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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 26 — Dec. 21, 2009
  • pp: 23672–23677
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Interference from a nonlocal double-slit through one-photon process

Shu Gan, Su-Heng Zhang, Jun Xiong, and Kaige Wang  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23672-23677 (2009)
http://dx.doi.org/10.1364/OE.17.023672


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Abstract

In this paper, we report an interference experiment in which a spatially incoherent light source illuminates two spatially separated apertures, whose superposition at the same place forms a double-slit. The experimental result exhibits a well-defined interference fringe solely through intensity measurements, in agreement with the theoretical analysis by means of the first-order spatial interference of the incoherent light. Consequently, the nonlocal double-slit interference with thermal light should be attributed to the first-order spatial correlation of incoherent field.

© 2009 OSA

1. Introduction

In classical optics, interference is implemented through intensity observation in a detection plane where two or more light beams are superposed. This is regarded as the first-order or one-photon interference. Recently, it has been shown that interference phenomena may occur through intensity correlation measurements or two-photon coincidence measurements even if the first-order interference disappears, such as “ghost” imaging, “ghost” interference, subwavelength interference and nonlocal double-slit interference [1

1. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995). [CrossRef] [PubMed]

5

5. E. J. S. Fonseca, P. H. S. Ribeiro, S. Pádua, and C. H. Monken, “Quantum interference by a nonlocal double slit,” Phys. Rev. A 60(2), 1530–1533 (1999). [CrossRef]

]. These effects, regarded as the second-order or two-photon interference, manifest nonlocal features since an entangled two-photon source is involved. As an example, in the nonlocal double-slit interference, a pair of signal and idler photons generated by spontaneous parametric down conversion are scattered by two spatially separated apertures: none of them is a double-slit but their superposition at the same place forms a double-slit [5

5. E. J. S. Fonseca, P. H. S. Ribeiro, S. Pádua, and C. H. Monken, “Quantum interference by a nonlocal double slit,” Phys. Rev. A 60(2), 1530–1533 (1999). [CrossRef]

]. Though each intensity profile of the signal and idler beams does not exhibit any fringe, an interference pattern can be observed in the two-photon coincidence measurements of the two beams. These effects were attributed to the nonlocal character of the quantum entanglement. Recent theoretical and experimental results demonstrated that the similar second-order interference effects to the above can be performed by using a thermal light source [6

6. R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““Two-Photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002). [CrossRef] [PubMed]

24

24. L. Gao, J. Xiong, L. F. Lin, W. Wang, S. H. Zhang, and K. G. Wang, “Interference from nonlocal double-slit with pseudo-thermal light,” Opt. Commun. 281(10), 2838–2841 (2008). [CrossRef]

]. Gao et al. [24

24. L. Gao, J. Xiong, L. F. Lin, W. Wang, S. H. Zhang, and K. G. Wang, “Interference from nonlocal double-slit with pseudo-thermal light,” Opt. Commun. 281(10), 2838–2841 (2008). [CrossRef]

] demonstrated that the interference from a nonlocal double-slit can be performed through the intensity correlation measurements of thermal light. The similarity between the two-photon entangled source and the thermal light source arouses different physical explanations, such as quantum vs. classical interpretation, to the nature of the second-order correlation of thermal light [25

25. G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006). [CrossRef] [PubMed]

, 26

26. A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Comment on ‘can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?’,” Phys. Rev. Lett. 98(3), 039301, discussion 039302 (2007). [CrossRef] [PubMed]

]. There is still no consensus so far, and hence new experimental results would be helpful to reach the proper understanding.

2. Experimental results

In contrast to common knowledge that irregular phase distribution of an incoherent source shall degrade interference pattern in intensity observation, Zhang et al. first demonstrated that a spatially incoherent light source is capable of obtaining the coherence information through just the intensity distribution itself [27

27. S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

]. Here we report such an experiment in which the nonlocal double-slit interference can also be implemented through one-photon process. As sketched in Fig. 1
Fig. 1 Experimental scheme of an unbalanced interferometer using an incoherent light source. The interferometer is formed by two mirrors, M1 and M2, and two beamsplitters, BS1 and BS2. Polarizer P1 and Glan prism P2 are used for modulating the light intensity, and G is a rotating ground glass disk. Lens L is inserted into the middle of path 2, where A2 and CCD camera are located at the two focal planes of lens L.
, the experimental setup is very similar to the recent proposal [27

27. S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

] on the first-order interference effect in an unbalanced interferometer using spatially incoherent light source, but with a nonlocal double-slit replacing the real double-slit. The source field is divided into two parts by the beamsplitter BS1: one illuminates aperture A1 in path 1 and the other illuminates aperture A2 in path 2. BS2 is a 50/50 beamsplitter, where the interference of the two fields may occur. Aperture A1, a wire with a diameter of L1=0.2 mm and aperture A2, a slit with a width of L2=0.4 mm, are placed at the equal distance z0=1 cm from BS1, and their superposition at the same position forms a double-slit of slit width b=0.1 mm and spacing d=0.3 mm. The distance between the aperture and charge-coupled device (CCD) camera is z1=38 cm, and the two arms of the interferometer have the same optical path. A lens of focal length f=19 cm is set in the middle of path 2, so aperture A2 and the CCD screen are located in the two focal planes of lens L. The equal-optical-path condition can assure that one photon interferes with itself after passing through the two arms. However, there are different diffraction configurations in the two arms and it is the key in the present scheme since balanced interferometer washes out the information of the object [27

27. S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

].

To further demonstrate above effect, a true thermal light source should be taken into account. We replace the pseudo-thermal light source in Fig. 1 by a Na lamp of wavelength 589.3 nm with an illumination area of 10×10 mm2. In this case, the coherence time of the Na lamp is much shorter than the responses time of the CCD camera, so the interference patterns can appear directly on the CCD screen, as shown in Fig. 3
Fig. 3 Same as in Fig. 2 but with a Na lamp replacing the pseudo-thermal light source in the scheme of Fig. 1.
. The patterns are similar to that in Fig. 2, except for the slightly different spacings, owing to the different wavelengths of the two sources.

3. Theoretical analysis

We now present the theoretical explanation for the experimental results. Let Es(x)and Ej(x) be the source field at BS1 and the field of path j(=1,2) at the recording plane, respectively, andx, the transverse position across the beam. The field diffraction in path j is described as
Ej(x)=hj(x,x0)Es(x0)dx0,
(1)
where the impulse response function hj(x,x0) of path j(=1,2) is written as [24

24. L. Gao, J. Xiong, L. F. Lin, W. Wang, S. H. Zhang, and K. G. Wang, “Interference from nonlocal double-slit with pseudo-thermal light,” Opt. Commun. 281(10), 2838–2841 (2008). [CrossRef]

]
h1(x,x0)=k2πiz0z1exp[ik(z0+z1)]A1(x1)exp[ik2z0(x1x0)2+ik2z1(xx1)2]dx1,
(2a)
h2(x,x0)=k2πiz0fexp[ik(z0+2f)]A2(x2)exp[ik2z0(x2x0)2ikfxx2]dx2.
(2b)
k is the wavenumber of the beam; A1(x)=1rect(x/L1) and A2(x)=rect(x/L2)are designated as the transmission functions of the two apertures, respectively, and their product D(x) is a double-slit function with slit width b=(L2L1)/2 and spacing d=(L2+L1)/2, i.e., D(x)=A1(x)A2(x)=rect[(xd/2)/b]+rect[(x+d/2)/b]. The propagation of the mutual coherence in the interferometer is given by
Ei(x1)Ej(x2)hi(x1,x0)hj(x2,x0)Es(x0)Es(x0)dx0dx0.
(3)
The intensity patterns at the two outgoing ports of the interferometer are obtained to be
I1,2(x)=E1(x)E1(x)+E2(x)E2(x)±[E1(x)E2(x)+c .c .],
(4)
where Ej(x)Ej(x) and E1(x)E2(x)stand for the intensity pattern in path j and the interference term, respectively.

For a spatially incoherent light source, the first-order field correlation function satisfiesEs(x0)Es(x0)=Isδ(x0x0), and the interference term is written as
E1(x)E2(x)Ish1(x,x0)h2(x,x0)dx0=Isk22πfexp[ikx24f]A1(x1)A2(x1)exp[ikx124fikxx12f]dx1[Isk/(2πf)]exp[ikx2/(4f)]D˜[kx/(2f)],
(5)
where z1=2fhas been used. The approximation in the last step is valid when the size of the double-slit is much less than the area of the diffraction pattern, and the Fourier transform of the double-slit function D(x) is deduced asD˜(q)=(2b/2π)sinc(qb/2)cos(qd/2). Obviously, Eq. (5) is equivalent to the result that a real double-slit is set at the position of aperture A2 in the interferometer [27

27. S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

]. However, the two intensity distributions, E1(x)E1(x)andE2(x)E2(x), are homogeneous. Figure 5
Fig. 5 One-dimensional interference patterns corresponding to that of Fig. 2. Experimental data and theoretical simulation are given by open circles and solid lines, respectively.
shows the numerical simulation of Eq. (5), fitting well with the experimental results in Fig. 2, apart from minor asymmetry. Any misalignment in the optical system may cause the asymmetry in the interference pattern.

As for the spatially coherent light, it hasEs(x0)Es(x0)=Es(x0)Es(x0), and the first-order correlation function Eq. (3) is separable as
Ei(x1)Ej(x2)hi(x1,x0)Es(x0)dx0×hj(x2,x0)Es(x0)dx0.
(6)
As a result, there is no joint diffraction between the two arms to form an effective double-slit. For simplicity, we assume the Gaussian intensity distribution with a plane wave front for the laser beam, i.e., Es(x0)~exp(x02/σ2), where σ characterizes the spot size. Using Eq. (6) and Eq. (4), we calculate 1D interference patterns in Fig. 6
Fig. 6 One-dimensional interference patterns corresponding to that of Fig. 4. Experimental data and theoretical simulation are given by open circles and solid lines, respectively. The spot size of the laser beam is taken as σ=0.8 mm.
. As we expected, the net interference pattern in Fig. 6 (c) corresponds to the product of the diffraction fields of the two apertures, and the intensity background in Fig. 6 (d) coincides with the sum of the two diffraction patterns of A1 and A2. No information about the double-slit can be obtained when A1 and A2 are illuminated coherently. The theoretical curves are in a good agreement with the experimental results for the coherent light case of Fig. 4. A slight mismatch of some side-peaks comes from our simple laser model in the theoretical simulation.

4. Summary

Acknowledgment

This work was supported by the National Fundamental Research Program of China, Project No. 2006CB921404, and the National Natural Science Foundation of China, Project No. 10874019.

References and links

1.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995). [CrossRef] [PubMed]

2.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995). [CrossRef] [PubMed]

3.

E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868–2871 (1999). [CrossRef]

4.

A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87(12), 123602 (2001). [CrossRef] [PubMed]

5.

E. J. S. Fonseca, P. H. S. Ribeiro, S. Pádua, and C. H. Monken, “Quantum interference by a nonlocal double slit,” Phys. Rev. A 60(2), 1530–1533 (1999). [CrossRef]

6.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““Two-Photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002). [CrossRef] [PubMed]

7.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004). [CrossRef] [PubMed]

8.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004). [CrossRef]

9.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004). [CrossRef] [PubMed]

10.

J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004). [CrossRef] [PubMed]

11.

K. G. Wang and D. Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004). [CrossRef]

12.

Y. J. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29(23), 2716–2718 (2004). [CrossRef] [PubMed]

13.

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94(18), 183602 (2005). [CrossRef] [PubMed]

14.

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005). [CrossRef]

15.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005). [CrossRef] [PubMed]

16.

J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. G. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005). [CrossRef] [PubMed]

17.

D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005). [CrossRef] [PubMed]

18.

Y. H. Zhai, X. H. Chen, D. Zhang, and L. A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005). [CrossRef]

19.

G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006). [CrossRef]

20.

L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006). [CrossRef]

21.

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96(18), 183901 (2006). [CrossRef] [PubMed]

22.

M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73(5), 053802 (2006). [CrossRef]

23.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53(5-6), 739–760 (2006). [CrossRef]

24.

L. Gao, J. Xiong, L. F. Lin, W. Wang, S. H. Zhang, and K. G. Wang, “Interference from nonlocal double-slit with pseudo-thermal light,” Opt. Commun. 281(10), 2838–2841 (2008). [CrossRef]

25.

G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006). [CrossRef] [PubMed]

26.

A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Comment on ‘can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?’,” Phys. Rev. Lett. 98(3), 039301, discussion 039302 (2007). [CrossRef] [PubMed]

27.

S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(050.1940) Diffraction and gratings : Diffraction
(090.2880) Holography : Holographic interferometry

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: September 28, 2009
Revised Manuscript: November 7, 2009
Manuscript Accepted: November 30, 2009
Published: December 10, 2009

Citation
Shu Gan, Su-Heng Zhang, Jun Xiong, and Kaige Wang, "Interference from a nonlocal double-slit through one-photon process," Opt. Express 17, 23672-23677 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-26-23672


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References

  1. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995). [CrossRef] [PubMed]
  2. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995). [CrossRef] [PubMed]
  3. E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868–2871 (1999). [CrossRef]
  4. A. F. Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87(12), 123602 (2001). [CrossRef] [PubMed]
  5. E. J. S. Fonseca, P. H. S. Ribeiro, S. Pádua, and C. H. Monken, “Quantum interference by a nonlocal double slit,” Phys. Rev. A 60(2), 1530–1533 (1999). [CrossRef]
  6. R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““Two-Photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002). [CrossRef] [PubMed]
  7. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004). [CrossRef] [PubMed]
  8. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004). [CrossRef]
  9. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004). [CrossRef] [PubMed]
  10. J. Cheng and S. S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004). [CrossRef] [PubMed]
  11. K. G. Wang and D. Z. Cao, “Subwavelength coincidence interference with classical thermal light,” Phys. Rev. A 70(4), 041801 (2004). [CrossRef]
  12. Y. J. Cai and S. Y. Zhu, “Ghost interference with partially coherent radiation,” Opt. Lett. 29(23), 2716–2718 (2004). [CrossRef] [PubMed]
  13. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiments with thermal light,” Phys. Rev. Lett. 94(18), 183602 (2005). [CrossRef] [PubMed]
  14. D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005). [CrossRef]
  15. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005). [CrossRef] [PubMed]
  16. J. Xiong, D. Z. Cao, F. Huang, H. G. Li, X. J. Sun, and K. G. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005). [CrossRef] [PubMed]
  17. D. Zhang, Y. H. Zhai, L. A. Wu, and X. H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30(18), 2354–2356 (2005). [CrossRef] [PubMed]
  18. Y. H. Zhai, X. H. Chen, D. Zhang, and L. A. Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4), 043805 (2005). [CrossRef]
  19. G. Scarcelli, V. Berardi, and Y. H. Shih, “Phase-conjugate mirror via two-photon thermal light imaging,” Appl. Phys. Lett. 88(6), 061106 (2006). [CrossRef]
  20. L. Basano and P. Ottonello, “Experiment in lensless ghost imaging with thermal light,” Appl. Phys. Lett. 89(9), 091109 (2006). [CrossRef]
  21. R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96(18), 183901 (2006). [CrossRef] [PubMed]
  22. M. Bache, D. Magatti, F. Ferri, A. Gatti, E. Brambilla, and L. A. Lugiato, “Coherent imaging of a pure phase object with classical incoherent light,” Phys. Rev. A 73(5), 053802 (2006). [CrossRef]
  23. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53(5-6), 739–760 (2006). [CrossRef]
  24. L. Gao, J. Xiong, L. F. Lin, W. Wang, S. H. Zhang, and K. G. Wang, “Interference from nonlocal double-slit with pseudo-thermal light,” Opt. Commun. 281(10), 2838–2841 (2008). [CrossRef]
  25. G. Scarcelli, V. Berardi, and Y. H. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006). [CrossRef] [PubMed]
  26. A. Gatti, M. Bondani, L. A. Lugiato, M. G. A. Paris, and C. Fabre, “Comment on ‘can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?’,” Phys. Rev. Lett. 98(3), 039301, discussion 039302 (2007). [CrossRef] [PubMed]
  27. S. H. Zhang, L. Gao, J. Xiong, L. J. Feng, D. Z. Cao, and K. G. Wang, “Spatial interference: from coherent to incoherent,” Phys. Rev. Lett. 102(7), 073904 (2009). [CrossRef] [PubMed]

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