Abstract

Time-domain analysis of field correlations provided by the interferogram from a nonredundant pinhole array is performed. It is shown that the described single measurement is identically equal to a series of Young’s two-pinhole experiments. Proper postmeasurement analysis, taking into account the finite coherence time of the source, results in a sampling of the spatial–temporal coherence function.

© 2013 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 University, 1995).
  2. O. V. Angelsky, C. Y. Zenkova, M. P. Gorsky, and N. V. Gorodyns’ka, Appl. Opt. 48, 2784 (2009).
    [CrossRef]
  3. E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
    [CrossRef]
  4. L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
    [CrossRef]
  5. R. Castañeda and Z. Jaroszewicz, Opt. Commun. 173, 115 (2000).
    [CrossRef]
  6. J. Garcia-Sucerquia and R. Castañeda, Opt. Commun. 228, 9 (2003).
    [CrossRef]
  7. Y. Mejia and A. I. Gonzalez, Opt. Commun. 273, 428 (2007).
    [CrossRef]
  8. A. I. Gonzalez and Y. Mejia, J. Opt. Soc. Am. A 28, 1107 (2011).
    [CrossRef]
  9. B. Davis, Opt. Express 15, 2837 (2007).
    [CrossRef]

2011 (1)

2009 (1)

2007 (3)

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

B. Davis, Opt. Express 15, 2837 (2007).
[CrossRef]

Y. Mejia and A. I. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

2003 (1)

J. Garcia-Sucerquia and R. Castañeda, Opt. Commun. 228, 9 (2003).
[CrossRef]

2000 (1)

R. Castañeda and Z. Jaroszewicz, Opt. Commun. 173, 115 (2000).
[CrossRef]

1989 (1)

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Angelsky, O. V.

Boiko, D. L.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

Castañeda, R.

J. Garcia-Sucerquia and R. Castañeda, Opt. Commun. 228, 9 (2003).
[CrossRef]

R. Castañeda and Z. Jaroszewicz, Opt. Commun. 173, 115 (2000).
[CrossRef]

Davis, B.

Friberg, A. T.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Garcia-Sucerquia, J.

J. Garcia-Sucerquia and R. Castañeda, Opt. Commun. 228, 9 (2003).
[CrossRef]

Gonzalez, A. I.

A. I. Gonzalez and Y. Mejia, J. Opt. Soc. Am. A 28, 1107 (2011).
[CrossRef]

Y. Mejia and A. I. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Gorodyns’ka, N. V.

Gorsky, M. P.

Jaroszewicz, Z.

R. Castañeda and Z. Jaroszewicz, Opt. Commun. 173, 115 (2000).
[CrossRef]

Kapon, E.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

Lousberg, G. P.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

Lundeberg, L. D. A.

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

Mandel, L.

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

Mejia, Y.

A. I. Gonzalez and Y. Mejia, J. Opt. Soc. Am. A 28, 1107 (2011).
[CrossRef]

Y. Mejia and A. I. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Tervonen, E.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Turunen, J.

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Wolf, E.

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

Zenkova, C. Y.

Appl. Opt. (1)

Appl. Phys. B (1)

E. Tervonen, J. Turunen, and A. T. Friberg, Appl. Phys. B 49, 409 (1989).
[CrossRef]

Appl. Phys. Lett. (1)

L. D. A. Lundeberg, G. P. Lousberg, D. L. Boiko, and E. Kapon, Appl. Phys. Lett. 90, 021103 (2007).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (3)

R. Castañeda and Z. Jaroszewicz, Opt. Commun. 173, 115 (2000).
[CrossRef]

J. Garcia-Sucerquia and R. Castañeda, Opt. Commun. 228, 9 (2003).
[CrossRef]

Y. Mejia and A. I. Gonzalez, Opt. Commun. 273, 428 (2007).
[CrossRef]

Opt. Express (1)

Other (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

Interference pattern normalized to the peak intensity from three pinholes transmitting the simulated stochastic planar source (circles), and the corresponding analytical solution (solid curve).

Fig. 2.
Fig. 2.

Fourier spectrum of the interferogram of Fig. 1, normalized to the intensity at 0 μm separation (simulation: circles; analytical: solid curve).

Fig. 3.
Fig. 3.

Degree of coherence function for separations of, from top to bottom, 100 μm (apertures at 100 and 0 μm), 200 μm (0 and 200 μm), and 300 μm (100 and 200 μm) (simulation: circles; analytical: solid curve).

Equations (10)

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U(R,ω)=h(R)n=1NV(R,ω)δ(RRn),
UFF(r,ω)=eik0zik0z2πzeik0r2/2zH(k0rz)×n=1NV(Rn,ω)eik0Rn·r/z,
SFF(r,ω)=(k02πz)2|H(k0rz)|2×n=1Nm=1NW(Rn,Rm,ω)eik0(RnRm)·r/z,
ΓFF(r,r,τ)=12π0S(r,ω)eiωτdω=1(2πzc)2d2dτ2|H(k¯0rz)|2n=1Nm=1NΓ(Rn,Rm,τ1zc(RnRm)·r),
Γ˜FF(ρ,0)=1(2πzc)2Λ(ρ)[n=1Nd2dτ2Γ(Rn,Rn,τ)|τ=0δ(ρ)+n=m+1Nm=1N1ρx2ω¯3|XnXm|3×W(Rn,Rm,ω¯ρxXnXm)×δ(ρyYnYmXnXmρx)],
ΓFF(mn)(r,r,0)=1(2π)2|H(k¯0rz)|21(XnXm)2×d2dx2Γ(Rn,Rm,1zc(RnRm)·r)(k¯02πz)2|H(k¯0rz)|2×Γ(Rn,Rm,1zc(RnRm)·r),
Γ(x1,x2,τ)=f(x1,x2)Γt(τ),
f(x1,x2)=e(x12+x22)/σx2e(x1x2)2/2σc2,
Γt(τ)=eτ2/τc2eiω0τ.
G(r,r,t,t)=δ(tt|rr|c)|rr|,

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