Abstract

Intensity interferometry (II), the landmark of the second-order correlation, enables very long baseline observations at optical wavelengths, providing imaging with microarcsecond resolution. However, the unreliability of traditional phase retrieval algorithms required to reconstruct images in II has hindered its development. We here develop a method that circumvents this challenge, which enables II to reliably image complex shaped objects. Instead of measuring the whole object, we measure it part by part with a probe moving in a ptychographic way: adjacent parts overlap with each other. A relevant algorithm is developed to reliably and rapidly recover the object in a few iterations. Moreover, we propose an approach to remove the requirement for a precise knowledge of the probe, providing an error-tolerance of more than 50% for the location of the probe in our experiments. Furthermore, we extend II to short distance scenarios, providing a lensless imaging method with incoherent light and paving a way towards applications in X-ray imaging.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature,  178, 1046–1048 (1956).
    [Crossref]
  2. E. M. Purcell, “The Question of Correlation between Photons in Coherent Light Rays,” Nature,  178, 1449–1450 (1956).
    [Crossref]
  3. U. Fano, “Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources,” Am. J. Phys. 29, 539–545 (1961).
    [Crossref]
  4. B. L. Morgan and L. Mandel, “Measurement of Photon Bunching in a Thermal Light Beam,” Phys. Rev. Lett. 16, 1012–1015 (1966).
    [Crossref]
  5. R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
    [Crossref]
  6. 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, 3429–3431 (1995).
    [Crossref]
  7. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).
  8. R. H. 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. Roy. Soc. Lon. A,  242, 300–324 (1957).
    [Crossref]
  9. H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
    [Crossref] [PubMed]
  10. D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
    [Crossref] [PubMed]
  11. A.X. Zhang, Y.H. He, L.A. Wu, L.M. Chen, and B.B. Wang,“Table-top X-ray Ghost Imaging with Ultra-Low Radiation,” Optica,  5, 374–377 (2018).
    [Crossref]
  12. A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
    [Crossref] [PubMed]
  13. R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
    [Crossref]
  14. G. Baym, “The physics of hanbury brown–twiss intensity interferometry: from stars to nuclear collisions,” Acta Phys. Pol 29, 1839 (1998).
  15. D. Dravins and S. Lebohec, “Stellar intensity interferometry: astrophysical targets for sub-milliarcsecond imaging,” Proc. SPIE7734, (2010).
    [Crossref]
  16. P. R. Lawson, “Principles of long baseline stellar interferometry,” in “Principles of Long Baseline Stellar Interferometry,” 50–60 (JPL2000).
  17. D. W. Mccarthy and F.J. Low,“Initial results of spatial interferometry at 5 microns,” Astrophys. J.,  202, 37–40 (1975).
    [Crossref]
  18. D. H. Staelin and M. Shao, “Long-baseline optical interferometer for astrometry,” J. Opt. Soc. Am. 67, 81–86 (1978).
  19. R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” J. Astrophys. 15, 13–19 (1994).
  20. R. H. Brown and D. Scarl, “The intensity interferometer, its application to astronomy,” Phys. Tod. 28, 54–55 (1975).
    [Crossref]
  21. S. L. Bohec and J. Holder, “Optical intensity interferometry with atmospheric cherenkov telescope arrays,” Astrophys. J. 649, 399–405 (2006).
    [Crossref]
  22. V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
    [Crossref]
  23. D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
    [Crossref]
  24. W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
    [Crossref]
  25. J. R. Fienup, “Reconstruction of an object from the modulus of its fourier transform,” Opt. Lett. 3, 27 (1978).
    [Crossref] [PubMed]
  26. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [Crossref] [PubMed]
  27. C. C. Wackerman and J. R. Fienup, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
    [Crossref]
  28. H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [Crossref] [PubMed]
  29. L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica,  2, 104–111 (2015).
    [Crossref]
  30. W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultra,  10, 187–198 (1982).
    [Crossref]
  31. C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
    [Crossref]
  32. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultra,  109, 1256–1262 (2009).
    [Crossref]
  33. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
    [Crossref]
  34. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592 (2013).
    [Crossref] [PubMed]
  35. P. van Cittert, “Die wahrscheinliche schwingungsverteilung in einer von einer lichtquelle direkt oder mittels einer linse beleuchteten ebene,” Physica,  1, 201–210 (1934).
    [Crossref]
  36. F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica,  5, 785–795 (1938).
    [Crossref]
  37. O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
    [Crossref]
  38. J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
    [Crossref]
  39. W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
    [Crossref]
  40. H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
    [Crossref]
  41. V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [Crossref]
  42. T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
    [Crossref] [PubMed]
  43. F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
    [Crossref]
  44. L. I. Goldfischer, “Autocorrelation function and power spectral density of laser-produced speckle patterns,” J. Opt. Soc. Am. 55247 (1965).
    [Crossref]
  45. J.R. Fienup and P.S. Idell, “Imaging Correlography With Sparse Arrays Of Detectors,” Opti. Eng 27(9), 279778 (1988).

2018 (2)

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

A.X. Zhang, Y.H. He, L.A. Wu, L.M. Chen, and B.B. Wang,“Table-top X-ray Ghost Imaging with Ultra-Low Radiation,” Optica,  5, 374–377 (2018).
[Crossref]

2017 (2)

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

2016 (2)

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
[Crossref]

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

2013 (3)

H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
[Crossref]

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592 (2013).
[Crossref] [PubMed]

2012 (3)

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
[Crossref]

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

2011 (1)

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

2009 (2)

C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultra,  109, 1256–1262 (2009).
[Crossref]

2006 (1)

S. L. Bohec and J. Holder, “Optical intensity interferometry with atmospheric cherenkov telescope arrays,” Astrophys. J. 649, 399–405 (2006).
[Crossref]

2005 (1)

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

2004 (2)

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

1998 (1)

G. Baym, “The physics of hanbury brown–twiss intensity interferometry: from stars to nuclear collisions,” Acta Phys. Pol 29, 1839 (1998).

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, 3429–3431 (1995).
[Crossref]

1994 (1)

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” J. Astrophys. 15, 13–19 (1994).

1988 (1)

J.R. Fienup and P.S. Idell, “Imaging Correlography With Sparse Arrays Of Detectors,” Opti. Eng 27(9), 279778 (1988).

1986 (1)

1982 (2)

W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultra,  10, 187–198 (1982).
[Crossref]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[Crossref] [PubMed]

1978 (2)

1975 (2)

R. H. Brown and D. Scarl, “The intensity interferometer, its application to astronomy,” Phys. Tod. 28, 54–55 (1975).
[Crossref]

D. W. Mccarthy and F.J. Low,“Initial results of spatial interferometry at 5 microns,” Astrophys. J.,  202, 37–40 (1975).
[Crossref]

1966 (1)

B. L. Morgan and L. Mandel, “Measurement of Photon Bunching in a Thermal Light Beam,” Phys. Rev. Lett. 16, 1012–1015 (1966).
[Crossref]

1965 (1)

1964 (1)

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

1963 (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

1961 (1)

U. Fano, “Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources,” Am. J. Phys. 29, 539–545 (1961).
[Crossref]

1957 (1)

R. H. 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. Roy. Soc. Lon. A,  242, 300–324 (1957).
[Crossref]

1956 (2)

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature,  178, 1046–1048 (1956).
[Crossref]

E. M. Purcell, “The Question of Correlation between Photons in Coherent Light Rays,” Nature,  178, 1449–1450 (1956).
[Crossref]

1938 (1)

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica,  5, 785–795 (1938).
[Crossref]

1934 (1)

P. van Cittert, “Die wahrscheinliche schwingungsverteilung in einer von einer lichtquelle direkt oder mittels einer linse beleuchteten ebene,” Physica,  1, 201–210 (1934).
[Crossref]

Alejandra, V.

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

Ayyer, K.

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

Baym, G.

G. Baym, “The physics of hanbury brown–twiss intensity interferometry: from stars to nuclear collisions,” Acta Phys. Pol 29, 1839 (1998).

Bean, R.

Benz, A.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Berenguer, F.

Bertolotti, J.

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Bhatti, D.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Blum, C.

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Bocklage, L.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Bohec, S. L.

S. L. Bohec and J. Holder, “Optical intensity interferometry with atmospheric cherenkov telescope arrays,” Astrophys. J. 649, 399–405 (2006).
[Crossref]

Brenner, G.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Brown, R. H.

R. H. Brown and D. Scarl, “The intensity interferometer, its application to astronomy,” Phys. Tod. 28, 54–55 (1975).
[Crossref]

R. H. 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. Roy. Soc. Lon. A,  242, 300–324 (1957).
[Crossref]

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature,  178, 1046–1048 (1956).
[Crossref]

Cantelli, V.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Chapman, H. N.

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

Chen, B.

Chen, H.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
[Crossref]

Chen, L.M.

Classen, A.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

Diaz, A.

Dravins, D.

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

D. Dravins and S. Lebohec, “Stellar intensity interferometry: astrophysical targets for sub-milliarcsecond imaging,” Proc. SPIE7734, (2010).
[Crossref]

Du, G.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Fano, U.

U. Fano, “Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources,” Am. J. Phys. 29, 539–545 (1961).
[Crossref]

Faulkner, H. M.

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Fienup, J.R.

J.R. Fienup and P.S. Idell, “Imaging Correlography With Sparse Arrays Of Detectors,” Opti. Eng 27(9), 279778 (1988).

Giuliano, S.

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

Glauber, R. J.

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

Goldfischer, L. I.

Gorobtsov, O.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Haije, F.

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

Han, S.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Hanbury-Brown, R.

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” J. Astrophys. 15, 13–19 (1994).

He, Y.H.

Holder, J.

S. L. Bohec and J. Holder, “Optical intensity interferometry with atmospheric cherenkov telescope arrays,” Astrophys. J. 649, 399–405 (2006).
[Crossref]

Hoppe, W.

W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultra,  10, 187–198 (1982).
[Crossref]

Humphry, M. J.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

Idell, P.S.

J.R. Fienup and P.S. Idell, “Imaging Correlography With Sparse Arrays Of Detectors,” Opti. Eng 27(9), 279778 (1988).

Jensen, H.

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

Katz, O.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
[Crossref]

Kraus, B.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

Lagendijk, Ad

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Lawson, P. R.

P. R. Lawson, “Principles of long baseline stellar interferometry,” in “Principles of Long Baseline Stellar Interferometry,” 50–60 (JPL2000).

Lebohec, S.

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

D. Dravins and S. Lebohec, “Stellar intensity interferometry: astrophysical targets for sub-milliarcsecond imaging,” Proc. SPIE7734, (2010).
[Crossref]

Liu, C.

C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
[Crossref]

Liu, J.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Liu, Y.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Low, F.J.

D. W. Mccarthy and F.J. Low,“Initial results of spatial interferometry at 5 microns,” Astrophys. J.,  202, 37–40 (1975).
[Crossref]

Lu, R.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Maiden, A. M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultra,  109, 1256–1262 (2009).
[Crossref]

Malvimat, V.

V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
[Crossref]

Mandel, L.

B. L. Morgan and L. Mandel, “Measurement of Photon Bunching in a Thermal Light Beam,” Phys. Rev. Lett. 16, 1012–1015 (1966).
[Crossref]

Martienssen, W.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Mccarthy, D. W.

D. W. Mccarthy and F.J. Low,“Initial results of spatial interferometry at 5 microns,” Astrophys. J.,  202, 37–40 (1975).
[Crossref]

Mehringer, T.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Menzel, A.

Mercurio, G.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Midgley, P. A.

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

Milena, D.

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

Morgan, B. L.

B. L. Morgan and L. Mandel, “Measurement of Photon Bunching in a Thermal Light Beam,” Phys. Rev. Lett. 16, 1012–1015 (1966).
[Crossref]

Mosk, P.

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Nuñez, P. D.

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

Paganin, D. M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Pelliccia, D.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Peng, T.

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
[Crossref]

Peterson, I.

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, 3429–3431 (1995).
[Crossref]

Purcell, E. M.

E. M. Purcell, “The Question of Correlation between Photons in Coherent Light Rays,” Nature,  178, 1449–1450 (1956).
[Crossref]

Rack, A.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Robinson, I. K.

Rodenburg, J. M.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592 (2013).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultra,  109, 1256–1262 (2009).
[Crossref]

C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
[Crossref]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Rohlsberger, R.

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

Saha, P.

V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
[Crossref]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

Scarl, D.

R. H. Brown and D. Scarl, “The intensity interferometer, its application to astronomy,” Phys. Tod. 28, 54–55 (1975).
[Crossref]

Scheel, M.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

Schneider, R.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Scully, M. O.

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

Sergienko, A. 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, 3429–3431 (1995).
[Crossref]

Shao, M.

Shih, Y.

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

Shih, Y. H.

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, 3429–3431 (1995).
[Crossref]

Silberberg, Y.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
[Crossref]

Small, E.

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
[Crossref]

Spiller, E.

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Staelin, D. H.

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, 3429–3431 (1995).
[Crossref]

Tang, Z.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Tian, L.

Twiss, R. Q.

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” J. Astrophys. 15, 13–19 (1994).

R. H. 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. Roy. Soc. Lon. A,  242, 300–324 (1957).
[Crossref]

R. H. 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. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

van Cittert, P.

P. van Cittert, “Die wahrscheinliche schwingungsverteilung in einer von einer lichtquelle direkt oder mittels einer linse beleuchteten ebene,” Physica,  1, 201–210 (1934).
[Crossref]

van Putten, E.G.

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Vila-Comamala, J.

Vos Allard, W. L.

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Wackerman, C. C.

Waller, L.

Walther, T.

C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
[Crossref]

Wang, B.B.

Wang, W.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Wenthaus, L.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Wu, L.A.

Wucknitz, O.

V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
[Crossref]

Xiao, T.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Xie, H.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Xu, Z.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Yanhua, S.

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

Yu, H.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Yuan, Y.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Zanthier, J. V.

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

Zernike, F.

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica,  5, 785–795 (1938).
[Crossref]

Zhang, A.X.

Zhang, F.

Zheng, H.

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Zhu, D.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

Acta Phys. Pol (1)

G. Baym, “The physics of hanbury brown–twiss intensity interferometry: from stars to nuclear collisions,” Acta Phys. Pol 29, 1839 (1998).

Am. J. Phys. (2)

U. Fano, “Quantum Theory of Interference Effects in the Mixing of Light from Phase-Independent Sources,” Am. J. Phys. 29, 539–545 (1961).
[Crossref]

W. Martienssen and E. Spiller, “Coherence and fluctuations in light beams,” Am. J. Phys. 32, 919–926 (1964).
[Crossref]

Appl. Opt. (1)

Astro. Phys. (1)

D. Dravins, S. Lebohec, H. Jensen, and P. D. Nuñez, “Optical intensity interferometry with the cherenkov telescope array,” Astro. Phys. 43, 331–347 (2013).
[Crossref]

Astrophys. J. (2)

S. L. Bohec and J. Holder, “Optical intensity interferometry with atmospheric cherenkov telescope arrays,” Astrophys. J. 649, 399–405 (2006).
[Crossref]

D. W. Mccarthy and F.J. Low,“Initial results of spatial interferometry at 5 microns,” Astrophys. J.,  202, 37–40 (1975).
[Crossref]

J. Astrophys. (1)

R. Hanbury-Brown and R. Q. Twiss, “Correlation between photons in two coherent beams of light,” J. Astrophys. 15, 13–19 (1994).

J. Opt. Soc. Am. (2)

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

Mon. Not. Roy. Astro. Soc. (1)

V. Malvimat, O. Wucknitz, and P. Saha, “Intensity interferometry with more than two detectors?” Mon. Not. Roy. Astro. Soc. 437, 798–803 (2014).
[Crossref]

Nature (2)

R. H. Brown and R. Q. Twiss, “A test of a new type of stellar interferometer on sirius,” Nature,  178, 1046–1048 (1956).
[Crossref]

E. M. Purcell, “The Question of Correlation between Photons in Coherent Light Rays,” Nature,  178, 1449–1450 (1956).
[Crossref]

Nature Photo. (2)

O. Katz, E. Small, and Y. Silberberg, “Looking around corners and through thin turbid layers in real time with scattered incoherent light,” Nature Photo. 6, 549–553 (2012).
[Crossref]

J. Bertolotti, E.G. van Putten, C. Blum, Ad Lagendijk, W. L. Vos Allard, and P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature Photo. 491, 232–234 (2012).
[Crossref]

Nature Phys. (1)

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, and L. Bocklage, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nature Phys. 1412 (2017).
[Crossref]

Opt. Commun. (1)

W. Wang, Z. Tang, H. Zheng, H. Chen, Y. Yuan, J. Liu, Y. Liu, and Z. Xu, “Intensity correlation imaging with sunlight-like source,” Opt. Commun. 414, 92–97 (2018).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Opti. Eng (1)

J.R. Fienup and P.S. Idell, “Imaging Correlography With Sparse Arrays Of Detectors,” Opti. Eng 27(9), 279778 (1988).

Optica (2)

Phys. Lett. (1)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon “ghost” imaging with thermal light,” Phys. Lett. 94, 557–559 (2004).

Phys. Rev. (1)

R. J. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130, 2529–2539 (1963).
[Crossref]

Phys. Rev. A (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, 3429–3431 (1995).
[Crossref]

H. Chen, T. Peng, and Y. Shih, “100% correlation of chaotic thermal light,” Phys. Rev. A,  88, 023808 (2013).
[Crossref]

Phys. Rev. Lett. (7)

V. Alejandra, S. Giuliano, D. Milena, and S. Yanhua, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref]

T. Peng, H. Chen, Y. Shih, and M. O. Scully, “Delayed-choice quantum eraser with thermal light,” Phys. Rev. Lett. 112, 180401 (2014).
[Crossref] [PubMed]

B. L. Morgan and L. Mandel, “Measurement of Photon Bunching in a Thermal Light Beam,” Phys. Rev. Lett. 16, 1012–1015 (1966).
[Crossref]

A. Classen, K. Ayyer, H. N. Chapman, R. Rohlsberger, and J. V. Zanthier, “Incoherent diffractive imaging via intensity correlations of hard x rays,” Phys. Rev. Lett. 119, 053401 (2017).
[Crossref] [PubMed]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117, 113901 (2016).
[Crossref] [PubMed]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117, 113902 (2016).
[Crossref] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[Crossref] [PubMed]

Phys. Tod. (1)

R. H. Brown and D. Scarl, “The intensity interferometer, its application to astronomy,” Phys. Tod. 28, 54–55 (1975).
[Crossref]

Physica (2)

P. van Cittert, “Die wahrscheinliche schwingungsverteilung in einer von einer lichtquelle direkt oder mittels einer linse beleuchteten ebene,” Physica,  1, 201–210 (1934).
[Crossref]

F. Zernike, “The concept of degree of coherence and its application to optical problems,” Physica,  5, 785–795 (1938).
[Crossref]

Proc. Roy. Soc. Lon. A (1)

R. H. 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. Roy. Soc. Lon. A,  242, 300–324 (1957).
[Crossref]

Ultra (2)

W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultra,  10, 187–198 (1982).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultra,  109, 1256–1262 (2009).
[Crossref]

Ultra. (3)

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultra. 120, 64–72 (2012).
[Crossref]

C. Liu, T. Walther, and J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultra. 109, 1263–1275 (2009).
[Crossref]

F. Haije, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultra. 111, 1117–1123 (2011).
[Crossref]

Other (2)

D. Dravins and S. Lebohec, “Stellar intensity interferometry: astrophysical targets for sub-milliarcsecond imaging,” Proc. SPIE7734, (2010).
[Crossref]

P. R. Lawson, “Principles of long baseline stellar interferometry,” in “Principles of Long Baseline Stellar Interferometry,” 50–60 (JPL2000).

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Figures (11)

Fig. 1
Fig. 1 A nebula is imaged with a telescope array on the ground. All the telescopes together measure the nebula section by section. The yellow dashed circles indicate three overlapping sections.
Fig. 2
Fig. 2 The flowchart of the algorithm. The dashed rectangle indicates the small loop of calculating the phases of different sections. The outer of the rectangle is the big iterative loop. The exiting condition is whether the maximum of iteration number is reached or a satisfactory image is obtained.
Fig. 3
Fig. 3 The object is made of hollow letters of “51201816”. The pseudo-thermal source is built with a laser beam scattered by a rotating ground glass (RGG). The scattered light is collimated by a lens and then projected onto the object, mimicking incoherent light illuminating the object. A light cone is placed in front of the camera as a section selector. Its head is 80 mm away from the object. Its body is 150 mm long.
Fig. 4
Fig. 4 (a) the recovered image with PIII within 10 iterations. (b) the reconstructed image after 1000 ER iterations ; (b) the reconstructed image after 1000 HIO iterations; (d), (e) and (f) are the corresponding relative residuals VS iterations for PIII, ER and HIO, respectively. Scale bar: 200pixels.
Fig. 5
Fig. 5 (a) One of the captured speckle patterns for the first probe. (b) The average autocorrelation function calculated from 100 speckles for the first probe. Scale bar: 650 µm.
Fig. 6
Fig. 6 (a) The recovered images after nine big iterations. (b) The corresponding relative residual VS. iteration (only the first nine iterations). (c) The variance of the relative residual in 1000 iterations. Scale bar: 500 µm.
Fig. 7
Fig. 7 (a) The actual position and size of the j − 1 and j-th probes. The diameter of the probes is a.(b) The gray dashed circles indicate the inaccurate estimation of the j − 1 and j-th probes. The deviation of the j-th probe is δj = (j − 1)∗h. The red dotted circles present the two loose supports which are enlarged to a diameter of a′.
Fig. 8
Fig. 8 Recovered images with different loose rates when the shift deviation is 25%. (a) loose rate=0. (b) loose rate=25%. All the reconstructions take 20 iterations.
Fig. 9
Fig. 9 Recovered images with different loose rates when the shift deviation is 50%. (a) loose rate=0. (b) loose rate=25%. (c) loose rate=75%. All the reconstructions take 20 iterations.
Fig. 10
Fig. 10 The schematic of the short-distance experiment setup. The probe is of a circular aperture with a diameter of 3 mm.
Fig. 11
Fig. 11 (a) The recovered image of “51201816” after 9 PIII iterations. Scale bar: 500 µm (b) The recovered image of the resolution chart board after 9 PIII iterations. The left column is of group 2, and the right column is of group 3. Scale bar: 100 µm.

Equations (10)

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Δ G ( 2 ) ( r 1 , r 2 ) Δ I 1 ( t , r 1 ) Δ I 2 ( t + τ , r 2 ) = C | γ 12 | 2 ,
γ 12 ( Δ r ) E 1 ( r 1 ) E 2 ( r 2 ) = e i ϕ Γ ( ρ ) exp [ i 2 π λ z ( Δ r ρ ) ] d ρ ,
| Δ r { Γ ( ρ ) } | 2 = | γ 12 | 2 = Δ G ( 2 ) ( Δ r ) / C Δ g ( 2 ) ( Δ r ) ,
A j ( Δ r ) = | Δ r { Γ ( ρ ) P j ( ρ ) ) } | = Δ g j ( 2 ) ( Δ r ) .
F k , j = A j F k , j | F k , j | .
Θ k , j ( ρ ) = { R e { Θ k , j ( ρ ) } , P j ( ρ ) = 1 [ R e { Θ k , j ( ρ ) } 0 ] 0 , P j ( ρ ) = 0 [ R e { Θ k , j ( ρ ) } < 0 ] ,
Γ ( ρ ) = Γ ( ρ ) [ 1 P j ( ρ ) ] + Θ k , j ( ρ ) .
P j ( ρ ) P ( ρ R j ) = { 1 , if | ρ R j | a 0 , if | ρ R j | > a ,
E ( r 1 ) E * ( r 2 ) = 1 λ 2 z 2 e i k 2 z ( r 1 2 r 2 2 ) T ( ρ ) T * ( ρ ) e i k 2 z ( ρ 2 ρ 2 ) × e i k z ( r 1 ρ r 2 ρ ) d ρ d ρ
| γ 12 | 2 | Γ ( ρ ) P ( ρ ) e i k z ρ ( r 1 r 2 ) d ρ | 2 .

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