Abstract

After a brief theoretical introduction, the procedure for plotting the sections of an imaging cone from a point source, for one single zone of a lens in the presence of one or more aberrations is explained. The process is much simplified by a convenient graphical construction. A method is then described for projecting the sections due to coma and astigmatism on a screen so that they may be shown to a class. Photographs are included in the paper which show how remarkably the projected sections agree with the theoretically computed figures.

© 1933 Optical Society of America

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References

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  1. Gleichen, Theory of Modern Optical Instruments, p. 78.
  2. Conrady, Applied Optics and Optical Design, p. 277.
  3. Martin, Applied Optics, 1, 130. See also, Trans. Opt. Soc. 27, 96 (1925–6).
  4. Pelletan, Optigue Appliquée, p. 58.
  5. Conrady, M. N. Roy. Astron. Soc. 79, 64 (1918); and also see Czapski, Grundzüge der Theorie der optischen Instrumente, p. 151, 1904 edition; Southall, Geometrical Optics, p. 467; Glazebrook, Dictionary of Applied Physics4, 313.
  6. Conrady, Applied Optics and Optical Design, p. 279.
  7. Gullstrand has given similar photographs for other aberrations, see Die Naturwissenschaften 14, 664 (1926).
    [CrossRef]

1926 (1)

Gullstrand has given similar photographs for other aberrations, see Die Naturwissenschaften 14, 664 (1926).
[CrossRef]

1918 (1)

Conrady, M. N. Roy. Astron. Soc. 79, 64 (1918); and also see Czapski, Grundzüge der Theorie der optischen Instrumente, p. 151, 1904 edition; Southall, Geometrical Optics, p. 467; Glazebrook, Dictionary of Applied Physics4, 313.

Conrady,

Conrady, M. N. Roy. Astron. Soc. 79, 64 (1918); and also see Czapski, Grundzüge der Theorie der optischen Instrumente, p. 151, 1904 edition; Southall, Geometrical Optics, p. 467; Glazebrook, Dictionary of Applied Physics4, 313.

Conrady, Applied Optics and Optical Design, p. 279.

Conrady, Applied Optics and Optical Design, p. 277.

Gleichen,

Gleichen, Theory of Modern Optical Instruments, p. 78.

Martin,

Martin, Applied Optics, 1, 130. See also, Trans. Opt. Soc. 27, 96 (1925–6).

Pelletan,

Pelletan, Optigue Appliquée, p. 58.

Die Naturwissenschaften (1)

Gullstrand has given similar photographs for other aberrations, see Die Naturwissenschaften 14, 664 (1926).
[CrossRef]

M. N. Roy. Astron. Soc. (1)

Conrady, M. N. Roy. Astron. Soc. 79, 64 (1918); and also see Czapski, Grundzüge der Theorie der optischen Instrumente, p. 151, 1904 edition; Southall, Geometrical Optics, p. 467; Glazebrook, Dictionary of Applied Physics4, 313.

Other (5)

Conrady, Applied Optics and Optical Design, p. 279.

Gleichen, Theory of Modern Optical Instruments, p. 78.

Conrady, Applied Optics and Optical Design, p. 277.

Martin, Applied Optics, 1, 130. See also, Trans. Opt. Soc. 27, 96 (1925–6).

Pelletan, Optigue Appliquée, p. 58.

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Figures (9)

Fig. 1
Fig. 1

The relation between optical path difference and transverse aberration.

Fig. 2
Fig. 2

Coordinates of a point in the exit pupil of the lens.

Fig. 3
Fig. 3

Aberration cone sections in paraxial focal plane for three zones of the lens.

Fig. 4
Fig. 4

Procedure for plotting cone sections at different distances along the axis given the computed section at one such distance. (This case represents a mixture of one “part” of coma and three “parts” of astigmatism.) Only one side of each figure need be plotted as they are all symmetrical about the vertical axis.

Fig. 5
Fig. 5

Theoretical cross sections of image cone in the presence of coma and astigmatism.

Fig. 6
Fig. 6

Diagram of essential apparatus (with the exception of the projection screen which lies to the left of the diagram).

Fig. 7
Fig. 7

Photograph of essential equipment used in producing various ratios of coma and astigmatism.

Fig. 8
Fig. 8

Experimentally determined cone sections for one zone.

Fig. 9
Fig. 9

Image cone sections for a complete lens, in presence of pure coma.

Equations (14)

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O P D = ( A / 4 l ) ( x 2 + y 2 ) 2 + ( B / l ) y ( x 2 + y 2 ) h + ( C / 2 l ) ( x 2 + 3 y 2 ) h 2 + ( D / 2 l ) ( x 2 + y 2 ) h 2 + ( E / l ) y h 3 .
α x = O P D / x             and             α y = O P D / y .
x = - l ( O P D / x ) , and y = - l ( O P D / y ) .
x = - A x ( x 2 + y 2 ) - 2 B x y h - C x h 2 - D x h 2 , y = - A y ( x 2 + y 2 ) - B ( x 2 + 3 y 2 ) h - 3 C y h 2 - D y h 2 - E h 3 . }
x = s sin θ ;             y = s cos θ ,
x = - A s 3 sin θ - B s 2 h sin 2 θ - C s h 2 sin θ - D s h 2 sin θ , y = - A s 3 cos θ - B s 2 h ( 2 + cos 2 θ ) - 3 C s h 2 cos θ - D s h 2 cos θ - E h 3 . }
x = - A s 3 sin θ             and             y = - A s 3 cos θ .
x = - B s 2 h sin 2 θ ;             y = - B s 2 h ( 2 + cos 2 θ ) .
x = - C s h 2 sin θ             and             y = - 3 C s h 2 cos θ .
x = - D s h 2 sin θ             and             y = - D s h 2 cos θ .
x = 0             and             y = - E h 3 .
x = - 2 s 2 h sin 2 θ - 2 s h 2 sin θ , y = - 2 s 2 h ( 2 + cos 2 θ ) - 6 s h 2 cos θ .
x = - k ( s sin θ ) ;             y = - k ( s cos θ ) .
x = - B sin 2 θ - k sin θ , y = - B ( 2 + cos 2 θ ) - k cos θ .