Abstract

We describe a robust method by which the spatial coherence from all pairs of points along a line may be simultaneously acquired from an image formed by diffraction from a phase discontinuity. In contrast to other methods, this approach can accurately reveal weak correlations in the tails of a coherence function.

© 2012 Optical Society of America

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References

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  10. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 276–287.

2011 (2)

2009 (1)

2006 (1)

1998 (2)

1996 (1)

1992 (1)

K. A. Nugent, Phys. Rev. Lett. 68, 2261 (1992).
[CrossRef]

1938 (1)

F. Zernike, Physica 5, 785 (1938).
[CrossRef]

Alonso, M. A.

Borghi, R.

Cho, S.

González, A. I.

Iaconis, C.

Konforti, N.

Lohmann, A. W.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 276–287.

Mejía, Y.

Mendlovic, D.

Nugent, K. A.

K. A. Nugent, Phys. Rev. Lett. 68, 2261 (1992).
[CrossRef]

Santarsiero, M.

Shabtay, G.

Tamura, S.

Tu, J.

Walmsley, I. A.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995), pp. 276–287.

Zernike, F.

F. Zernike, Physica 5, 785 (1938).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Illustration of (a) δI(p;0), (b) the exact and estimated W¯(0;x), and (c) the reconstructed W¯(x0;x) for a GSM field with ρ=0.1 and kσ=100; (d) Max[δW¯0(x0;x)] and its estimates in Eqs. (8) and (10) for varying ρ.

Fig. 2.
Fig. 2.

Illustration of the experimental setup.

Fig. 3.
Fig. 3.

Illustration of (a) δI(p;x0) for ψ, (b) the fitted θ versus ψ, (c) the average (black) and standard deviation (gray) of Re(W¯0) (solid) and Im(W¯0) (dashed) for four data sets, and (d) its interpolated estimate compared to all the 11 estimates, whose real parts (even functions) are shown only for x>0 and imaginary parts (odd functions) only for x<0.

Equations (10)

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I(p)=k2πW¯(x¯;x)exp(ikxp)dxdx¯,
It(p;x0)=k2πW¯(x¯;x)[1a(θ,x)rect(x¯x0x)]×exp(ikxp)dxdx¯,
δI(p;x0)It(p;x0)I(p)=k2πexp(ikxp)×a(θ,x)x0|x|2x0+|x|2W¯(x¯;x)dx¯dx.
W¯(x¯;x)=n=0(x¯x0)nn!nx0nW¯(x0;x).
δI(p;x0)=(1124k22x022p2+)δI0(p;x0),
δI0(p;x0)=k2πexp(ikxp)a(θ,x)|x|W¯(x0;x)dx.
W¯0(x0;x)=1|x|a(θ,x)δI(p;x0)exp(ikxp)dp.
δW¯0(x0;x)|x|24a(θ,x)exp(ikxp)2δI(p;x0)x02dp.
W(x1;x2)=exp[x12+x222σ2(x2x1)22Δ2],
Max[δW¯0(x0;x)]exp(1)3(1+2ρ2)0.121+2ρ2,

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