Abstract

The effects of imaging with coherent light are investigated and related to the parameters of an imaging system. Theoretical results are presented to describe the imaging parameters and the coherent field effects. The experimental results show the coherent field effects of edge ringing and shifting, speckling and field-of-view limitation. Incoherent results are presented in some cases for comparison.

© 1966 Optical Society of America

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References

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  1. T. J. Skinner, thesis, Boston University (1964).
  2. T. J. Skinner, J. Opt. Soc. Am. 53, 1350A (1963).
  3. M. Born and E. Wolf, Principles of Optics (Pergamon Press, N. Y., 1959).
  4. T. H. Maiman, Phys. Rev. 4, 1145 (1961).
    [Crossref]
  5. E. Abbe, Archiv Mikroskopische Anat. 9, 413 (1873).
    [Crossref]
  6. A. B. Porter, Phil. Mag. 11, 154 (1906).
  7. A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., Inc., New York, 1962).
  8. B. M. Oliver, Proc. IEEE 51, 220 (1963).
    [Crossref]
  9. J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).
  10. L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).Refs. 8, 9, and 10 are not intended to be a comprehensive list for this subject.
    [Crossref]
  11. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).
  12. A. S. Milinowski, J. Opt. Soc. Am. 54, 1406A (1964).
  13. T. J. Skinner, J. Opt. Soc. Am. 51, 1246 (1961).
    [Crossref]

1965 (1)

1964 (1)

A. S. Milinowski, J. Opt. Soc. Am. 54, 1406A (1964).

1963 (2)

T. J. Skinner, J. Opt. Soc. Am. 53, 1350A (1963).

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

1962 (1)

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

1961 (2)

1906 (1)

A. B. Porter, Phil. Mag. 11, 154 (1906).

1873 (1)

E. Abbe, Archiv Mikroskopische Anat. 9, 413 (1873).
[Crossref]

Abbe, E.

E. Abbe, Archiv Mikroskopische Anat. 9, 413 (1873).
[Crossref]

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, N. Y., 1959).

Goldfischer, L. I.

Gordon, E. I.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Maiman, T. H.

T. H. Maiman, Phys. Rev. 4, 1145 (1961).
[Crossref]

Milinowski, A. S.

A. S. Milinowski, J. Opt. Soc. Am. 54, 1406A (1964).

Oliver, B. M.

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

Papoulis, A.

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., Inc., New York, 1962).

Parrent, G. B.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

Porter, A. B.

A. B. Porter, Phil. Mag. 11, 154 (1906).

Rigden, J. D.

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Skinner, T. J.

T. J. Skinner, J. Opt. Soc. Am. 53, 1350A (1963).

T. J. Skinner, J. Opt. Soc. Am. 51, 1246 (1961).
[Crossref]

T. J. Skinner, thesis, Boston University (1964).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon Press, N. Y., 1959).

Archiv Mikroskopische Anat. (1)

E. Abbe, Archiv Mikroskopische Anat. 9, 413 (1873).
[Crossref]

J. Opt. Soc. Am. (4)

Phil. Mag. (1)

A. B. Porter, Phil. Mag. 11, 154 (1906).

Phys. Rev. (1)

T. H. Maiman, Phys. Rev. 4, 1145 (1961).
[Crossref]

Proc. IEEE (1)

B. M. Oliver, Proc. IEEE 51, 220 (1963).
[Crossref]

Proc. IRE (1)

J. D. Rigden and E. I. Gordon, Proc. IRE 50, 2367 (1962).

Other (4)

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill Book Co., Inc., New York, 1962).

T. J. Skinner, thesis, Boston University (1964).

M. Born and E. Wolf, Principles of Optics (Pergamon Press, N. Y., 1959).

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice Hall, Englewood Cliffs, N. J., 1964).

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Figures (12)

F. 1
F. 1

Optical system diagram for imaging with coherent and incoherent fields.

F. 2
F. 2

Coherent (a) and incoherent (b) images of an edge.

F. 3
F. 3

Microdensitometer traces of a coherent (a) and incoherent (b) image of an edge.

F. 4
F. 4

Theoretical plot of the intensity distribution for a coherent and incoherent image of an edge.

F. 5
F. 5

Transilluminated coherent (a) and incoherent (b) image of a high-contrast resolution target.

F. 6
F. 6

Optical system for imaging with reflected coherent light.

F. 7
F. 7

Coherent (a) and incoherent (b) image of a high-contrast resolution target with reflected light.

F. 8
F. 8

Speckling density in a coherent image of ground glass with an (a) f/9 and (b) f/64 imaging system.

F. 9
F. 9

Coherent image of a matte surface resolution target print.

F. 10
F. 10

Intensity distribution in the Fraunhofer plane of one (a) and two (b) pinholes illuminated with a diffuse coherent field.

F. 11
F. 11

Intensity distribution in the Fraunhofer plane of two pinholes illuminated with a time-varying diffuse coherent field.

F. 12
F. 12

Photograph of a high-contrast resolution target illuminated with a gas laser diffused with a milk–water solution.

Tables (2)

Tables Icon

Table I Speckling density.

Tables Icon

Table II Field of view.

Equations (9)

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I im ( x ) = | ψ ob ( y ) a sinc π a ( x + m y ) ( 1 + m ) λ f d y | 2 ,
I im ( x ) = I ob ( y ) a 2 sinc 2 π a ( x + m y ) ( 1 + m ) λ f d y ,
( i . e . , I ob ( y ) = 0 , y < 0 I 0 , y 0 )
I im ( r ) = 1 2 + 1 / π Si ( r / 2 ) 2 for coherent illumination
I im ( r ) = 1 2 + 1 / π Si ( r ) ( 1 cos r ) / r for incoherent illumination ,
D = 0.212 ( 1 + m ) λ f / a .
f c = m a / ( 1 + m ) λ f .
I im = I ob / m 2 ,
tan θ = x / s m a / 2 ( m + 1 ) f ,