Abstract

The rotating prisms used in high-speed motion-picture cameras have been designed empirically since their first use thirty-two years ago. During that period, there have been advances made in glass technology and fabrication which have resulted in the production of better images. This paper summarizes the latest state of the art wherein it is demonstrated that prism design should not be confined to the D line of the spectrum, but expanded to cover the uv and ir portions of the spectrum. The prism design shall cover: (1) selection of the average angle of incidence for exposure; (2) the choice of glass or other transparent media; (3) the correlationship between image and film velocity; and (4) discussion of the inherent aberrations, namely, nonlinear distortion, sagittal and tangential coma, prismatic astigmatism, change in back focus due to prism rotation; (5) shuttering action; and (6) aperture design. There have only been fragmentary data published on the subject to date. It is necessary to secure this thirty years’ experience before this datum is forever lost. Recommendation for future action is made, including computer studies for optimization of design.

© 1966 Optical Society of America

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Corrections

John H. Waddell, "Errata to Volume 5: Rotating Prism Design for Continuous Image Compensation Cameras," Appl. Opt. 7, 367-367 (1968)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-7-2-367

References

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  1. J. F. Leventhal, Trans. Soc. Motion Picture Engrs. 12, 1068 (1928).
  2. H. D. Taylor, Proc. Phys. Soc. (London), 46, 283 (1934).
    [CrossRef]
  3. H. D. Taylor, Proc. Phys. Soc. 46, 889 (1934).
    [CrossRef]
  4. H. D. Taylor, Proc. Phys. Soc. (London), 49, 663 (1937).
    [CrossRef]
  5. J. H. Waddell, J. Soc. Motion Picture Television Engrs. 73, 648 (1964).
  6. J. H. Waddell, J. Soc. Motion Picture Television Engrs. 53, 496 (1949).
  7. J. Kudar, Proc. Phys. Soc. (London), 58, 586 (1946).
    [CrossRef]
  8. J. Kudar, in High Speed Photography (Soc. of Motion Picture and Television Engrs., New York, 1952), Vol. 4, pp. 81–84.
  9. W. J. Hyzer, Engineering and Scientific High Speed Photography (The Macmillan Company, New York, 1962), p. 171.

1964 (1)

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 73, 648 (1964).

1949 (1)

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 53, 496 (1949).

1946 (1)

J. Kudar, Proc. Phys. Soc. (London), 58, 586 (1946).
[CrossRef]

1937 (1)

H. D. Taylor, Proc. Phys. Soc. (London), 49, 663 (1937).
[CrossRef]

1934 (2)

H. D. Taylor, Proc. Phys. Soc. (London), 46, 283 (1934).
[CrossRef]

H. D. Taylor, Proc. Phys. Soc. 46, 889 (1934).
[CrossRef]

1928 (1)

J. F. Leventhal, Trans. Soc. Motion Picture Engrs. 12, 1068 (1928).

Hyzer, W. J.

W. J. Hyzer, Engineering and Scientific High Speed Photography (The Macmillan Company, New York, 1962), p. 171.

Kudar, J.

J. Kudar, Proc. Phys. Soc. (London), 58, 586 (1946).
[CrossRef]

J. Kudar, in High Speed Photography (Soc. of Motion Picture and Television Engrs., New York, 1952), Vol. 4, pp. 81–84.

Leventhal, J. F.

J. F. Leventhal, Trans. Soc. Motion Picture Engrs. 12, 1068 (1928).

Taylor, H. D.

H. D. Taylor, Proc. Phys. Soc. (London), 49, 663 (1937).
[CrossRef]

H. D. Taylor, Proc. Phys. Soc. (London), 46, 283 (1934).
[CrossRef]

H. D. Taylor, Proc. Phys. Soc. 46, 889 (1934).
[CrossRef]

Waddell, J. H.

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 73, 648 (1964).

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 53, 496 (1949).

J. Soc. Motion Picture Television Engrs. (2)

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 73, 648 (1964).

J. H. Waddell, J. Soc. Motion Picture Television Engrs. 53, 496 (1949).

Proc. Phys. Soc. (1)

H. D. Taylor, Proc. Phys. Soc. 46, 889 (1934).
[CrossRef]

Proc. Phys. Soc. (London) (3)

H. D. Taylor, Proc. Phys. Soc. (London), 49, 663 (1937).
[CrossRef]

H. D. Taylor, Proc. Phys. Soc. (London), 46, 283 (1934).
[CrossRef]

J. Kudar, Proc. Phys. Soc. (London), 58, 586 (1946).
[CrossRef]

Trans. Soc. Motion Picture Engrs. (1)

J. F. Leventhal, Trans. Soc. Motion Picture Engrs. 12, 1068 (1928).

Other (2)

J. Kudar, in High Speed Photography (Soc. of Motion Picture and Television Engrs., New York, 1952), Vol. 4, pp. 81–84.

W. J. Hyzer, Engineering and Scientific High Speed Photography (The Macmillan Company, New York, 1962), p. 171.

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Figures (21)

Fig. 1
Fig. 1

Continuous projector.

Fig. 2
Fig. 2

Skew rays—lengthening of back focus.

Fig. 3
Fig. 3

Rotating prism.

Fig. 4
Fig. 4

Principle of rotating prism.

Fig. 5
Fig. 5

Effect of index of refraction on angle of refraction.

Fig. 6
Fig. 6

Nonlinearity of refracted image.

Fig. 7
Fig. 7

Four-sided prism.

Fig. 8
Fig. 8

Prism thickness variations with index of refraction and angle of incidence.

Fig. 9
Fig. 9

Nonlinearity of prism and film velocity.

Fig. 10
Fig. 10

Camera exposure. E = exposure × 100/(rotational angle/picture).

Fig. 11
Fig. 11

Effect of wavelength on index of refraction.

Fig. 12
Fig. 12

16-mm prisms for uv, visible and ir light.

Fig. 13
Fig. 13

(A)–(H) Image formation rotating shutters.

Fig. 14
Fig. 14

Image formation.

Fig. 15
Fig. 15

Effect of fixed aperture position with image plane.

Fig. 16
Fig. 16

Film and image planes.

Fig. 17
Fig. 17

Increase in back focus due to prism rotation (unit thickness).

Fig. 18
Fig. 18

Nonlinear distortion. Four-sided 16-mm prism, i = 10°.

Fig. 19
Fig. 19

Prismatic astigmatism. Four-sided 16-mm prism, i = 10° (corrected for thickness).

Fig. 20
Fig. 20

Prismatic astigmatism. 16-mm prism, nd = 1.6968, i = 10°.

Fig. 21
Fig. 21

Tangential coma. Four-sided 16-mm prism, i = 10°, sagittal coma = 1 3 tangential coma.

Tables (9)

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Table I Light Efficiency Based on Number of Prism Faces and their Shuttering Effects from Figure 1

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Table II Sprocket Pitch Dimensionsa for Various Picture Formats

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Table III Shuttering Action of Various Rotating Apertures

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Table IV Effect in Decreasing Exposure Time by Introducing a Fixed Slit in Juxtaposition to the Film Plane

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Table V Conversion of C Mount Lenses to Compensate for Back or Shoulder Focus

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Table VI Effect of Film Base Thickness on Out of Focus Pictures

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Table VII Lens Movement from Infinity Position. Focal Length of Lens

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Table VIII Effect of Back Focus Increase for Prisms Designed for a Specific Angle of Incidence with Varying Indices of Refraction

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Table IX Change in Back Focus of Central Ray Due to Prism Rotation

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

n = sin i / sin r ,
d = i - r ,
S S = tan d ,
S S = t sin i ( i - r ) cos r ,
S S = t sin i [ 1 - cos i ( n 2 - sin 2 i ) 1 2 ] .
F d = P x i 360 / P F ,
t = F d / S S ,
S S = t sin d cos r .
S S = t sin i - sin 2 i 2 ( n 2 - sin 2 i ) ½ ,
V d = n d - 1 n F - n C ,
V e = n e - 1 n F - n C ,
T = S / V ,
L S = L W - L H ( in diopters ) ,
v = u F u - F ,
F I = n - 1 n t ,
u + v = ( m + 1 ) 2 m F ,
m = v u = v - F F = F u - F .
Length of CR on rotation = t / cos d .
t ( n - 1 n ) ( n + 1 2 n 2 - 1 6 ) x 3 ,
t ( n - 1 n ) ( n + 1 n 2 ) x 2 .
3 2 t ( n - 1 n ) ( n + 1 n 2 ) i y 2 ,
Tangential coma 3 .

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