Abstract

The influence of spatial coherence on holographic processes is treated theoretically. An experimental check is reported.

© 1967 Optical Society of America

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References

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  1. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949). E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 54, 1295 (1964).
    [CrossRef]
  2. A. W. Lohmann, J. Opt. Soc. Am. 55, 1555 (1965).
    [CrossRef]
  3. P. J. Peters, Appl. Phys. Letters 8, 209 (1966).
    [CrossRef]
  4. G. W. Stroke and D. G. Falconer, Phys. Letters 15, 238 (1965).
    [CrossRef]
  5. G. W. Stroke and R. C. Restrick, Appl. Phys. Letters 7, 229 (1965).
    [CrossRef]
  6. D. J. De Bitetto, Appl. Phys. Letters 8, 1555 (1966).
    [CrossRef]
  7. M. Lurie, J. Opt. Soc. Am. 56, 1369 (1966).
    [CrossRef]
  8. M. Lurie, J. Opt. Soc. Am. 56, 1415A (1966).
    [CrossRef]
  9. L. Mandel, Congrès sur les Progrès Recents en Optique Physique, Paris2–7 Mai 1966, and J. Opt. Soc. Am. 56, 1636 (1966).
    [CrossRef]
  10. G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).
  11. While this work was being done, a paper appeared on the same subject [ Reynolds and De Velis, IEEE Trans. Antennas Propagation AP-15, 41 (1967)]. In that paper the authors calculated the effect of spatial coherence by numerical integration in the case of field produced by a slit source.
    [CrossRef]
  12. W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  13. M. Born and E. Wolf, Principles of Optics, 2nd ed. (Pergamon Press, New York, 1964).
  14. For an account on this subject see, for example, Ref. 13.
  15. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Company, New York, 1965).

1967 (1)

While this work was being done, a paper appeared on the same subject [ Reynolds and De Velis, IEEE Trans. Antennas Propagation AP-15, 41 (1967)]. In that paper the authors calculated the effect of spatial coherence by numerical integration in the case of field produced by a slit source.
[CrossRef]

1966 (5)

M. Lurie, J. Opt. Soc. Am. 56, 1369 (1966).
[CrossRef]

P. J. Peters, Appl. Phys. Letters 8, 209 (1966).
[CrossRef]

D. J. De Bitetto, Appl. Phys. Letters 8, 1555 (1966).
[CrossRef]

M. Lurie, J. Opt. Soc. Am. 56, 1415A (1966).
[CrossRef]

G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).

1965 (3)

G. W. Stroke and D. G. Falconer, Phys. Letters 15, 238 (1965).
[CrossRef]

G. W. Stroke and R. C. Restrick, Appl. Phys. Letters 7, 229 (1965).
[CrossRef]

A. W. Lohmann, J. Opt. Soc. Am. 55, 1555 (1965).
[CrossRef]

1964 (1)

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

1949 (1)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949). E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 54, 1295 (1964).
[CrossRef]

Born, M.

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

De Bitetto, D. J.

D. J. De Bitetto, Appl. Phys. Letters 8, 1555 (1966).
[CrossRef]

De Velis,

While this work was being done, a paper appeared on the same subject [ Reynolds and De Velis, IEEE Trans. Antennas Propagation AP-15, 41 (1967)]. In that paper the authors calculated the effect of spatial coherence by numerical integration in the case of field produced by a slit source.
[CrossRef]

Falconer, D. G.

G. W. Stroke and D. G. Falconer, Phys. Letters 15, 238 (1965).
[CrossRef]

Gabor, D.

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949). E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 54, 1295 (1964).
[CrossRef]

Golovei, P. M.

G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).

Kalinktna, I. K.

G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).

Kosourov, G. I.

G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).

Lohmann, A. W.

Lurie, M.

M. Lurie, J. Opt. Soc. Am. 56, 1415A (1966).
[CrossRef]

M. Lurie, J. Opt. Soc. Am. 56, 1369 (1966).
[CrossRef]

Mandel, L.

L. Mandel, Congrès sur les Progrès Recents en Optique Physique, Paris2–7 Mai 1966, and J. Opt. Soc. Am. 56, 1636 (1966).
[CrossRef]

Martienssen, W.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Company, New York, 1965).

Peters, P. J.

P. J. Peters, Appl. Phys. Letters 8, 209 (1966).
[CrossRef]

Restrick, R. C.

G. W. Stroke and R. C. Restrick, Appl. Phys. Letters 7, 229 (1965).
[CrossRef]

Reynolds,

While this work was being done, a paper appeared on the same subject [ Reynolds and De Velis, IEEE Trans. Antennas Propagation AP-15, 41 (1967)]. In that paper the authors calculated the effect of spatial coherence by numerical integration in the case of field produced by a slit source.
[CrossRef]

Spiller, E.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Stroke, G. W.

G. W. Stroke and R. C. Restrick, Appl. Phys. Letters 7, 229 (1965).
[CrossRef]

G. W. Stroke and D. G. Falconer, Phys. Letters 15, 238 (1965).
[CrossRef]

Wolf, E.

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

Am. J. Phys. (1)

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Appl. Phys. Letters (3)

P. J. Peters, Appl. Phys. Letters 8, 209 (1966).
[CrossRef]

G. W. Stroke and R. C. Restrick, Appl. Phys. Letters 7, 229 (1965).
[CrossRef]

D. J. De Bitetto, Appl. Phys. Letters 8, 1555 (1966).
[CrossRef]

IEEE Trans. Antennas Propagation (1)

While this work was being done, a paper appeared on the same subject [ Reynolds and De Velis, IEEE Trans. Antennas Propagation AP-15, 41 (1967)]. In that paper the authors calculated the effect of spatial coherence by numerical integration in the case of field produced by a slit source.
[CrossRef]

J. Opt. Soc. Am. (3)

JETP Letters (1)

G. I. Kosourov, I. K. Kalinktna, and P. M. Golovei, JETP Letters 4, 57 (1966).

Phys. Letters (1)

G. W. Stroke and D. G. Falconer, Phys. Letters 15, 238 (1965).
[CrossRef]

Proc. Roy. Soc. (London) (1)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949). E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 54, 1295 (1964).
[CrossRef]

Other (4)

L. Mandel, Congrès sur les Progrès Recents en Optique Physique, Paris2–7 Mai 1966, and J. Opt. Soc. Am. 56, 1636 (1966).
[CrossRef]

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

For an account on this subject see, for example, Ref. 13.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Company, New York, 1965).

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Figures (3)

Fig. 1
Fig. 1

Experimental arrangement for the construction process with spatially partially coherent light. The object consists of a hole in an opaque screen.

Fig. 2
Fig. 2

Detail of the reconstructed image made with coherent light. The lines which are well resolved are 200 μ, 100 μ, and 80 μ apart.

Fig. 3
Fig. 3

Detail of the reconstructed image made with spatially partially coherent light. The lines still resolved are 200 μ apart.

Equations (16)

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γ 12 ( τ ) = μ 12 e 2 π i ν τ ,
μ 12 = μ ( ξ ) ,
I ( ξ ) = I 0 { 2 + μ ( ξ ) e 2 π i ν τ + μ * ( ξ ) e 2 π i ν τ } ,
I ( ξ ) = I 0 { 2 + μ ( ξ ) exp [ 2 π i ( ν / c ) ξ θ ] + μ * ( ξ ) exp [ 2 π i ( ν / c ) θ ξ ] } .
χ ( φ ) = + μ ( ξ ) exp [ 2 π i ( ν / c ) ( θ φ ) ξ ] d ξ .
Δ φ = { π / 2 + π / 2 ( φ θ ) 2 | χ ( φ ) | 2 d φ π / 2 + π / 2 | χ ( φ ) | 2 d φ } 1 2 .
Δ φ = c 2 π ν { + | d μ ( ξ ) d ξ | 2 d ξ + | μ ( ξ ) | 2 d ξ } 1 2 ,
μ ( ξ ) = exp [ ( 2 π σ / λ ) 2 | ξ | / a ] ,
d = f Δ φ = 2 π f σ 2 / λ a ,
d 20 μ .
| μ 12 | = | exp ( 2 π i / λ ) Δ δ 12 | ,
Δ δ 12 = δ ( P 1 ) δ ( P 2 )
σ Δ δ 12 = 2 σ 2 [ 1 exp ( | ξ | / a ) ] ;
exp { i η ( 2 π / λ ) 1 2 σ 2 ( 4 π 2 / λ 2 ) } ,
| μ 12 | = | exp { ( 2 π / λ ) 2 σ 2 [ 1 exp ( | ξ | / a ) ] } |
| μ 12 | | exp { ( 2 π / λ ) 2 σ 2 | ξ | / a } | .