Abstract

A new type of confocal microscope is described which makes use of intensity correlations between spatially correlated beams of light. It is shown that this apparatus leads to significantly improved transverse resolution.

© 2010 Optical Society of America

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  9. W. Denk, and K. Svoboda, “Photon Upmanship: Why Multiphoton Imaging is More than a Gimmick,” Neuron 18, 351–357 (1997).
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  11. R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. Lond. A Math. Phys. Sci. 242, 300–324 (1957).
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    [CrossRef] [PubMed]
  21. C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
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  24. 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]
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  28. 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, 063602 (2006).
    [CrossRef] [PubMed]
  29. 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]
  30. 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]
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    [CrossRef] [PubMed]
  37. Y. Bai, and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
    [CrossRef]
  38. L.-H. Ou, and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. At. Mol. Opt. Phys. 40, 1833–1844 (2007).
    [CrossRef]
  39. D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
    [CrossRef]
  40. I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
    [CrossRef]
  41. Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
    [CrossRef]
  42. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-Order Thermal Ghost Imaging,” Opt. Lett. 34, 3343–3345 (2009).
    [CrossRef]
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2010 (1)

2009 (5)

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-Order Thermal Ghost Imaging,” Opt. Lett. 34, 3343–3345 (2009).
[CrossRef]

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

D. S. Simon, and A. V. Sergienko, “Spatial-dispersion cancellation in quantum interferometry,” Phys. Rev. A 80, 053813 (2009).
[CrossRef]

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

2008 (3)

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

2007 (2)

Y. Bai, and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

L.-H. Ou, and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. At. Mol. Opt. Phys. 40, 1833–1844 (2007).
[CrossRef]

2006 (1)

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, 063602 (2006).
[CrossRef] [PubMed]

2005 (4)

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]

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]

Y. J. Cai, and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056607 (2005).
[CrossRef]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

2004 (4)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

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]

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

2002 (2)

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-Photon Ellipsometry,” J. Opt. Soc. Am. B 19, 656–662 (2002).
[CrossRef]

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] [PubMed]

2001 (2)

1997 (3)

W. Denk, and K. Svoboda, “Photon Upmanship: Why Multiphoton Imaging is More than a Gimmick,” Neuron 18, 351–357 (1997).
[CrossRef] [PubMed]

K. D. Mielenz, “Algorithms for Fresnel Diffraction at Rectangular and Circular Apertures,” J. Res. Natl. Inst. Stand. Technol. 103, 497–508 (1997).

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

1996 (1)

R. H. Webb, “Confocal Optical Microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

1995 (1)

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

1992 (2)

J. D. Franson, “Nonlocal Cancellation of Dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

1990 (1)

W. Denk, J. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

1988 (1)

M. Minsky, “Memoir on Inventing the Confocal Scanning Microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

1972 (1)

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic Fluctuations in a Reacting System-Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

1958 (1)

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light,” Proc. R. Soc. Lond. A Math. Phys. Sci. 243, 291–319 (1958).
[CrossRef]

1957 (1)

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. Lond. A Math. Phys. Sci. 242, 300–324 (1957).
[CrossRef]

1956 (1)

R. Hanbury Brown, and R. Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[CrossRef]

Abouraddy, A. F.

Agafonov, I. N.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

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]

Bai, Y.

Y. Bai, and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

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] [PubMed]

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] [PubMed]

Berardi, V.

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, 063602 (2006).
[CrossRef] [PubMed]

Bonato, C.

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

Bonora, S.

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

Boyd, R. W.

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, 5562–5573 (2010).
[CrossRef] [PubMed]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-Order Thermal Ghost Imaging,” Opt. Lett. 34, 3343–3345 (2009).
[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] [PubMed]

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]

Bycenski, K. J.

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

Cai, Y. J.

Y. J. Cai, and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056607 (2005).
[CrossRef]

Cao, D.-Z.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Carcia, P. F.

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

Chan, K. W. C.

Chekhova, M. V.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Chen, X. H.

Chen, X.-H.

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

Denk, W.

W. Denk, and K. Svoboda, “Photon Upmanship: Why Multiphoton Imaging is More than a Gimmick,” Neuron 18, 351–357 (1997).
[CrossRef] [PubMed]

W. Denk, J. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Di Giuseppe, G.

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

Elson, E.

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic Fluctuations in a Reacting System-Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[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]

Franson, J. D.

J. D. Franson, “Nonlocal Cancellation of Dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

French, R. H.

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

Gao, L.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

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]

Han, S.

Y. Bai, and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Hanbury Brown, R.

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light,” Proc. R. Soc. Lond. A Math. Phys. Sci. 243, 291–319 (1958).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. Lond. A Math. Phys. Sci. 242, 300–324 (1957).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[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]

Iskhakov, T. Sh.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Jones, D. J.

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

Kuang, L.-M.

L.-H. Ou, and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. At. Mol. Opt. Phys. 40, 1833–1844 (2007).
[CrossRef]

Kwiat, P. G.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

Lemon, M. F.

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

Lin, L.-F.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Liu, Q.

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[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]

Luo, K.-H.

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[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]

Magde, D.

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic Fluctuations in a Reacting System-Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Mielenz, K. D.

K. D. Mielenz, “Algorithms for Fresnel Diffraction at Rectangular and Circular Apertures,” J. Res. Natl. Inst. Stand. Technol. 103, 497–508 (1997).

Minaeva, O.

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

Minsky, M.

M. Minsky, “Memoir on Inventing the Confocal Scanning Microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

Muthukrishnan, A.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

O’Sullivan, M. N.

Ou, L.-H.

L.-H. Ou, and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. At. Mol. Opt. Phys. 40, 1833–1844 (2007).
[CrossRef]

Penin, A. N.

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Pittman, T. B.

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

Reilly, M. H.

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

Saleh, B. E. A.

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-Photon Ellipsometry,” J. Opt. Soc. Am. B 19, 656–662 (2002).
[CrossRef]

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Ellipsometric Measurements Using Photon Pairs Generated by Parametric Down-Conversion,” Opt. Lett. 26, 1717–1719 (2001).
[CrossRef]

Scarcelli, G.

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, 063602 (2006).
[CrossRef] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

Scully, M. O.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

Sergienko, A. V.

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

D. S. Simon, and A. V. Sergienko, “Spatial-dispersion cancellation in quantum interferometry,” Phys. Rev. A 80, 053813 (2009).
[CrossRef]

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Entangled-Photon Ellipsometry,” J. Opt. Soc. Am. B 19, 656–662 (2002).
[CrossRef]

A. F. Abouraddy, K. C. Toussaint, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Ellipsometric Measurements Using Photon Pairs Generated by Parametric Down-Conversion,” Opt. Lett. 26, 1717–1719 (2001).
[CrossRef]

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

Shih, Y. H.

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, 063602 (2006).
[CrossRef] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

Simon, D. S.

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

D. S. Simon, and A. V. Sergienko, “Spatial-dispersion cancellation in quantum interferometry,” Phys. Rev. A 80, 053813 (2009).
[CrossRef]

Steinberg, A. M.

A. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

Strekalov, D. V.

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

Strickler, J.

W. Denk, J. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Sullivan, M. N. O.

Svoboda, K.

W. Denk, and K. Svoboda, “Photon Upmanship: Why Multiphoton Imaging is More than a Gimmick,” Neuron 18, 351–357 (1997).
[CrossRef] [PubMed]

Teich, M. C.

Toussaint, K. C.

Twiss, R. Q.

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light,” Proc. R. Soc. Lond. A Math. Phys. Sci. 243, 291–319 (1958).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. Lond. A Math. Phys. Sci. 242, 300–324 (1957).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[CrossRef]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

Villoresi, P.

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

Wang, K.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Webb, R. H.

R. H. Webb, “Confocal Optical Microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

Webb, W. W.

W. W. Webb, “Fluorescence Correlation Spectroscopy: Inception, Biophysical Experimentations, and Prospectus,” Appl. Opt. 40, 3969–3983 (2001).
[CrossRef]

W. Denk, J. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic Fluctuations in a Reacting System-Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Wu, L. A.

Wu, L.-A.

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Wu, W.

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

Xiong, J.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhai, Y. H.

Zhang, D.

Zhang, S.-H.

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

Zhu, S. Y.

Y. J. Cai, and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056607 (2005).
[CrossRef]

Zubairy, M. S.

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

Appl. Opt. (1)

Appl. Phys. Lett. (2)

P. F. Carcia, R. H. French, M. H. Reilly, M. F. Lemon, and D. J. Jones, “Optical superlattices-a strategy for designing phase-shift masks for photolithographys at 248 and 193 nm: Application to AIN/CrN,” Appl. Phys. Lett. 70, 2371–2372 (1997).
[CrossRef]

D.-Z. Cao, J. Xiong, S.-H. Zhang, L.-F. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nthorder intensity correlation of thermal light,” Appl. Phys. Lett. 92, 201102 (2008).
[CrossRef]

J. Opt. B (1)

A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).

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

J. Phys. At. Mol. Opt. Phys. (1)

L.-H. Ou, and L.-M. Kuang, “Ghost imaging with third-order correlated thermal light,” J. Phys. At. Mol. Opt. Phys. 40, 1833–1844 (2007).
[CrossRef]

J. Res. Natl. Inst. Stand. Technol. (1)

K. D. Mielenz, “Algorithms for Fresnel Diffraction at Rectangular and Circular Apertures,” J. Res. Natl. Inst. Stand. Technol. 103, 497–508 (1997).

Nature (1)

R. Hanbury Brown, and R. Q. Twiss, “A Test of a New Type of Stellar Interferometer on Sirius,” Nature 178, 1046–1048 (1956).
[CrossRef]

Neuron (1)

W. Denk, and K. Svoboda, “Photon Upmanship: Why Multiphoton Imaging is More than a Gimmick,” Neuron 18, 351–357 (1997).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (9)

I. N. Agafonov, M. V. Chekhova, T. Sh. Iskhakov, and A. N. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77, 053801 (2008).
[CrossRef]

Q. Liu, X.-H. Chen, K.-H. Luo, W. Wu, and L.-A. Wu, “Role of multiphoton bunching in high-order ghost imaging with thermal light sources,” Phys. Rev. A 79, 053844 (2009).
[CrossRef]

K. C. Toussaint, G. Di Giuseppe, K. J. Bycenski, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Quantum Ellipsometry Using Correlated Photon Beams,” Phys. Rev. A 70, 023801 (2004).
[CrossRef]

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, R3429–R3432 (1995).
[CrossRef] [PubMed]

J. D. Franson, “Nonlocal Cancellation of Dispersion,” Phys. Rev. A 45, 3126–3132 (1992).
[CrossRef] [PubMed]

Y. Bai, and S. Han, “Ghost imaging with thermal light by third-order correlation,” Phys. Rev. A 76, 043828 (2007).
[CrossRef]

C. Bonato, D. S. Simon, P. Villoresi, and A. V. Sergienko, “Multiparameter Entangled-state Engineering using Adaptive Optics,” Phys. Rev. A 79, 062304 (2009).
[CrossRef]

D. S. Simon, and A. V. Sergienko, “Spatial-dispersion cancellation in quantum interferometry,” Phys. Rev. A 80, 053813 (2009).
[CrossRef]

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

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

Y. J. Cai, and S. Y. Zhu, “Ghost imaging with incoherent and partially coherent light radiation,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (9)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-Photon Imaging with Thermal Light,” Phys. Rev. Lett. 94, 063601 (2005).
[CrossRef] [PubMed]

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, 063602 (2006).
[CrossRef] [PubMed]

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]

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] [PubMed]

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. M. Steinberg, P. G. Kwiat, and R. Y. Chiao, “Dispersion cancellation in a measurement of the single-photon propagation velocity in glass,” Phys. Rev. Lett. 68, 2421–2424 (1992).
[CrossRef] [PubMed]

O. Minaeva, C. Bonato, B. E. A. Saleh, D. S. Simon, and A. V. Sergienko, “Odd- and Even-Order Dispersion Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 102, 100504 (2009).
[CrossRef]

C. Bonato, A. V. Sergienko, B. E. A. Saleh, S. Bonora, and P. Villoresi, “Even-Order Aberration Cancellation in Quantum Interferometry,” Phys. Rev. Lett. 101, 233603 (2008).
[CrossRef] [PubMed]

D. Magde, E. Elson, and W. W. Webb, “Thermodynamic Fluctuations in a Reacting System-Measurement by Fluorescence Correlation Spectroscopy,” Phys. Rev. Lett. 29, 705–708 (1972).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci. (2)

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation,” Proc. R. Soc. Lond. A Math. Phys. Sci. 242, 300–324 (1957).
[CrossRef]

R. Hanbury Brown, and R. Q. Twiss, “Interferometry of the intensity fluctuations in light. II. An experimental test of the theory for partially coherent light,” Proc. R. Soc. Lond. A Math. Phys. Sci. 243, 291–319 (1958).
[CrossRef]

Rep. Prog. Phys. (1)

R. H. Webb, “Confocal Optical Microscopy,” Rep. Prog. Phys. 59, 427–471 (1996).
[CrossRef]

Scanning (1)

M. Minsky, “Memoir on Inventing the Confocal Scanning Microscope,” Scanning 10, 128–138 (1988).
[CrossRef]

Science (1)

W. Denk, J. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73–76 (1990).
[CrossRef] [PubMed]

Other (7)

M. Minsky, U.S. Patent # 3013467, Microscopy Apparatus (1957).

R. Pecora, Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy (Plenum Press, 1985).

K. S. Schmitz, An Introduction to Dynamic Light Scattering By Macromolecules (Academic Press, 1990).

B. J. Berne, and R. J. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics, (Dover Publications, 2000). (Reprint of 1976 Wiley edition.)

J. C. Mertz, Introduction to Optical Microscopy (Roberts and Company Publishers, 2009).

P.F. Carcia, G. Hughes, R.H. French, C. Torardi, G. Reynolds, L. Dieu, “Thin Films for Phase-Shift Masks”, Vacuum and Thin Film, Sept. 14–21, 1–10 (1999)

T. M. Cover, and J. A. Thomas, Elements of Information Theory (Wiley, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

(Color online) Schematic diagram for standard confocal microscope.

Fig. 2.
Fig. 2.

(Color online) Two methods for making a confocal microscope without a source pinhole.

Fig. 3.
Fig. 3.

(Color online) Schematic diagram for correlation confocal microscope with two branches, comprised of two confocal microscopes whose output is combined in a correlated manner.

Fig. 4.
Fig. 4.

(Color online) Comparison of images produced by correlated (blue solid) and standard uncorrelated (red dashed) confocal microscopes for two square objects (black dotted) separated by a gap. The correlated version shows a substantially improved ability to distinguish objects with small separation.

Fig. 5.
Fig. 5.

(Color online) Comparison of images produced by correlated (blue solid) and standard uncorrelated (red dashed) confocal microscopes for three square objects (black dotted) separated by gaps.

Fig. 6.
Fig. 6.

(Color online) Comparison of images produced by correlated (blue solid) and standard uncorrelated (red dashed) confocal microscopes for a more complicated object (black dotted).

Fig. 7.
Fig. 7.

(Color online) Comparison of transverse intensity point spread functions for standard correlated (blue solid) and uncorrelated (red dashed) confocal microscopes.

Fig. 8.
Fig. 8.

(Color online) Correlation confocal microscope with a single branch.

Fig. 9.
Fig. 9.

(Color online) To view thick samples, the phase modulation plane needs to be moved away from the object plane by distance ζ 2.

Equations (34)

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1z1+1z2=1f
hi(ξ,y)=eik2(y2z2+ξ22z1) p˜ (k(yz2+ξz1)) ,
p˜(q)=2πa2J1(aq)(aq)
hi(y)=hi(0,y)=eiky22z2p˜(kyz2)
h(y)=d2yh1(ξ,y)t(y+y)h2(y,x)x=ξ=0
= d2 y h1 (y) t (y+y) h2 (y) .
CSF(y)=h1(y) h2 (y) ,
PSF(y)=h1(y)h2(y)2.
PSF(y)[p˜(kyz2)]4(J1(kayz2)(kay/z2))4,
PSFwide(y)[p˜(kyz2)]2(J1(kayz2)(kay/z2))2.
eiϕ1(y)=ei(cy·b),eiϕ2(y)=ei(cy·b),
â0=12(â1iâ2).
b̂j=âj p˜2 (kyjz2) tj (yj+y) eiϕj(yj) eikyj22z2 d2 yj .
(12(b̂1ib̂2))20=12{[p˜2(ky1z2)t1(y1+y)eiϕ1(y1)eiky122z2d2y1]2â1†2
[p˜2(ky2z2)t2(y2+y)eiϕ2(y2)eiky222z2d2y2]2â2†2
2iâ1â2 p˜2 (ky1z2) p˜2 (ky2z2) t1 (y1+y) t1 (y2+y)ei[ϕ1(y1)+ϕ2(y2)] eik(y12+y22)2z2 d2 y1 d2 y2 } 0 .
â1=12(â3iâ4)
â2=12(â4iâ3),
A3(y)= d2 y d2 y p˜2 (kyz2) p˜2 (kyz2) t (y+y) t (y+y)
×eik(y2+y2)2z2(ei[ϕ(y)+ϕ(y)]+ei[ϕ(y)+ϕ(y)]2ei[ϕ(y)ϕ(y)]).
A3(y)= d2 y d2 y p˜2 (kyz2) p˜2 (kyz2) t (y+y) t (y+y)eik(y2+y2)2z2
×[cos(ϕ(y)+ϕ(y))cos(ϕ(y)ϕ(y))isin(ϕ(y)ϕ(y))].
Rc(y)=A3(y)2,
PSF(y)=[1cos(2ϕ(y))]p˜4(kyz2)=sin2(ϕ(y))p˜4(kyz2),
h1(ξ=0,y)=eik2z2y2 ei(cb·y) p˜ (kz2(y+ζ2kb)) ,
h1(ξ=0,y)=eik2z2y2 ei(cb·y) p˜ (kz2y) ,
PSFstandard(δz)=sinc4 (κδz) ,
A3(y,δz1,δ2)= d2 y d2 y t (y+y) t (y+y) eik(y2+y2)2z2
×E(4κδza,ka2z2y)E(+4κδza,ka2z2y)
×E(4κδzb,ka2z2y)E(+4κδzb,ka2z2y)
×[cos(ϕ(y)+ϕ(y))cos(ϕ(y)ϕ(y))isin(ϕ(y)ϕ(y))].
E(u,v)[L(u,v)+iM(u,v)]=201J0(νρ)ei2uρ2ρdρ,
PSFaxial(δza,δzb)=E(4κδza,0)E(4κδza,0)E(4κδzb,0)E(4κδzb,0)2
=sinc4(κδza)sinc4(κδzb).

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