Abstract

No abstract available.

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1970), Ch. X.
  2. L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
    [Crossref]
  3. C. L. Mehta, J. Opt. Soc. Am. 58, 1233 (1968).
    [Crossref]
  4. D. Beard, Appl. Phys. Lett. 15, 227 (1969).
    [Crossref]
  5. J. W. Goodman, J. Opt. Soc. Am. 60, 506 (1970).
    [Crossref]
  6. D. Kohler and L. Mandel, J. Opt. Soc. Am. 63, 126 (1973).
    [Crossref]
  7. C. Drane and G. B. Parrent, Trans. IRE AP-10, 126 (1962).
  8. G. W. Swenson and N. C. Mathur, Proc. IEEE,  56, 2114 (1968).
    [Crossref]
  9. T. Hagfors and J. M. Moran, Proc. IEEE 58, 743 (1970).
    [Crossref]
  10. T. Sato and S. Wadaka, J. Acoust. Soc. Am. 58, 1013 (1975).
    [Crossref]
  11. M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  12. J. C. Leader, J. Opt. Soc. Am. 65, 740 (1975).
    [Crossref]
  13. J. W. Goodman, Proc. IEEE 53, 1688 (1965).
    [Crossref]
  14. V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971), p. 36.

1975 (2)

T. Sato and S. Wadaka, J. Acoust. Soc. Am. 58, 1013 (1975).
[Crossref]

J. C. Leader, J. Opt. Soc. Am. 65, 740 (1975).
[Crossref]

1973 (1)

1970 (2)

T. Hagfors and J. M. Moran, Proc. IEEE 58, 743 (1970).
[Crossref]

J. W. Goodman, J. Opt. Soc. Am. 60, 506 (1970).
[Crossref]

1969 (1)

D. Beard, Appl. Phys. Lett. 15, 227 (1969).
[Crossref]

1968 (2)

C. L. Mehta, J. Opt. Soc. Am. 58, 1233 (1968).
[Crossref]

G. W. Swenson and N. C. Mathur, Proc. IEEE,  56, 2114 (1968).
[Crossref]

1965 (2)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[Crossref]

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[Crossref]

1962 (1)

C. Drane and G. B. Parrent, Trans. IRE AP-10, 126 (1962).

Beard, D.

D. Beard, Appl. Phys. Lett. 15, 227 (1969).
[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, 4th ed. (Pergamon, Oxford, England, 1970), Ch. X.

Drane, C.

C. Drane and G. B. Parrent, Trans. IRE AP-10, 126 (1962).

Goodman, J. W.

Hagfors, T.

T. Hagfors and J. M. Moran, Proc. IEEE 58, 743 (1970).
[Crossref]

Kohler, D.

Leader, J. C.

Mandel, L.

D. Kohler and L. Mandel, J. Opt. Soc. Am. 63, 126 (1973).
[Crossref]

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[Crossref]

Mathur, N. C.

G. W. Swenson and N. C. Mathur, Proc. IEEE,  56, 2114 (1968).
[Crossref]

Mehta, C. L.

Moran, J. M.

T. Hagfors and J. M. Moran, Proc. IEEE 58, 743 (1970).
[Crossref]

Parrent, G. B.

C. Drane and G. B. Parrent, Trans. IRE AP-10, 126 (1962).

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

Sato, T.

T. Sato and S. Wadaka, J. Acoust. Soc. Am. 58, 1013 (1975).
[Crossref]

Swenson, G. W.

G. W. Swenson and N. C. Mathur, Proc. IEEE,  56, 2114 (1968).
[Crossref]

Tatarskii, V. I.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971), p. 36.

Wadaka, S.

T. Sato and S. Wadaka, J. Acoust. Soc. Am. 58, 1013 (1975).
[Crossref]

Wolf, E.

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[Crossref]

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1970), Ch. X.

Appl. Phys. Lett. (1)

D. Beard, Appl. Phys. Lett. 15, 227 (1969).
[Crossref]

J. Acoust. Soc. Am. (1)

T. Sato and S. Wadaka, J. Acoust. Soc. Am. 58, 1013 (1975).
[Crossref]

J. Opt. Soc. Am. (4)

Proc. IEEE (3)

G. W. Swenson and N. C. Mathur, Proc. IEEE,  56, 2114 (1968).
[Crossref]

T. Hagfors and J. M. Moran, Proc. IEEE 58, 743 (1970).
[Crossref]

J. W. Goodman, Proc. IEEE 53, 1688 (1965).
[Crossref]

Rev. Mod. Phys. (1)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 257 (1965).
[Crossref]

Trans. IRE (1)

C. Drane and G. B. Parrent, Trans. IRE AP-10, 126 (1962).

Other (3)

M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, England, 1970), Ch. X.

V. I. Tatarskii, The Effects of the Turbulent Atmosphere on Wave Propagation (Israel Program for Scientific Translations, Jerusalem, 1971), p. 36.

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

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 (3)

FIG. 1
FIG. 1

Coordinate systems of the object and observation planes. O, an object on the (u, v) plane; P1, P2, points on the object; Q1, Q2, two observation points on the detection plane, i.e., (x, y) plane; r(Pn, Qn) (n = 1, 2), distance between the points Pn and Qn; r1, r2, distances between the origin of the object plane and the point Q1, Q2, respectively; D, distance between the object and the observation planes.

FIG. 2
FIG. 2

Symmetric-scanning method in the two-dimensional case. R1, R2, detectors of the field.

FIG. 3
FIG. 3

Effects of inclination and displacement of the observation plane. If symmetric scanning is done on the (x′, y′) plane, which is inclined by θ0 for the object plane, and from ( x , y ) = ( x 0 , y 0 ) , then the image is reconstructed at ( u , v ) = ( x 0 , y 0 + D sin θ 0 ) , where u′, v′ are the coordinates conjugate to the x′, y′ coordinates.

Equations (13)

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

Γ d ( Q 1 , Q 2 ; τ ) = Γ s { P 1 , P 2 ; ( 1 / c ) [ r ( P 1 , Q 1 ) - r ( P 2 , Q 2 ) ] + τ } λ 2 r ( P 1 , Q 1 ) r ( P 2 , Q 2 ) d P 1 d P 2 ,
Γ s ( P 1 , P 2 ; τ ) = Γ s ( P 1 , P 2 ; 0 ) e j ω τ ,
Γ d ( Q 1 , Q 2 ; 0 ) e j ω τ = Γ s ( P 1 , P 2 ; 0 ) exp { j k [ r ( P 1 , Q 1 ) - r ( P 2 , Q 2 ) ] } λ 2 r ( P 1 , Q 1 ) r ( P 2 , Q 2 ) × d P 1 d P 2 e j ω τ ,
Γ s ( u 1 , v 1 , u 2 , v 2 ; 0 ) = Γ s i ( u 1 + u 2 2 , v 1 + v 2 2 ) × Γ s c ( u 1 - u 2 , v 1 - v 2 ) ,
u i = u 1 + u 2 2 , u c = u 1 - u 2 , v i = v 1 + v 2 2 , v c = v 1 - v 2 , x i = x 1 + x 2 2 , x c = x 1 - x 2 , y i = y 1 + y 2 2 , y c = y 1 - y 2 .
Γ d ( x 1 , y 1 , x 2 , y 2 ; 0 ) = exp [ j ( k / D ) ( x i x c + y i y c ) ] λ 2 D 2 × - Γ s i ( u i , v i ) exp [ - j ( k / D ) ( x c u i + y c v i ) ] × [ - Γ s c ( u c , v c ) exp [ j ( k / D ) × ( - x i u c - y i v c + u i u c + v i v c ) ] d u c d v c ] d u i d v i .
Γ d ( x 1 , y 1 , - x 1 , - y 1 ; 0 ) = 1 λ 2 D 2 × - Γ s i ( u i , v i ) exp [ - j ( 2 k / D ) ( x 1 u i + y 1 v i ) ] × [ - Γ s c ( u c , v c ) exp [ j ( k / D ) ( u i u c + v i v c ) ] d u c d v c ] d u i d v i .
Γ d ( x 1 , y 1 , - x 1 , - y 1 ; 0 ) = const - Γ s i ( u i , v i ) exp [ - j 2 k / D ( x 1 u i + y 1 v i ) ] d u i d v i .
Γ s i ( u i , v i ) = const - Γ d ( x 1 , y 1 , - x 1 , - y 1 ; 0 ) × exp [ j ( 2 k / D ) ( x 1 u i + y 1 v i ) ] × d [ ( 2 k / D ) x 1 ] d [ ( 2 k / D ) y 1 ] .
α i = α 1 + α 2 2 ,             α c = α 1 - α 2 ,             β i = β 1 + β 2 2 ,             β c = β 1 - β 2 ,
Γ d ( x 1 , y 1 , x 2 , y 2 ; 0 ) = exp [ j k ( r 1 - r 2 ) ] λ 2 r 1 r 2 × - Γ s i ( u i , v i ) exp [ - j k ( α c u i + β c v i ) ] d u i d v i × - Γ s c ( u c , v c ) exp [ - j k ( α i u c + β i v c ) ] d u c d v c .
Γ d ( x 1 , y 1 , - x 1 , - y 1 ; 0 ) = const - Γ s i ( u i , v i ) × exp [ - j 2 k ( α 1 u i + β 1 v i ) ] d u i d v i .
Γ s i ( u i , v i ) = const - Γ d ( x 1 , y 1 , - x 1 , - y 1 ; 0 ) × exp [ j 2 k ( α 1 u i + β 1 v i ) ] d ( 2 k α 1 ) d ( 2 k β 1 ) .