Abstract

Reconstructed image scanning can be provided by simple rotation of a hologram. Motion of the image is described as a function of the rotated angle. Application to the problem of beam forming and deflection is discussed.

© 1967 Optical Society of America

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References

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  1. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [CrossRef]
  2. E. N. Leith, J. Upatnicks, K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
    [CrossRef]
  3. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, N. Massey, Appl. Opt. 5, 1303 (1966).
    [CrossRef] [PubMed]
  4. N. George, J. W. Matthew, Appl. Phys. Letters 9, 212 (1966).
    [CrossRef]
  5. G. B. Parrent, G. O. Reynolds, Soc. Phot. Instr. Engrs. J. 3, 219 (1965).

1966

1965

Appl. Opt.

Appl. Phys. Letters

N. George, J. W. Matthew, Appl. Phys. Letters 9, 212 (1966).
[CrossRef]

J. Opt. Soc. Am.

Soc. Phot. Instr. Engrs. J.

G. B. Parrent, G. O. Reynolds, Soc. Phot. Instr. Engrs. J. 3, 219 (1965).

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Figures (3)

Fig. 1
Fig. 1

Describing the location of the center of curvature Po for a spherical wave. P(x,y) is a point in the xy plane.

Fig. 2
Fig. 2

A hologram of a point object is rotated relative to the fixed xyz coordinates giving a reconstructed image which rotates in the image space.

Fig. 3
Fig. 3

Intensity distribution of the scannable reconstructed real image of a (simulated) point object.

Equations (7)

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Φ = ( 2 π / λ c ) r c + ( 2 π / λ o ) r r - ( 2 π / λ o ) r o ,
Φ = k c 2 { x 2 [ 1 R c + μ m 2 R r - μ m 2 R o ] + y 2 [ 1 R c + μ m 2 R r - μ m 2 R o ] - 2 x [ x c R c + μ ( x r cos α - y r sin α ) m R r - μ ( x o cos α - y o sin α ) m R o ] - 2 y [ y c R c + μ ( x r sin α + y r cos α ) m R r - μ ( x o sin α + y o cos α ) m R o ] + ( R c + R r - R o ) + ( Δ c + Δ r - Δ o ) } ,
k c = ( 2 π / λ c ) , μ = ( λ c / λ o )
x b = R b [ x c R c + μ m ( x r R r - x o R o ) cos α - μ m ( y r R r - y o R o ) sin α ] , y b = R b [ y c R c + μ m ( x r R r - x o R o ) sin α + μ m ( y r R r - y o R o ) cos α ] , R b = m 2 R c R r R o m 2 R r R o + μ R c R o - μ R c R r .
[ ( x r R r - x o R o ) 2 + ( y r R r - y o R o ) 2 ] μ 2 / m 2 R b 2 .
x b = R b [ sin β c cos α c + ( μ / m ) ( sin β r cos α r - sin β o cos α o ) cos α - ( μ / m ) ( sin β r sin α r - sin β o sin α o ) sin α ] , y b = R t [ sin β c sin α c + ( μ / m ) ( sin β r cos α r - sin β o cos α o ) sin α + ( μ / m ) ( sin β r sin α r - sin β o sin α o ) cos α ] .
[ ( sin β r cos α r - sin β o cos α o ) 2 + ( sin β r sin α r - sin β o sin α o ) 2 ] u 2 m 2 R b 2 .

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