Abstract

On the assumption that a hologram is a superposition of zone plates, one from each point in the object, the authors have produced, by sequential printing of zone plates, holograms which reconstruct a pattern of several bright points on a dark field. The pattern may be prescribed in advance and may be three dimensional. The validity of the method is examined mathematically.

© 1968 Optical Society of America

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References

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  1. D. Gabor, Proc. Roy. Soc. London A197, 454 (1949).
  2. G. Rogers, Nature 166, 237 (1950).
    [CrossRef] [PubMed]
  3. See any introductory optics text, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc.New York, 1957) Third ed., p. 267.

1950 (1)

G. Rogers, Nature 166, 237 (1950).
[CrossRef] [PubMed]

1949 (1)

D. Gabor, Proc. Roy. Soc. London A197, 454 (1949).

Gabor, D.

D. Gabor, Proc. Roy. Soc. London A197, 454 (1949).

Jenkins, F. A.

See any introductory optics text, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc.New York, 1957) Third ed., p. 267.

Rogers, G.

G. Rogers, Nature 166, 237 (1950).
[CrossRef] [PubMed]

White, H. E.

See any introductory optics text, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc.New York, 1957) Third ed., p. 267.

Nature (1)

G. Rogers, Nature 166, 237 (1950).
[CrossRef] [PubMed]

Proc. Roy. Soc. London (1)

D. Gabor, Proc. Roy. Soc. London A197, 454 (1949).

Other (1)

See any introductory optics text, e.g., F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill Book Company, Inc.New York, 1957) Third ed., p. 267.

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Figures (6)

Fig. 1
Fig. 1

The optical system for the production of zone plates. Coherent, collimated light from the left reaches the photographic plate H partially as a plane wavefront; but part is intercepted by the divergent lens L of focal length f and reaches the plate as a spherical wavefront. The lens to plate separation is d. The spherical waves and the plane waves (extended) are tangent at C. Distance from C is called y, and x is some arbitrary reference mark.

Fig. 2
Fig. 2

Action of the zone plate in collimated light of the same wavelength as used in Fig. 1. The notation is the same as in Fig. 1. The zone plate produces a virtual point image at V and a real point image at R.

Fig. 3
Fig. 3

The real image reconstructed from a synthetic hologram. This image was recorded directly onto photographic film placed in the plane of R (Fig. 2). The image was 7 mm high.

Fig. 4
Fig. 4

The synthetic hologram which reconstructed the image of Fig. 3. During reconstruction, the edges were masked off so that each zone plate completely filled the area used. Each piece of the broken hologram reconstructs the complete image.

Fig. 5
Fig. 5

Photomicrographs of portions of two synthetic holograms. Upper figure, the hologram of a single point. Lower figure, the hologram used to produce Fig. 3. In each case the fringe spacing is of the order of 20 μ.

Fig. 6
Fig. 6

A simple and conventional scheme for making a hologram H of a pattern of small holes in an opaque screen A. D is the separation between A and H. The reference beam is brought in at the angle θ. A right-handed rectangular coordinate system (such as indicated) is used.

Equations (5)

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I ( y ) = a p 2 + a s 2 + 2 a s a p cos ( π y 2 / λ r ) .
or             π y 2 λ r = 2 n π , y max = ( 2 n λ r ) 1 / 2 .
I ( x , y , D ) = E R 2 + n E n 2 + 2 n E R E n cos [ k y θ - k Φ n ] + n m n E m E n cos [ k Φ m - k Φ n ] .
Φ n ( x - x n ) 2 + ( y - y n ) 2 2 D + Λ n .
I ( x , y , D ) = n E R n 2 + n E n 2 + 2 n E R n E n cos [ k y θ - k Φ n ] .

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