 , L s k = + 32.42967 , sin U = - 0.1560874 , H s k = + 15.89595 , C B = - 11.64157 , sin U z = - 0.001918651 , sin I = + 0.4542757 , tan U z = - 0.001918655 , sin I = + 0.2771174 , sin U y = - 0.4580886 , L s k 2 = + 32.27967 H s k 2 = + 15.89595 sin U y 2 = - 0.4580886 sin U z 2 = - 0.001918651 tan U z 2 = - 0.001918655 } transfer equations.