Abstract

Two image-coding capabilities associated with far-field holograms are analytically and experimentally evaluated. It is demonstrated that preprocessed information concerning the shape of a small object can be efficiently coded into the fringe structure associated with a far-field hologram. In addition, the resultant record has a smaller bandwidth than the original object, and this reduces the resolution requirements when the hologram is used as the input to an information processing system.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. A. Tyler, B. J. Thompson, Opt. Acta 23, 685 (1976).
    [CrossRef]
  2. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 753.
  4. H. M. Smith, Principles of Holography (Wiley, New York, 1975), Chap. 3.
  5. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]

1976 (1)

G. A. Tyler, B. J. Thompson, Opt. Acta 23, 685 (1976).
[CrossRef]

1964 (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 753.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

Smith, H. M.

H. M. Smith, Principles of Holography (Wiley, New York, 1975), Chap. 3.

Thompson, B. J.

G. A. Tyler, B. J. Thompson, Opt. Acta 23, 685 (1976).
[CrossRef]

Tyler, G. A.

G. A. Tyler, B. J. Thompson, Opt. Acta 23, 685 (1976).
[CrossRef]

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 753.

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Acta (1)

G. A. Tyler, B. J. Thompson, Opt. Acta 23, 685 (1976).
[CrossRef]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), p. 753.

H. M. Smith, Principles of Holography (Wiley, New York, 1975), Chap. 3.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Geometry associated with far-field hologram formation.

Fig. 2
Fig. 2

Optical Fourier transforms: (a) wire as input; (b) plane wave hologram of wire as input; (c) spherical wave hologram of wire as input.

Fig. 3
Fig. 3

Summary of space bandwidth relationships.

Fig. 4
Fig. 4

Resolution enhancement experiment.

Fig. 5
Fig. 5

Results of resolution enhancement experiment: (a) image of two glass spheres with stop wide open; (b) image of object in (a) with stop closed; (c) resulting image when spherical wave hologram is used as the input to the system with stop position as in (b); (d) image of a glass sphere and rectangle; (e) image of object in (d) with stop position as in (b); (f) resulting image when spherical wave hologram is used as the input to the system with stop position as in (b).

Fig. 6
Fig. 6

(a) Far-field hologram of wire; (b) densitometer trace; (c) computer plot (after Tyler and Thompson1).

Fig. 7
Fig. 7

Correlation experiment.

Fig. 8
Fig. 8

Results of correlation experiment: (a) the array (black denotes holes); (b) Fourier transform of (a) and illuminating function of (d); (c) resulting correlation peaks in image plane of (d); (d) hologram of 90-μm glass sphere.

Equations (7)

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

[ 1 A ( ξ , η ) ] ( { exp [ i k R + i k 2 R ( ξ 2 + η 2 ) ] } / R ) ,
π λ ( 1 z + 1 R ) ( ξ 2 + η 2 ) max 1 ,
I ( x , y ) = | 1 + i ( R + z ) λ R z exp [ i k 2 z 0 ( x 2 + y 2 ) ] A ˜ ( x λ z , y λ z ) | 2 ,
A ˜ ( x λ z , y λ z ) = A ( ξ , η ) × exp { 2 π i [ ξ ( x λ z ) + η ( y λ z ) ] } d ξ d η .
I ˜ ( x λ f , y λ f ) = I ( x , y ) × exp { 2 π i [ x ( x λ f ) + y ( y λ f ) ] } d x d y ,
I ˜ ( x λ f , y λ f ) = δ ( x λ f , y λ f ) ( 1 + z R ) 2 × exp [ i π λ f ( z 0 f ) ( x 2 + y 2 ) ] A ˜ [ x λ f ( 1 + z R ) , y λ f ( 1 + z R ) ] ( 1 + z R ) 2 exp [ i π λ f ( z 0 f ) ( x 2 + y 2 ) ] × A ˜ * [ x λ f ( 1 + z R ) , y λ f ( 1 + z R ) ] + ( R + z R ) 2 A * ( α , β ) A ( α z f x , β z f y ) d α d β ,
V ( μ , ν ) = 1 exp [ i k 2 z ( μ 2 + ν 2 ) ] λ 2 z 2 × exp [ i k 2 z ( ξ 2 + η 2 ) ] A * ( ξ , η ) P ˜ [ ( μ ξ ) λ z , ( ν η ) λ z ] d ξ d η + i exp [ i k 4 z ( μ 2 + ν 2 ) ] 2 λ z A ˜ ( μ 2 λ z , ν 2 λ z ) + 1 λ 2 z 2 | A ˜ ( μ λ z , ν λ z ) | 2 ,

Metrics