Abstract

A new method for registering stereograms in which an orientated speckle pattern supplies the desired directivity for obtaining horizontal parallax is presented. This is accomplished by employing an optical system whose pupil consists of a double-fan aperture. In this way, the stereogram has a built-in reconstruction mechanism, and the stereo image can be observed with almost any extended white light source and without using any optical device. Furthermore, more than two points of view of the 3-D scene can be stored in a single plate by adequate positioning of the above-mentioned aperture.

© 1983 Optical Society of America

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References

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  1. For example, J. P. C. Southall, Mirrors, Prisms and Lenses (Dover, New York, 1964), pp. 747–761.
  2. J. Hamasaki, in Proceedings, Optics in Four Dimensions Conference, L. M. Narducci, M. A. Machado, Eds. (AIP, New York, 1981), pp. 531–556.
  3. G. G. Mu, C. K. Chiang, H. K. Liu, Opt. Lett. 6, 263 (1981).
    [CrossRef] [PubMed]
  4. V. Kopf, International Optical Computing Conference, Zürich (IEEE, New York, 1974), Catalog No. 74, p. 862-3C.
  5. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1981

Chiang, C. K.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hamasaki, J.

J. Hamasaki, in Proceedings, Optics in Four Dimensions Conference, L. M. Narducci, M. A. Machado, Eds. (AIP, New York, 1981), pp. 531–556.

Kopf, V.

V. Kopf, International Optical Computing Conference, Zürich (IEEE, New York, 1974), Catalog No. 74, p. 862-3C.

Liu, H. K.

Mu, G. G.

Southall, J. P. C.

For example, J. P. C. Southall, Mirrors, Prisms and Lenses (Dover, New York, 1964), pp. 747–761.

Opt. Lett.

Other

V. Kopf, International Optical Computing Conference, Zürich (IEEE, New York, 1974), Catalog No. 74, p. 862-3C.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

For example, J. P. C. Southall, Mirrors, Prisms and Lenses (Dover, New York, 1964), pp. 747–761.

J. Hamasaki, in Proceedings, Optics in Four Dimensions Conference, L. M. Narducci, M. A. Machado, Eds. (AIP, New York, 1981), pp. 531–556.

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Figures (6)

Fig. 1
Fig. 1

Schematic arrangement of the experimental setup used for obtaining an orientated speckle pattern. A lens L1 collimates the light from a coherent source S. A second lens L2, provided with a mask M, images a diffuser D on a photosensitive plate H.

Fig. 2
Fig. 2

(a) Scheme of the double-fan aperture employed. (b) Photograph of the optical Fourier transform of the aperture shown in (a). (c) Photograph of the optical Fourier transform of an orientated speckle pattern register corresponding to a double exposure in which the double-fan aperture was rotated 60°.

Fig. 3
Fig. 3

Graph of the normalized autocorrelation function corresponding to the double-fan pupil function. The u axis is parallel to the bisector of both circular sectors of the pupil.

Fig. 4
Fig. 4

Schematic arrangement of the experimental setup corresponding to the Fresnel geometry: S is a laser source; L1 is a collimating lens; D is a diffuser; M is the mask; T is a register of one point of view of a 3-D object; and H is the photosensitive plate.

Fig. 5
Fig. 5

Schematic arrangement of an experimental setup employed for recording stereograms: S is a laser source; O is a 3-D object; M is the mask; and C is a photographic camera.

Fig. 6
Fig. 6

(a), (b), and (c) show the images corresponding to three different points of view of a bibelot used as a 3-D object.

Equations (9)

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U ( x , y ) = D ( x , y ) * h ( x , y ) ,
I ( x , y ) = | D ( x , y ) * h ( x , y ) | 2 .
t ˜ ( u , υ ) = F { t ( x , y ) } = k 1 δ ( u , υ ) k 2 [ F { D ( x , y ) * h ( x , y ) } F { D ( x , y ) * h ( x , y ) } ] ,
t ˜ ( u , υ ) = k + D ˜ ( u , υ ) P ( s ) ( u , υ ) D ˜ * ( u + u , υ + υ ) × P ( s ) ( u + u , υ + υ ) d u d υ .
Δ ( u , υ ; u , υ ) = D ˜ ( u , υ ) D ˜ * ( u + u , υ + υ )
t ˜ ( u , υ ) = P ( s ) ( u , υ ) P ( s ) ( u + u , υ + υ ) Δ ( u , υ ; u , υ ) d u d υ .
( u 0 , υ 0 ) = P ( s ) ( u , υ ) P ( s ) ( u + u 0 , υ + υ 0 ) d u d υ = [ P ( s ) P ( s ) ] ( u 0 , υ 0 ) .
t ˜ ( u , υ ) = ( u , υ ) Δ ( u , υ ; u , υ ) d u d υ = Δ ¯ ( u , υ ) ( u , υ ) ,
t ˜ ( u , υ ) = Δ ¯ ( u , υ ) [ P ( s ) ( u , υ ) P ( s ) ( u , υ ) ] .

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