Abstract

The space-shift-variant two-point correlation function of a transversely spatially localized optical field of arbitrary coherence at a remote plane is measured with a novel interferometric technique. The method permits reconstruction of the correlation function by a simple resorting of the measured data. In the case of a coherent field the experimentally measured correlation function is shown to factorize, as expected, and the field amplitude and phase are also reconstructed.

© 1996 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
    [CrossRef]
  2. D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, Opt. Lett. 20, 1181 (1995).
    [CrossRef] [PubMed]
  3. R. Gase, T. Gase, K. Bluthner, Opt. Lett. 20, 2045 (1995).
    [CrossRef] [PubMed]
  4. D. Kohler, L. Mandel, J. Opt. Soc. Am. 63, 126 (1972).
    [CrossRef]
  5. P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).
  6. N. Streibl, Opt. Commun. 49, 6 (1984); K. Ichikawa, A. W. Lohmann, M. Takeda, Appl. Opt. 27, 3433 (1988).
    [CrossRef] [PubMed]
  7. K. H. Brenner, A. W. Lohmann, Opt. Commun. 42, 310 (1982).
    [CrossRef]
  8. K. Creath, in Progress in Optics XXVI, E. Wolf, eds. (Elsevier, Amsterdam, 1988), p. 349.
    [CrossRef]
  9. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1989), Chap. 10.
  10. See, for example, D. Malacara, Optical Shop Testing (Wiley, New York, 1978), p. 328.
  11. If the shear is not introduced in the object space of the imaging system, then the interferograms exhibit tiltlike fringes perpendicular to the direction of shear that arise from the spherical phase front that is imposed upon the field by the lenses.

1996 (1)

S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
[CrossRef]

1995 (2)

1985 (1)

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

1984 (1)

N. Streibl, Opt. Commun. 49, 6 (1984); K. Ichikawa, A. W. Lohmann, M. Takeda, Appl. Opt. 27, 3433 (1988).
[CrossRef] [PubMed]

1982 (1)

K. H. Brenner, A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

1972 (1)

Beck, M.

Bluthner, K.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1989), Chap. 10.

Brenner, K. H.

K. H. Brenner, A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Clarke, L.

Creath, K.

K. Creath, in Progress in Optics XXVI, E. Wolf, eds. (Elsevier, Amsterdam, 1988), p. 349.
[CrossRef]

DeSantis, P.

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

Gase, R.

Gase, T.

Gori, F.

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

Guattari, G.

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

John, S.

S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
[CrossRef]

Kohler, D.

Lohmann, A. W.

K. H. Brenner, A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Malacara, D.

See, for example, D. Malacara, Optical Shop Testing (Wiley, New York, 1978), p. 328.

Mandel, L.

Mayer, A.

McAlister, D. F.

Palma, C.

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

Pang, G.

S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
[CrossRef]

Raymer, M. G.

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984); K. Ichikawa, A. W. Lohmann, M. Takeda, Appl. Opt. 27, 3433 (1988).
[CrossRef] [PubMed]

Webster, J. M.

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1989), Chap. 10.

Yang, Y.

S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
[CrossRef]

J. Biomed. Opt. (1)

S. John, G. Pang, Y. Yang, J. Biomed. Opt. 1, 180 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Photog. Sci. (1)

P. DeSantis, F. Gori, G. Guattari, C. Palma, J. M. Webster, J. Photog. Sci. 33, 197 (1985).

Opt. Commun. (2)

N. Streibl, Opt. Commun. 49, 6 (1984); K. Ichikawa, A. W. Lohmann, M. Takeda, Appl. Opt. 27, 3433 (1988).
[CrossRef] [PubMed]

K. H. Brenner, A. W. Lohmann, Opt. Commun. 42, 310 (1982).
[CrossRef]

Opt. Lett. (2)

Other (4)

K. Creath, in Progress in Optics XXVI, E. Wolf, eds. (Elsevier, Amsterdam, 1988), p. 349.
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1989), Chap. 10.

See, for example, D. Malacara, Optical Shop Testing (Wiley, New York, 1978), p. 328.

If the shear is not introduced in the object space of the imaging system, then the interferograms exhibit tiltlike fringes perpendicular to the direction of shear that arise from the spherical phase front that is imposed upon the field by the lenses.

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

Experimental apparatus: The configuration shown is used to measure Re Γ(x, x′). One measures Im Γ(x, x′) by simply rotating the half-wave plate out of the plane of the page by 45°.

Fig. 2
Fig. 2

Magnitude of the measured correlation functions for (a) the constant relative phase field and (b) the random relative phase field.

Fig. 3
Fig. 3

(a) Magnitude of the correlation function and (b) intensity profile and phase structure for the single coherent beam.

Equations (5)

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

Γ ( x , x ) = E ( x ) E * ( x ) ,
I det ( y ; s ) = Γ ( y + s 2 , y + s 2 ) + Γ ( y s 2 , y s 2 ) + 2 Re Γ ( y + s 2 , y s 2 ) ,
0 μ = d x d x | Γ ( x , x ) | 2 [ d x Γ ( x , x ) ] 2 1 ,
| E ( x ) | = Γ ( x , x ) ,
Arg [ E ( x ) ] = tan 1 [ Im Γ ( x , x ) Re Γ ( x , x ) ] + ϕ 0 .

Metrics