Abstract

An analogy is drawn between holographic imaging with coherent light and interferometric imaging with incoherent light. By means of a spatially offset incoherent reference source, the amplitude and phase of the complex coherence factor of an incoherent object may be encoded as amplitude and phase modulations of a function derived from classical visibility measurements. This imaging technique shares several properties with holography, including the ability to image through a distorting medium and the ability to form three-dimensional images.

© 1970 Optical Society of America

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References

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  1. D. Gabor, Nature 161, 777 (1948).
    [Crossref]
  2. J. DeVelis and G. Reynolds, Theory and Applications of Holography (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967).
  3. Howard K. Smith, Principles of Holography (John Wiley & Sons, Inc., New York, 1969).
  4. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).
    [Crossref]
  5. C. L. Mehta, J. Opt. Soc. Am. 58, 1233 (1968).
    [Crossref]
  6. M. Born and E. Wolf, Principles of Optics, 2nd rev. ed. (Pergamon Press, Inc., New York, 1964), p. 508.
  7. E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
    [Crossref]
  8. P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
    [Crossref]
  9. A. Walther, Opt. Acta 10, 41 (1963).
    [Crossref]
  10. D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
    [Crossref]
  11. J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
    [Crossref]
  12. J. D. Gaskill, J. Opt. Soc. Am. 58, 600 (1968).
    [Crossref]
  13. J. D. Gaskill, J. Opt. Soc. Am. 59, 308 (1969).
    [Crossref]
  14. A. Kozma and N. Massey, Appl. Opt. 8, 393 (1969).
    [Crossref] [PubMed]
  15. A. T. Moffett, IEEE Trans. Ant. Prop. AP-16, 172 (1968).
    [Crossref]
  16. T. D. Beard, J. Opt. Soc. Am. 59, 1525A (1969).

1969 (3)

1968 (3)

1966 (2)

D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[Crossref]

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

1963 (3)

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[Crossref]

A. Walther, Opt. Acta 10, 41 (1963).
[Crossref]

E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).
[Crossref]

1962 (1)

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[Crossref]

1948 (1)

D. Gabor, Nature 161, 777 (1948).
[Crossref]

Beard, T. D.

T. D. Beard, J. Opt. Soc. Am. 59, 1525A (1969).

Born, M.

M. Born and E. Wolf, Principles of Optics, 2nd rev. ed. (Pergamon Press, Inc., New York, 1964), p. 508.

DeVelis, J.

J. DeVelis and G. Reynolds, Theory and Applications of Holography (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967).

Gabor, D.

Gaskill, J. D.

Goodman, J. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

Goss, W. P.

Huntley, W. H.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

Jackson, D. W.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

Kozma, A.

Lehmann, M.

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

Leith, E. N.

Marathay, A. S.

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[Crossref]

Massey, N.

Mehta, C. L.

Moffett, A. T.

A. T. Moffett, IEEE Trans. Ant. Prop. AP-16, 172 (1968).
[Crossref]

Reynolds, G.

J. DeVelis and G. Reynolds, Theory and Applications of Holography (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967).

Roman, P.

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[Crossref]

Smith, Howard K.

Howard K. Smith, Principles of Holography (John Wiley & Sons, Inc., New York, 1969).

Upatnieks, J.

Walther, A.

A. Walther, Opt. Acta 10, 41 (1963).
[Crossref]

Wolf, E.

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 2nd rev. ed. (Pergamon Press, Inc., New York, 1964), p. 508.

Appl. Opt. (1)

Appl. Phys. Letters (1)

J. W. Goodman, W. H. Huntley, D. W. Jackson, and M. Lehmann, Appl. Phys. Letters 8, 311 (1966).
[Crossref]

IEEE Trans. Ant. Prop. (1)

A. T. Moffett, IEEE Trans. Ant. Prop. AP-16, 172 (1968).
[Crossref]

J. Opt. Soc. Am. (6)

Nature (1)

D. Gabor, Nature 161, 777 (1948).
[Crossref]

Nuovo Cimento (1)

P. Roman and A. S. Marathay, Nuovo Cimento 30, 1452 (1963).
[Crossref]

Opt. Acta (1)

A. Walther, Opt. Acta 10, 41 (1963).
[Crossref]

Proc. Phys. Soc. (London) (1)

E. Wolf, Proc. Phys. Soc. (London) 80, 1269 (1962).
[Crossref]

Other (3)

J. DeVelis and G. Reynolds, Theory and Applications of Holography (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1967).

Howard K. Smith, Principles of Holography (John Wiley & Sons, Inc., New York, 1969).

M. Born and E. Wolf, Principles of Optics, 2nd rev. ed. (Pergamon Press, Inc., New York, 1964), p. 508.

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Figures (3)

Fig. 1
Fig. 1

Recording a lensless-Fourier-transform hologram.

Fig. 2
Fig. 2

Interferometric imaging with (a) Young’s two-pinhole interference, (b) a Fizeau stellar interferometer, and (c) a Michelson stellar interferometer.

Fig. 3
Fig. 3

Interferometric imaging through a distorting medium.

Equations (15)

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U ( x ) = A exp [ j π λ z ( x - ξ r ) 2 ] + a ( x ) exp [ j ψ ( x ) ] exp [ j π λ z x 2 ] .
I ( x ) = A 2 + a 2 ( x ) + 2 A a ( x ) cos [ 2 π ξ r λ z x + ψ ( x ) + ϕ ] ,
μ 12 ( s ) = 1 I 0 - I ( ξ ) exp ( - j 2 π λ z ξ s ) d ξ ,
I 0 = - I ( ξ ) d ξ ,
I ˜ ( ξ ) = I r δ ( ξ - ξ r ) + I ( ξ ) .
μ ˜ 12 ( s ) = I r exp ( - j ( 2 π / λ z ) ξ r s ) + I 0 μ 12 ( s ) I r + I 0 ,
μ ˜ 12 ( s ) 2 = ( I r + I 0 ) - 2 { I r 2 + I 0 2 V 2 ( s ) + 2 I r I 0 V ( s ) cos [ 2 π ξ r λ z s + ψ ( s ) ] } ,
μ 12 ( s ) = I 0 V ( s ) e j ψ ( s ) exp [ j ( θ 1 - θ 2 ) ] ,
μ ˜ 12 ( s ) = 1 I r + I 0 { I r exp ( - j 2 π ξ r λ z s ) exp [ j ( θ 1 - θ 2 ) ] + I 0 V ( s ) e j ψ ( s ) exp [ j ( θ 1 - θ 2 ) ] }
μ ˜ 12 ( s ) 2 = ( I r + I 0 ) - 2 { I r 2 + I 0 2 V 2 ( s ) + 2 I r I 0 cos [ 2 π ξ r λ z s + ψ ( s ) ] } .
μ 12 ( x 1 , x 2 ) = exp ( j π s 2 λ z ) exp ( j 2 π x 2 s λ z ) × 1 I 0 - I ( ξ ) exp ( - j 2 π λ z ξ s ) d ξ .
I ˜ ( ξ ) = I r δ ( ξ - ξ r ; z r ) + I 0 δ ( ξ - ξ 0 ; z 0 ) .
μ ˜ 12 ( s ) = ( I r + I 0 ) - 1 { I r exp [ j ( π s 2 λ z r - 2 π λ z r ξ r s ) ] + I 0 exp [ j ( π s 2 λ z 0 - 2 π λ z 0 ξ 0 s ) ] } ,
μ ˜ 12 ( s ) 2 = ( I r + I 0 ) - 2 { I r 2 + I 0 2 + 2 I r I 0 cos [ 2 π λ ( ξ r z r - ξ 0 z 0 ) s + π s 2 λ ( 1 z r - 1 z 0 ) ] } .
f = z r z 0 / ( z r - z 0 ) .