Abstract

The mutual-intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We demonstrate an optical system for displaying the mutual intensity of a one-dimensional input beam. The experimental system is based on the fact that the mutual intensity of a signal can be expressed as the ensemble averaging of a cross-correlation operation between two related optical signals. The setup consists of a Sagnac interferometer followed by an optoelectronic joint transform correlator. Experimental results demonstrate the capabilities of the mutual-intensity analyzer.

© 1998 Optical Society of America

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References

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  1. E. Wolf, Proc. R. Soc. London 230, 246 (1955).
    [CrossRef]
  2. L. Mandel and E. Wolf, Rev. Mod. Phys.231 (1965).
    [CrossRef]
  3. L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
    [CrossRef]
  4. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  5. E. Wolf, J. Opt. Soc. Am. 68, 6 (1982).
    [CrossRef]
  6. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
    [CrossRef]
  7. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
    [CrossRef]
  9. C. Iaconis and I. A. Walmsley, Opt. Lett. 21, 1783 (1996).
    [CrossRef] [PubMed]
  10. W. D. Montgomery, Opt. Lett. 2, 120 (1978).
    [CrossRef] [PubMed]
  11. J. E. Rau, J. Opt. Soc. Am 56, 1490 (1966).
    [CrossRef]
  12. C. S. Weaver and J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]

1996 (1)

1982 (2)

1978 (1)

1976 (1)

1966 (2)

1965 (1)

L. Mandel and E. Wolf, Rev. Mod. Phys.231 (1965).
[CrossRef]

1955 (1)

E. Wolf, Proc. R. Soc. London 230, 246 (1955).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Goodman, J. W.

C. S. Weaver and J. W. Goodman, Appl. Opt. 5, 1248 (1966).
[CrossRef] [PubMed]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Iaconis, C.

Mandel, L.

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

L. Mandel and E. Wolf, Rev. Mod. Phys.231 (1965).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
[CrossRef]

Montgomery, W. D.

Rau, J. E.

J. E. Rau, J. Opt. Soc. Am 56, 1490 (1966).
[CrossRef]

Walmsley, I. A.

Weaver, C. S.

Wolf, E.

E. Wolf, J. Opt. Soc. Am. 68, 6 (1982).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
[CrossRef]

L. Mandel and E. Wolf, J. Opt. Soc. Am. 66, 529 (1976).
[CrossRef]

L. Mandel and E. Wolf, Rev. Mod. Phys.231 (1965).
[CrossRef]

E. Wolf, Proc. R. Soc. London 230, 246 (1955).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
[CrossRef]

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Appl. Opt. (1)

J. Opt. Soc. Am (1)

J. E. Rau, J. Opt. Soc. Am 56, 1490 (1966).
[CrossRef]

J. Opt. Soc. Am. (3)

Opt. Lett. (2)

Proc. R. Soc. London (1)

E. Wolf, Proc. R. Soc. London 230, 246 (1955).
[CrossRef]

Rev. Mod. Phys. (1)

L. Mandel and E. Wolf, Rev. Mod. Phys.231 (1965).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, Cambridge, England, 1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Proposed experimental setup.

Fig. 2
Fig. 2

Results obtained for the coherent illumination: (a) joint power spectrum and (b) mutual intensity.

Fig. 3
Fig. 3

Results obtained for the incoherent illumination: (a) joint power spectrum and (b) mutual intensity.

Equations (10)

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WR1,R2,ν=VR1,νV*R2,ν,
VR,t=uR,texpi2πνt,
Γx1,x2=Wx1,x2,ν=ux1,tu*x2,t.
ux1,t+ux2,t2=Γ11+Γ22+Γ12+Γ21,
Γij=uxi,tu*xj,t, i,j=1,2.
lmx1,x2=ux1,t+ux2,texpimπ22, m=0,1,2,3,
4Γx1,x2=4Γ12x1,x2=m=03lmx1,x2exp-imπ2.
Γx,-y=uy,tδx*ux,tδy,
fx,y,t=uy,tδx+x0+ux-x0,tδy.
Γcohx,y=rectx/Δxrecty/Δx,Γincx,y=rectx/Δxδx-y.

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