Abstract

Computational ghost imaging (CGI) enables an image to be recorded using a single-pixel detector. The image can be reconstructed from correlations between the scene and a series of known projected intensity patterns. In this work we investigate the performance of CGI using pseudo non-diffracting (ND) speckle patterns. We demonstrate an extended depth-of-field that is 2–3 times greater than that achievable with conventional speckle, when only computing each intensity pattern to a single depth. In addition, the average speckle grain size of ND speckle is reduced by a factor of 1.5 relative to conventional speckle, which enhances the lateral Rayleigh-limit resolving power of our reconstructed images. However, the point-spread function (PSF) of our imaging system takes the form of a Bessel beam, which manifests itself as long-range correlations between speckle grains in the projected patterns. We discuss the trade-off between enhancement of the depth-of-field and the lateral resolution when using ND speckle, at the expense of a reduction in image contrast. Our work demonstrates that the tailoring of lateral and axial correlations in projected intensity patterns permits PSF engineering in CGI.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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Corrections

16 June 2016: A correction was made to the acknowledgments.


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References

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  1. T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429 (1995).
    [Crossref] [PubMed]
  2. A. F. Abouraddy, B. E. Saleh, A. V. Sergienko, and M. C. Teich, “Role of entanglement in two-photon imaging,” Phys. Rev. Lett. 87, 123602 (2001).
    [Crossref] [PubMed]
  3. R. S. Bennink, S. J. Bentley, and R. W. Boyd, ““Two-photon” coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
    [Crossref]
  4. R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92, 033601 (2004).
    [Crossref] [PubMed]
  5. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70, 013802 (2004).
    [Crossref]
  6. J. H. Shapiro and R. W. Boyd, “The physics of ghost imaging,” Quantum Inf. Process. 11, 949–993 (2012).
    [Crossref]
  7. 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, 183602 (2005).
    [Crossref] [PubMed]
  8. A. Valencia, G. Scarcelli, M. D. Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [Crossref] [PubMed]
  9. D. Zhang, Y.-H. Zhai, L.-A. Wu, and X.-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
    [Crossref] [PubMed]
  10. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
    [Crossref]
  11. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2, 405–450 (2010).
    [Crossref]
  12. M. Levoy, “Light fields and computational imaging,” Computer pp. 46–55 (2006).
    [Crossref]
  13. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
    [Crossref] [PubMed]
  14. D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.
  15. M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
    [Crossref]
  16. M.-J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24 (10), 10476–10485 (2016).
  17. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
    [Crossref]
  18. J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).
  19. J. W. Goodman, Speckle phenomena in optics: theory and applications (Roberts and Company Publishers, 2007).
  20. D. M. Cottrell, J. M. Craven, and J. A. Davis, “Nondiffracting random intensity patterns,” Opt. Lett. 32, 298–300 (2007).
    [Crossref] [PubMed]
  21. R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21, 1656–1668 (2013).
    [Crossref] [PubMed]
  22. R. Y. Gu, R. N. Mahalati, and J. M. Kahn, “Noise-reduction algorithms for optimization-based imaging through multi-mode fiber,” Opt. Express 22, 15118–15132 (2014).
    [Crossref] [PubMed]
  23. J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [Crossref]
  24. J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [Crossref] [PubMed]
  25. D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
    [Crossref]
  26. T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
    [Crossref] [PubMed]
  27. Z. Bouchal, “Controlled spatial shaping of nondiffracting patterns and arrays,” Opt. Lett. 27, 1376–1378 (2002).
    [Crossref]
  28. J. Courtial, G. Whyte, Z. Bouchal, and J. Wagner, “Iterative algorithms for holographic shaping of non-diffracting and self-imaging light beams,” Opt. Express 14, 2108–2116 (2006).
    [Crossref] [PubMed]
  29. M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713–31724 (2013).
    [Crossref]
  30. C. Paterson and R. Smith, “Higher-order bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
    [Crossref]
  31. T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
    [Crossref] [PubMed]
  32. F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
    [Crossref]
  33. R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
    [Crossref]
  34. Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
    [Crossref]
  35. N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
    [Crossref]
  36. E. T. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
    [Crossref]
  37. M. R. Dennis, A. C. Hamilton, and J. Courtial, “Superoscillation in speckle patterns,” Opt. Lett. 33, 2976–2978 (2008).
    [Crossref] [PubMed]
  38. M. Berry, “A note on superoscillations associated with bessel beams,” J. Opt. 15, 044006 (2013).
    [Crossref]
  39. Y. Bromberg and H. Cao, “Generating non-rayleigh speckles with tailored intensity statistics,” Phys. Rev. Lett. 112, 213904 (2014).
    [Crossref]

2016 (1)

2015 (1)

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

2014 (2)

R. Y. Gu, R. N. Mahalati, and J. M. Kahn, “Noise-reduction algorithms for optimization-based imaging through multi-mode fiber,” Opt. Express 22, 15118–15132 (2014).
[Crossref] [PubMed]

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

2013 (6)

M. Berry, “A note on superoscillations associated with bessel beams,” J. Opt. 15, 044006 (2013).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

E. T. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
[Crossref]

M. Boguslawski, S. Brake, J. Armijo, F. Diebel, P. Rose, and C. Denz, “Analysis of transverse anderson localization in refractive index structures with customized random potential,” Opt. Express 21, 31713–31724 (2013).
[Crossref]

R. N. Mahalati, R. Y. Gu, and J. M. Kahn, “Resolution limits for imaging through multi-mode fiber,” Opt. Express 21, 1656–1668 (2013).
[Crossref] [PubMed]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

2012 (2)

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

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

2011 (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

2010 (2)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2, 405–450 (2010).
[Crossref]

2009 (2)

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

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[Crossref] [PubMed]

2008 (2)

2007 (1)

2006 (1)

2005 (4)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

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, 183602 (2005).
[Crossref] [PubMed]

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

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

2004 (2)

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

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

2002 (2)

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

Z. Bouchal, “Controlled spatial shaping of nondiffracting patterns and arrays,” Opt. Lett. 27, 1376–1378 (2002).
[Crossref]

2001 (1)

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

1998 (1)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

1996 (1)

C. Paterson and R. Smith, “Higher-order bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

1995 (1)

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

1987 (2)

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Abouraddy, A. F.

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

Angelo, M. D.

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

Armijo, J.

Bache, M.

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, 183602 (2005).
[Crossref] [PubMed]

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

Baraniuk, R. G.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Baron, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Bennink, R. S.

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

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

Bentley, S. J.

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

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

Berry, M.

M. Berry, “A note on superoscillations associated with bessel beams,” J. Opt. 15, 044006 (2013).
[Crossref]

Betzig, E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Boguslawski, M.

Bouchal, Z.

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Bowman, R. W.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Boyd, R. W.

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

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

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

Brake, S.

Brambilla, E.

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, 183602 (2005).
[Crossref] [PubMed]

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

Bromberg, Y.

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

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

Cao, H.

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

Chen, X.-H.

Chlup, M.

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

Cižmár, T.

Cottrell, D. M.

Courtial, J.

Craven, J. M.

Davidson, M. W.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Davis, J. A.

Deacon, K. S.

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

Dennis, M. R.

Denz, C.

Dholakia, K.

T. Čižmár and K. Dholakia, “Tunable bessel light modes: engineering the axial propagation,” Opt. Express 17, 15558–15570 (2009).
[Crossref] [PubMed]

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Diebel, F.

Duarte, M. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Durnin, J.

J. Durnin, “Exact solutions for nondiffracting beams. i. the scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Eberly, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Edgar, M. P.

M.-J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24 (10), 10476–10485 (2016).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Erkmen, B. I.

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2, 405–450 (2010).
[Crossref]

Fahrbach, F. O.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Ferri, F.

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, 183602 (2005).
[Crossref] [PubMed]

Galbraith, C. G.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Galbraith, J. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Gao, L.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Gatti, A.

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, 183602 (2005).
[Crossref] [PubMed]

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

Gibson, G. M.

M.-J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24 (10), 10476–10485 (2016).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

J. W. Goodman, Speckle phenomena in optics: theory and applications (Roberts and Company Publishers, 2007).

Gu, R. Y.

Hamilton, A. C.

Hardy, N. D.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

Howell, J. C.

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

Kahn, J. M.

Katz, O.

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

Kelly, K. F.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Laska, J. N.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Levoy, M.

M. Levoy, “Light fields and computational imaging,” Computer pp. 46–55 (2006).
[Crossref]

Lugiato, L. A.

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, 183602 (2005).
[Crossref] [PubMed]

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

Magatti, D.

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, 183602 (2005).
[Crossref] [PubMed]

Mahalati, R. N.

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

Meyers, R. E.

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

Miceli, J.

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Milkie, D. E.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Mitchell, K. J.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Padgett, M.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Padgett, M. J.

M.-J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24 (10), 10476–10485 (2016).

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Paterson, C.

C. Paterson and R. Smith, “Higher-order bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Phillips, D. B.

Pittman, T.

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

Planchon, T. A.

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Radwell, N.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Rogers, E. T.

E. T. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
[Crossref]

Rohrbach, A.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Rose, P.

Saleh, B. E.

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

Sarvotham, S.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Scarcelli, G.

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

Sergienko, A.

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

Sergienko, A. V.

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

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

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

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2, 405–450 (2010).
[Crossref]

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

Shih, Y.

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

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

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

Silberberg, Y.

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

Simon, P.

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Smith, R.

C. Paterson and R. Smith, “Higher-order bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Strekalov, D.

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

Sun, B.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Sun, M.-J.

Takhar, D.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Teich, M. C.

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

Tunick, A. D.

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

Valencia, A.

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

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Wagner, J.

Wakin, M. B.

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Welsh, S. S.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Whyte, G.

Wu, L.-A.

Zhai, Y.-H.

Zhang, D.

Zheludev, N. I.

E. T. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
[Crossref]

Adv. Opt. Photonics (1)

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2, 405–450 (2010).
[Crossref]

Appl. Phys. Lett. (1)

R. E. Meyers, K. S. Deacon, A. D. Tunick, and Y. Shih, “Virtual ghost imaging through turbulence and obscurants using bessel beam illumination,” Appl. Phys. Lett. 100, 061126 (2012).
[Crossref]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46, 15–28 (2005).
[Crossref]

J. Opt. (2)

E. T. Rogers and N. I. Zheludev, “Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging,” J. Opt. 15, 094008 (2013).
[Crossref]

M. Berry, “A note on superoscillations associated with bessel beams,” J. Opt. 15, 044006 (2013).
[Crossref]

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

Nat. Methods (1)

T. A. Planchon, L. Gao, D. E. Milkie, M. W. Davidson, J. A. Galbraith, C. G. Galbraith, and E. Betzig, “Rapid three-dimensional isotropic imaging of living cells using bessel beam plane illumination,” Nat. Methods 8, 417–423 (2011).
[Crossref] [PubMed]

Nat. Photonics (1)

F. O. Fahrbach, P. Simon, and A. Rohrbach, “Microscopy with self-reconstructing beams,” Nat. Photonics 4, 780–785 (2010).
[Crossref]

Opt. Commun. (2)

Z. Bouchal, J. Wagner, and M. Chlup, “Self-reconstruction of a distorted nondiffracting beam,” Opt. Commun. 151, 207–211 (1998).
[Crossref]

C. Paterson and R. Smith, “Higher-order bessel waves produced by axicon-type computer-generated holograms,” Opt. Commun. 124, 121–130 (1996).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rev. A (5)

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87, 023820 (2013).
[Crossref]

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

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

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

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

Phys. Rev. Lett. (7)

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, 183602 (2005).
[Crossref] [PubMed]

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

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

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

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

J. Durnin, J. Miceli, and J. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

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

Quantum Inf. Process. (1)

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

Sci. Rep. (1)

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 510669 (2015).
[Crossref]

Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Other (4)

D. Takhar, J. N. Laska, M. B. Wakin, M. F. Duarte, D. Baron, S. Sarvotham, K. F. Kelly, and R. G. Baraniuk, “A new compressive imaging camera architecture using optical-domain compression,” in “Electronic Imaging 2006,” (International Society for Optics and Photonics, 2006), pp. 606509.

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

J. W. Goodman, Speckle phenomena in optics: theory and applications (Roberts and Company Publishers, 2007).

M. Levoy, “Light fields and computational imaging,” Computer pp. 46–55 (2006).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1 (a) A schematic of our CGI setup. A 633 nm wavelength laser beam is transmitted through a single mode fibre to create a TEM 00 Gaussian mode. This is reflected by mirror M1 and illuminates a phase-only SLM (optically addressed Hamamatsu X8267-14) which is used to spatially modulate the phase of the beam. The beam waist of the illuminating beam is 4 mm. The SLM is placed at the back focal plane of a lens L1 of focal length 400 mm. The SLM phase modulation (which is described in Fig. 2(a,e)) generates a speckle pattern (shown in the inset) at the front focal plane of lens L1, in the +1 order of the diffracted beam. An aperture is used to select only the +1 diffraction order beam and block all other orders. A telescope (L2 and L3, of focal lengths 30 mm and 60 mm respectively) is used to magnify (by a factor of 2) and re-image the speckle pattern to the front focal plane of L3, conjugate to the front focal plane of L1. The front focal plane of L3 represents an axial position of z = 0. A binary transmissive object is placed at any plane in-between L3 and a photodetector (ThorLabs PDA100A-EC) positioned at a distance of 400 mm behind L3. The photodiode records the total intensity of light transmitted through the object. (b–e) The formation of a computational ghost image using ND speckle: (b) shows a transmissive object (height 1 mm), and (c–e) show reconstructions after the projection of increasing numbers of speckle patterns.
Fig. 2
Fig. 2 Numerical simulations of speckle generation using an SLM. (a–d) Conventional speckle. (e–h) Pseudo-non-diffracting speckle. (a,e) Relative phase of super-pixels on the SLM (greyscale value maps to phase, white = 0 rad. and black = 2π rad.). (b,f) Intensity pattern in Fourier plane of SLM. (c,g) Intensity pattern of speckle after propagation for 0.2 m. (d,h) Side-view cross-section of speckle intensity distribution over a propagation distance of 0.4 m. Red dashed lines in (d,h) correspond to planes (b,f) respectively. White dashed lines in (d,h) correspond to planes (c,g) respectively. Arrows in (b,c,f,g) indicate the vertical plane cross-section viewed in (d,h).
Fig. 3
Fig. 3 Controlling the depth-of-field around a single plane in a CGI system. All images are reconstructed from 5500 speckle patterns. The transmissive object (1 mm in height) is shown as inset bottom right. R = 2.3 mm. The super-pixels are of dimension 0.3×0.3 mm in each case. Top row: images reconstructed using conventional speckle generated from a disk shaped aperture of radius rmax = R on the SLM. Middle row: images reconstructed using ND speckle generated from an annular shaped aperture of maximum radius rmax = R and minimum radius rmin = 2.0 mm on the SLM. Bottom row: images reconstructed using conventional speckle generated from a disk shaped aperture of radius rmax = 1.5R on the SLM.
Fig. 4
Fig. 4 CGI resolving power. Upper row (a,c,e,g,i,k) conventional speckle. Lower row (b,d,f,h,j,l) ND speckle. (a,b) PSFs. (b) shows IND(ρ) given by Eq. (5) with rmin = 0.87rmax as in our experiments. (c–j) show a comparison of experimentally measured images of double slits in a modified 1951 USAF resolution test chart, imaged with conventional (upper row) and ND (lower row) speckle. The slit width and separation δS is given in each case. Cross-sections through the images of the slits are shown at the bottom of each image in white. The slits correspond to the following 1951 USAF resolution chart group-element labels: (c,d) 1–4, (e,f) 2–3, (g,h) 3–1, and (i,j) 3–2. (k,l) Simulation showing a comparison of the resolving power and contrast for conventional and ND speckle. Each vertical column of pixels in images (k) and (l) is a line-profile taken through two δ-functions convolved with the conventional (k) and ND (l) PSFs. The height of the line profile is plotted as intensity. From right to left the separation between the δ-functions, δS, is linearly increased. The separation at which the δ-functions are no longer resolvable as separate points is marked as δSmin.

Equations (5)

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

I = S P S P ,
z s t a b l e = 2 π f 2 k ( r m a x 2 r m i n 2 ) ,
z r a n g e = D f 2 r m i n ,
I ( ρ ) = I 0 | J 1 ( k r ρ / f ) / ρ | 2 ,
I N D ( ρ ) = I 0 | ( r m a x / ρ ) J 1 ( k ρ r m a x / f ) ( r m i n / ρ ) J 1 ( k ρ r m i n / f ) | 2 ,

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