Abstract

Direct sunlight is often deemed incoherent, hence unsuitable for antenna power conversion. However, all radiation exhibits spatial coherence when detected on a sufficiently small scale. We report the first direct measurement of the spatial coherence of solar beam radiation, achieved with a customized tabletop cyclic-shearing interferometer. Good agreement is found between experiment and theory, with promising ramifications for solar aperture antennas.

© 2012 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge, 1999).
  2. R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
    [CrossRef]
  3. G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459(2004).
    [CrossRef]
  4. H. Mashaal and J. M. Gordon, Opt. Lett. 36, 900(2011).
    [CrossRef]
  5. É. Verdet, Leçons d’Optique Physique Vol. 1 (L’Imprimierie Impériale, 1869).
  6. Images from http://www.itp.uni-hanover.de/~zawischa/ITP/diffraction.html .
  7. R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).
  8. W. T. Welford, and R. Winston, J. Opt. Soc. Am. 72, 1244(1982).
    [CrossRef]
  9. P. Kotsidas, V. Modi, and J. M. Gordon, Opt. Express 19, 15584 (2011).
    [CrossRef]
  10. N. Ostroumov, J. M. Gordon, and D. Feuermann, Appl. Opt. 48, 4926 (2009).
    [CrossRef]

2011 (2)

2009 (1)

2004 (1)

2002 (1)

R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
[CrossRef]

1982 (1)

Agarwal, G. S.

Benítez, P.

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge, 1999).

Bortz, J.

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

Feuermann, D.

Gbur, G.

Gordon, J. M.

Kotsidas, P.

Littlejohn, R. G.

R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
[CrossRef]

Mashaal, H.

Miñano, J. C.

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

Modi, V.

Ostroumov, N.

Shatz, N.

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

Sun, Y.

R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
[CrossRef]

Verdet, É.

É. Verdet, Leçons d’Optique Physique Vol. 1 (L’Imprimierie Impériale, 1869).

Welford, W. T.

Winston, R.

R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
[CrossRef]

W. T. Welford, and R. Winston, J. Opt. Soc. Am. 72, 1244(1982).
[CrossRef]

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

Wolf, E.

G. S. Agarwal, G. Gbur, and E. Wolf, Opt. Lett. 29, 459(2004).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge, 1999).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

R. Winston, Y. Sun, and R. G. Littlejohn, Opt. Commun. 207, 41 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (4)

É. Verdet, Leçons d’Optique Physique Vol. 1 (L’Imprimierie Impériale, 1869).

Images from http://www.itp.uni-hanover.de/~zawischa/ITP/diffraction.html .

R. Winston, J. C. Miñano, and P. Benítez, with contributions from N. Shatz and J. Bortz, Nonimaging Optics (Elsevier, 2005).

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge, 1999).

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Figures (1)

Fig. 1.
Fig. 1.

(a) Low- and high-magnification photos [6] of a matte coin with etched features of the order of tens of micrometers. Under solar beam radiation, the speckle signifies light’s spatial coherence. The spatial coherence area of diffuse sunlight is orders of magnitude smaller, so the speckle disappears. (b) Schematic of the cyclic-shearing interferometer; M denotes mirrors; BS, beam splitters. (c) Measured and theoretical EMCFs. Solid circles, measurements for broadband solar beam radiation; solid curve, corresponding theoretical result. Solid squares, measurements for spectrally filtered  λ=0.5μm direct sunlight; dashed curve (- - - -), corresponding theoretical result. The first null in the EMCF is sometimes referred to as the coherence radius, although the EMCF function provides all the necessary information for evaluating spatial coherence at any radius [4].

Equations (4)

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ECCW=i2·E0(x,t),ECW=12·E0(x,t).
ECCW=i2·E0(xΔx2,t),ECW=12·E0(x+Δx2,t).
Eout(x,t)=i2[E0(xΔx2,t)+E0(x+Δx2,t)].
I¯(x)=12η|Eout(x,t)|2t=I¯04(xΔx2)+I¯04(x+Δx2)+14ηReE0*(xΔx2,t)·Eo(x+Δx2,t)t,I¯(0)=I¯02[1+Re{EMCF(Δx)}],

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