Abstract

We derive the complex degree of coherence that originates from generalized incoherent two- and three-dimensional sources. Further, we find the locus of maximum coherence and analyze the dependence of the decay of coherence on source thickness.

© 2004 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, 1995).
    [CrossRef]
  2. J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  4. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).
  5. H. Coufal, D. Psaltis, and G. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
    [CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Goodman, J. W.

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

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Mandel, L.

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

Wolf, E.

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

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

Other (5)

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

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

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980).

H. Coufal, D. Psaltis, and G. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, Berlin, 2000).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Illustration of the coherence that originates from a quasi-monochromatic, spatially incoherent volume source.

Fig. 2
Fig. 2

Illustration of the coherence that originates from a cylindrical, quasi-monochromatic, spatially incoherent source: The parameters that we used to calculate the locus of maximum coherence are λ=488 nm, R=5 mm, L=10 mm, and r1=10,10,100 mm, which led to N=512.3, α=0.1, vx1=6437.7, and vy1=6437.7.

Fig. 3
Fig. 3

Illustration of the coherence that originates from a quasi-monochromatic, spatially incoherent disk source: The parameters that we used to calculate the locus of maximum coherence are λ=488 nm, R=5 mm, and r1=10,10,100 mm, which led to N=512.3, vx1=6437.7, and vy1=6437.7.

Fig. 4
Fig. 4

Modulus of the degree of coherence along the line defined by Eqs. (12): The degree of coherence along the line is calculated for a disk source and three cylindrical sources with different values of α. The parameters used in the simulation were N=512.3, vx1=6437.7, and vy1=6437.7.

Fig. 5
Fig. 5

Contour map of the coherence that originates from a cylindrical source in the cross section at plane S along the line defined by Eqs. (12): The parameters used in the simulation are the same as for Fig. 2.

Equations (16)

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Jr1,r2=Ir1δr2-r1.
jr1,r2=1I0r11/2I0r21/2VIr1×expj2π/λr1-r1jλr1-r1×exp-j2π/λr2-r1-jλr2-r1d3r1,
I0ri=1λ2VIr1ri-r12d3r1.
jr1,r2 exp-j2π/λΔzλ2z1z1+ΔzI0r1I0r21/2V×Ix1,y1,z1expjπAz1x12+y12×expj2πBxz1x1+Byz1y1×expjπCz1dx1dy1dz1.
Az1=1λz1-z1-1λz1+Δz-z1,
Bxz1=-1λx1z1-z1-x2z1+Δz-z1,
Byz1=-1λy1z1-z1-y2z1+Δz-z1,
Cz1=x12+y12λz1-z1-x22+y22λz1+Δz-z1.
ηx=x1/R,    ηy=y1/R,    ξ=z1/z1,δ=Δz/z1,    vx1=2πλRz1x1,    vy1=2πλRz1y1,v1=vx12+vy12,    vx2=2πλRz1x2,vy2=2πλRz1y2,    v2=vx22+vy22.
jr1,r2=exp-j2π/λΔzα-α/2α/2expjπCξ×L2πAξ,2πBξdξ,
jr1,r2=exp-j2πλΔzexpjπC0×L2πA0,2πB0.
vx2=1+δvx1,    vy2=1+δvy1,
jr1,r2max=sincNF2δ1+δ.
Cξ14π2v12NF-δ+0ξ+δ1+δξ2.
jr1,r2maxsincNF2δ1+δ×1aF-a2-Fa2,
a=α14πv12NFδ1+δ1/2=Lz12πx12+y12Δzλ1+δ1/2

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