Abstract

The mutual intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We propose to use the mutual intensity as a carrier of information to avoid speckle noise in coherent illumination systems and to permit the use of complex functions that are prohibited spatially incoherent sources. To do this we require methods for encoding the information as a coherence function. An optical system for synthesizing a beam with a given mutual intensity function is proposed. The optical system permits the synthesis of any desired mutual intensity function. The illumination is supplied by a quasi-monochromatic, spatially incoherent source. Experimental results demonstrate the performance of this system for several cases.

© 1999 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. 37, 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/Interscience, Toronto, Canada, 1985).
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  9. A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A (to be published ).
  10. D. Mendlovic, G. Shabtay, A. W. Lohmann, and N. Konforti, Opt. Lett. 23, 1084 (1998).
    [CrossRef]
  11. J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
    [CrossRef]
  12. T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
    [CrossRef]
  13. H. Fujii and T. Asakura, Optik 39, 99 (1973).
  14. H. Fujii and T. Asakura, Optik 39, 284 (1973).
  15. M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
    [CrossRef]

1998 (1)

1996 (1)

M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

1982 (2)

1976 (1)

1973 (2)

H. Fujii and T. Asakura, Optik 39, 99 (1973).

H. Fujii and T. Asakura, Optik 39, 284 (1973).

1972 (1)

T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

1965 (1)

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

1955 (1)

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

Asakura, T.

H. Fujii and T. Asakura, Optik 39, 284 (1973).

H. Fujii and T. Asakura, Optik 39, 99 (1973).

T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Born, M.

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

Bunch, J. R.

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
[CrossRef]

Dongarra, J. J.

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
[CrossRef]

Erden, M.

M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

Fujii, H.

H. Fujii and T. Asakura, Optik 39, 284 (1973).

H. Fujii and T. Asakura, Optik 39, 99 (1973).

T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley/Interscience, Toronto, Canada, 1985).

Konforti, N.

Lohmann, A. W.

D. Mendlovic, G. Shabtay, A. W. Lohmann, and N. Konforti, Opt. Lett. 23, 1084 (1998).
[CrossRef]

A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A (to be published ).

Mandel, L.

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

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

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

Mendlovic, D.

D. Mendlovic, G. Shabtay, A. W. Lohmann, and N. Konforti, Opt. Lett. 23, 1084 (1998).
[CrossRef]

M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A (to be published ).

Moler, C. B.

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
[CrossRef]

Murata, K.

T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Ozaktas, H.

M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

Shabtay, G.

D. Mendlovic, G. Shabtay, A. W. Lohmann, and N. Konforti, Opt. Lett. 23, 1084 (1998).
[CrossRef]

A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A (to be published ).

Stewart, G. W.

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
[CrossRef]

Wolf, E.

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

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

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

L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
[CrossRef]

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

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

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

J. Opt. Soc. Am. (3)

Opt. Acta (1)

T. Asakura, H. Fujii, and K. Murata, Opt. Acta 19, 273 (1972).
[CrossRef]

Opt. Commun. (1)

M. Erden, H. Ozaktas, and D. Mendlovic, Opt. Commun. 125, 288 (1996).
[CrossRef]

Opt. Lett. (1)

Optik (2)

H. Fujii and T. Asakura, Optik 39, 99 (1973).

H. Fujii and T. Asakura, Optik 39, 284 (1973).

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. 37, 231 (1965).
[CrossRef]

Other (5)

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

J. W. Goodman, Statistical Optics (Wiley/Interscience, Toronto, Canada, 1985).

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

A. W. Lohmann, D. Mendlovic, and G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A (to be published ).

J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK Users' Guide (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1979).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for measuring spatial coherence.

Fig. 2
Fig. 2

Proposed system for synthesizing a light beam with a specific spatial coherence distribution.

Fig. 3
Fig. 3

Coherent case: (a) mask Mx,y, (b) joint power spectrum, (c) mutual intensity.

Fig. 4
Fig. 4

Fully incoherent case: (a) mask Mx,y, (b) joint power spectrum, (c) mutual intensity.

Fig. 5
Fig. 5

Partially coherent case: (a) mask Mx,y, (b) joint power spectrum, (c) mutual intensity.

Equations (10)

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

ΓR1,R2,t1,t2=uR1,t1u*R2,t2,
Γx1,x2=ux1,tu*x2,t.
Γx,-y=uy,tδx*ux,tδy,
uy1,tu*y2,t=I0δy1-y2,
vx,t=uy,tMx,ydy.
Γx1,x2=vx1,tv*x2,t=uy1,tu*y2,t×Mx1,y1M*x2,y2dy1dy2=I0δy1-y2Mx1,y1M*x2,y2dy1dy2=I0Mx1,yM*x2,ydy.
Γx1,x2=limT1T-T/2T/2vx1,tv*x2,tdt.
Γcohx,y=rectxΔxrectyΔx.
Γincx,y=rectxΔxδx-y.
Γpcohx,y=rectxΔxδx-y+δx+y.

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