Abstract

The geometric optics of a new 3-D imaging system, which has several innovative features, is discussed. The principles governing the primary design of the system are considered in some detail, and the calculation method employed in achieving the basic design parameters is presented. The aberration of the system is then investigated in detail using primary aberration theory, and the limitations imposed on a light beam passing through the arrangement is discussed quantitatively.

© 1988 Optical Society of America

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References

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  1. M. G. Lippmann, “Eppeuves Reversibles Donnant La Sensation Durelief,” J. Phys. Paris 821 (1908).
  2. H. E. Ives, “Optical Properties of a Lippman Lenticulated Sheet,” J. Opt. Soc. Am. 21, 171 (1931).
    [CrossRef]
  3. C. B. Burckhardt, “Optimum Parameters and Resolution Limitation of Integral Photography,” J. Opt. Soc. Am. 58, 71 (1968).
    [CrossRef]
  4. T. Okoshi, Three-Dimensional Techniques (Academic, New York, 1976), p. 103.
  5. R. L. de Montebello, “Wide-Angle Integral Photography—The Integram System,” Proc. Soc. Photo-Opt. Instrum. Eng. 102, 73 (1977).
  6. N. Davies, M. McCormick, L. Yang, “Three-Dimensional Imaging Systems: A New Development,” Appl. Opt. 27, 4520 (1988).
    [CrossRef] [PubMed]

1988 (1)

1977 (1)

R. L. de Montebello, “Wide-Angle Integral Photography—The Integram System,” Proc. Soc. Photo-Opt. Instrum. Eng. 102, 73 (1977).

1968 (1)

1931 (1)

1908 (1)

M. G. Lippmann, “Eppeuves Reversibles Donnant La Sensation Durelief,” J. Phys. Paris 821 (1908).

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Phys. Paris (1)

M. G. Lippmann, “Eppeuves Reversibles Donnant La Sensation Durelief,” J. Phys. Paris 821 (1908).

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

R. L. de Montebello, “Wide-Angle Integral Photography—The Integram System,” Proc. Soc. Photo-Opt. Instrum. Eng. 102, 73 (1977).

Other (1)

T. Okoshi, Three-Dimensional Techniques (Academic, New York, 1976), p. 103.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the optical system.

Fig. 2
Fig. 2

Aperture sharing.

Fig. 3
Fig. 3

Results of aperture sharing function.

Fig. 4
Fig. 4

Vignetting as a function of the distance between the sublens and photographic lens.

Fig. 5
Fig. 5

How individual sublens images are combined to form a common image on the image plane of the combined system.

Fig. 6
Fig. 6

Scheme used to examine the change in aberration of the combined system.

Fig. 7
Fig. 7

Graph representing the change in aberration in relation to the position of the aperture stop.

Equations (20)

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β en . p - ex . p = A 1 B 1 / A 1 B 1 = l / l .
2 tan θ = d / X F = d / F ;
2 tan θ = d / f ,
γ = 2 tan θ / 2 tan θ = f / F ,
β OB . p - I . p = l / γ = F / f .
2 ω = 2 tan - 1 ( D 2 / l ) ,
S = { π r 2 - r 2 ( θ - sin θ ) - R 2 2 [ sin - 1 ( r R sin θ ) - r R sin θ ] } / π r 2 ,
Z 0 = f ( D - d ) / l ;
Z = f D / l ;
Z 1 = f ( D + d ) / l ,
2 Ω = 2 Ω = 2 tan - 1 ( Φ 2 / l ) = 2 tan - 1 ( Φ 2 / l ) ,
C = 2 Ω / 2 ω = 2 tan - 1 ( Φ 2 / l ) = 2 tan - 1 ( D 2 / l ) ,
I c * - I c = ( L c * - r ) U c * / r - ( L c - r ) U c / r = ( H c * - H c ) / r - ( U c * - U c ) .
I c * - I c = ( H c * - H c ) / r
I c * - I c = I ( H c * - H c ) / H .
( H c * - H c ) / H = K ;             then I c * = K I + I c .
I c 1 * = K I 1 + I c 1 , I c 2 * = K I 2 + I c 2 , I c k * = K I k + I c k . }
S I * = S I , S II * = K S I + S II , S III * = K 2 S I + 2 K S II + S III , S IV * = S IV , S V * = K 3 S I + 3 K 2 S II + K ( 3 S III + S IV ) + S V . }
Σ S I * = Σ S I , Σ S II * = K Σ S I + Σ S II , Σ S III * = K 2 Σ S I + 2 K Σ S II + Σ S III , Σ S IV * = Σ S IV , Σ S V * = K 3 Σ S I + 3 K 2 Σ S II + K ( 3 Σ S III + Σ S IV ) + Σ S V . }
δ L k * = - 1 2 n k u k 2 1 k S I * ; S C k * = - 1 2 J 1 k S II * ; X tsk * = - 1 n k u k 2 1 k S III * ; X pk * = - 1 2 n k u k 2 1 k S IV * ; δ Y z k * = - 1 2 n k u k 2 1 k S V * , }

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