Abstract

It has been recently demonstrated in experiments how to create non-Rayleigh speckle fields through the use of a phase-only spatial light modulator. These non-Rayleigh speckle fields possess high-order correlations which could play important roles in correlation-based optical imaging methods such as thermal ghost imaging, in which case the Gaussian moment theorem is no longer applicable. Through numerical simulations we investigated at how non-Rayleigh and Rayleigh speckle fields affect the resolution and visibility for high-order thermal ghost imaging. The results show regardless of the speckle field used better resolution is achieved with the use of a higher-order and that sub-Rayleigh speckle fields lead to the best resolution regardless of ghost order.

© 2016 Optical Society of America

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References

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  1. A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85 (1970).
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    [Crossref]
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  4. J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
    [Crossref] [PubMed]
  5. S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
    [Crossref]
  6. Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112(21), 213904 (2014).
    [Crossref]
  7. X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
    [Crossref]
  11. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  13. E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
    [Crossref]
  14. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
    [Crossref]
  15. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
    [Crossref]
  16. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34(21), 3343–3345 (2009).
    [Crossref] [PubMed]
  17. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18(6), 5562–5573 (2010).
    [Crossref] [PubMed]
  18. J. W. Goodman, Fourier Optics, 3rd ed. (Englewood, CO: Roberts and Company, 2008).
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    [Crossref] [PubMed]

2016 (2)

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

2015 (1)

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

2014 (1)

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112(21), 213904 (2014).
[Crossref]

2013 (1)

2012 (2)

A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012).
[Crossref] [PubMed]

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

2010 (1)

2009 (2)

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett. 34(21), 3343–3345 (2009).
[Crossref] [PubMed]

2008 (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

2005 (2)

C. Ventalon and J. Mertz, “Quasi-confocal fluorescence sectioning with dynamic speckle illumination,” Opt. Lett. 30(24), 3350–3352 (2005).
[Crossref] [PubMed]

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

2004 (1)

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]

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the dertermination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

1971 (1)

1970 (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85 (1970).

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919 (1964).
[Crossref]

Bache, M.

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]

Boyd, R. W.

Brambilla, E.

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]

Bromberg, Y.

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112(21), 213904 (2014).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Cao, H.

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112(21), 213904 (2014).
[Crossref]

Chan, K. W. C.

Chen, P.-X.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

Cho, Y.-W.

D’Angelo, M.

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

Dunn, A. K.

A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012).
[Crossref] [PubMed]

Estes, L. E.

Fienup, J. R.

Gatti, A.

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]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the dertermination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Katz, O.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Kim, Y.-H.

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85 (1970).

Li, H.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Li, X.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Liu, W.-T.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

Lugiato, L. A.

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]

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919 (1964).
[Crossref]

Mertz, J.

Narducci, L. M.

Nie, Z.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

O’Sullivan, M. N.

Oh, J.-E.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the dertermination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Scarcelli, G.

J.-E. Oh, Y.-W. Cho, G. Scarcelli, and Y.-H. Kim, “Sub-Rayleigh imaging via speckle illumination,” Opt. Lett. 38(5), 682–684 (2013).
[Crossref] [PubMed]

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

Shapiro, J. H.

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

Shih, Y.

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

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Spiller, E.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919 (1964).
[Crossref]

Tai, Y.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Tuft, R. A.

Valencia, A.

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

Ventalon, C.

Wang, H.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Wang, J.

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Wang, W.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

Yang, X.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

Yu, R.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

Zhang, E.-F.

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

Zhang, S.

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

Am. J. Phys. (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32(12), 919 (1964).
[Crossref]

Ann. Biomed. Eng. (1)

A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

X. Li, Y. Tai, H. Li, J. Wang, H. Wang, and Z. Nie, “Generation of a super-Rayleigh speckle field via a spatial light modulator,” Appl. Phys. B 122(4), 82 (2016).
[Crossref]

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85 (1970).

J. Opt. (1)

E.-F. Zhang, W.-T. Liu, and P.-X. Chen, “Ghost imaging with non-negative exponential speckle patterns,” J. Opt. 17(8), 085602 (2015).
[Crossref]

J. Opt. Soc. Am. (1)

Laser Phys. (1)

S. Zhang, W. Wang, R. Yu, and X. Yang, “High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging,” Laser Phys. 26(5), 055007 (2016).
[Crossref]

Opt. Express (1)

Opt. Lett. (3)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the dertermination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Phys. Rev. A (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Phys. Rev. Lett. (3)

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

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]

Y. Bromberg and H. Cao, “Generating non-Rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112(21), 213904 (2014).
[Crossref]

Quantum Inform. Process. (1)

J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inform. Process. 11(4), 949–993 (2012).
[Crossref]

Other (1)

J. W. Goodman, Fourier Optics, 3rd ed. (Englewood, CO: Roberts and Company, 2008).

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Figures (6)

Fig. 1
Fig. 1 Schematic of the physical setup that we simulated. The configuration of the elements on the Spatial Light Modulator will determine the speckle field (Rayleigh, sub- or super-) incident upon the object and reference detector. A discretized space image of the object is formed through image computation of the measurements recorded by the bucket detector, reference detector, and post processing technique (high order ghost image).
Fig. 2
Fig. 2 Typical speckle patterns for super-Rayleigh (a1), Rayleigh (b1), and sub-Rayleigh (c1). (a2), (b2), and (c3) are normalized histograms showing the corresponding intensity distributions for super-Rayleigh, Rayleigh, and sub-Rayleigh respectively. The intensity distribution for the super-Rayleigh speckles were generated with the power k = 2. The sub-Rayleigh speckle distribution was generated with the amplitude pattern given by Eq. (6). 65536 speckle samples were used to generate each histogram. The RMS contrast for (a1), (b1), and (c1) are respectively 1.41, 0.99, and 0.46.
Fig. 3
Fig. 3 Rayleigh, sub-Rayleigh, and super-Rayleigh speckle fields and orders 1, 4 and 8 were used to create a ghost image of an ideal nested square. The ideal nested square contains decreasing line widths as it moves toward the center of the square.
Fig. 4
Fig. 4 (a), (b), and (c) represent the point spread with background subtraction for ghost orders 1 through 8 via super-Rayleigh, Rayleigh, and sub-Rayleigh respectively. The two vertical dashed lines in (a), (b), and (c) are to denote the “full width” of the Rayleigh point spread of ghost order 1, which is defined by the first intensity minimum around the central peak intensity. Regardless of the ghost order, the Rayleigh “full width” point spread remains constant for ghost orders 1 through 8. Each point spread image was created from 2.5 × 106 samples. The super-Rayleigh point spread (a) had an average RMS contrast value of 4.87. The Rayleigh point spread (b) had and an average RMS contrast of 0.997. The sub-Rayleigh point spread (c) had an average RMS contrast of 0.47.
Fig. 5
Fig. 5 Plot of the normalized central intensity versus the distance between two point objects. Each point which corresponds to an image that was constructed from 2.5 × 106 samples. The images were constructed using the same super-Rayleigh (dash-dotted lines), Rayleigh (solid lines), and sub-Rayleigh (dashed lines) fields as in Fig. 4. The solid horizontal line at 73% normalized central intensity represents the Rayleigh criterion for an incoherent source. Images constructed using sub-Rayleigh fields generate the smallest required point separation distance required for resolution and it does not depend on the ghost order. Minimum separation distance via Rayleigh and super-Rayleigh fields is dependent on ghost order. The convention of the symbols denoting the ghost orders is the same as that of Fig. 4.
Fig. 6
Fig. 6 Plot of the visibility as a function of RMS contrast for different ghost orders. RMS contrast values less than one represent varying degrees of sub-Rayleighness while RMS contrast values greater than one represent varying degrees of super-Rayleighness.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

G m,n ( x )= 1 N s=1 N [ I o ( s ) ] m [ I ( s ) ( x ) ] n ,
I o ( s ) = O( y ) I ( s ) ( y )dy .
U f ( u,v )= A iλf e i π λf ( 1 d f )( u 2 + v 2 ) t( x,y ) e i 2π λf ( xu+yv ) dxdy ,
t( x,y ) e iφ( x,y )
RMS= I 2 / I 2 1 .
| E ( x,y ) | 1 e | E( x,y ) 6 | ,
Visibility= I in I out I in + I out

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