Abstract

It is shown, using ghost-imaging techniques, that it is possible to reduce or even to annihilate the influence of aberrations connected with an arbitrary optical system. To this end, we consider a ghost-imaging setup, which consists of two arms, each containing an optical system. The reduction cancellation of the aberrations of the total imaging system is achieved by manipulating the values of the aberrations in one arm of the optical system. The technique is then applied for the optimal reconstruction of a weak phase object, manipulating the values of the defocusing such that the “Scherzer defocus condition” is obtained.

© 2013 Optical Society of America

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  34. J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78, 043823 (2008).
    [CrossRef]
  35. B. J. Hoenders, “On the reconstruction of a weak phase-amplitude object,” Optik 35, 116–133 (1972).
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    [CrossRef]
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2012 (2)

2011 (1)

T. Shirai, T. Setl, and A. T. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801 (2011).
[CrossRef]

2010 (2)

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

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

2008 (1)

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78, 043823 (2008).
[CrossRef]

2007 (1)

L. Bazano and P. Ottonello, “Ghost imaging: open secrets and puzzles for undergraduates,” Am. J. Phys. 75, 343–351 (2007).
[CrossRef]

2005 (1)

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

2004 (1)

2003 (2)

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

2002 (2)

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

V. Giovannetti, S. Lloyd, and L. Maccone, “Positioning and clock synchronization through entanglement,” Phys. Rev. A 65, 022309 (2002).
[CrossRef]

2001 (5)

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Subwavelength lithography over extended areas,” Phys. Rev. A 64, 013811 (2001).
[CrossRef]

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[CrossRef]

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

A. F. Abouraddy, B. E. A. Salehand, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

2000 (2)

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

1999 (2)

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

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

1996 (3)

P. H. S. Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef]

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef]

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

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

1988 (1)

D. N. Klyshko, “Combined EPR and two-slits experiments: interference of advanced waves,” Phys. Lett. 132, 299–304 (1988).
[CrossRef]

1980 (1)

D. Shafer, “Optical design with only two surfaces” in Proc. SPIE 0237, 256–261 (1980).
[CrossRef]

1972 (1)

B. J. Hoenders, “On the reconstruction of a weak phase-amplitude object,” Optik 35, 116–133 (1972).

1949 (1)

O. Scherzer, “The theoretical resolution limit of the electron microscope,” J. Appl. Phys. 20, 20–29 (1949).
[CrossRef]

Abouraddy, A. F.

A. F. Abouraddy, B. E. A. Salehand, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Angelo, M. D.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Barbosa, G. A.

P. H. S. Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef]

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef]

Bazano, L.

L. Bazano and P. Ottonello, “Ghost imaging: open secrets and puzzles for undergraduates,” Am. J. Phys. 75, 343–351 (2007).
[CrossRef]

Bjork, G.

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[CrossRef]

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Subwavelength lithography over extended areas,” Phys. Rev. A 64, 013811 (2001).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Brambilla, E.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Brida, G.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Cagliero, E.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Cai, Y.

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

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

Carter, C. B.

D. B. Williams and C. B. Carter, Transmission Electron Microscopy (Springer, 2009), Chap. 28.7.

Chekhova, M. V.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Cheng, J.

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78, 043823 (2008).
[CrossRef]

Cunha, M. O. T.

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Erkmen, B. I.

Falzetta, G.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Fonseca, E. J. S.

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

Friberg, A. T.

T. Shirai, H. Kellock, T. Setl, and A. T. Friberg, “Imaging through an aberrating medium with classical ghost diffraction,” J. Opt. Soc. Am. A 29, 1288–1292 (2012).
[CrossRef]

T. Shirai, T. Setl, and A. T. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801 (2011).
[CrossRef]

Gatti, A.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

Genovese, M.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Giovannetti, V.

V. Giovannetti, S. Lloyd, and L. Maccone, “Positioning and clock synchronization through entanglement,” Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000), Chap. 5.6.2, pp. 210–215.

Gramegna, M.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Hoenders, B. J.

B. J. Hoenders, “On the reconstruction of a weak phase-amplitude object,” Optik 35, 116–133 (1972).

Kellock, H.

Klyshko, D. N.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef]

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

D. N. Klyshko, “Combined EPR and two-slits experiments: interference of advanced waves,” Phys. Lett. 132, 299–304 (1988).
[CrossRef]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Kolobov, M. I.

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Positioning and clock synchronization through entanglement,” Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Lugiato, L. A.

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Positioning and clock synchronization through entanglement,” Phys. Rev. A 65, 022309 (2002).
[CrossRef]

Maréchal, A.

A. Maréchal, in Encyclopedia of Physics (Springer, 1956), Vol. 24, Sect. 67.

A. Maréchal, “Imagerie géométrique. Aberrations,” in Traite d’Optique Instrumentale. Section 1: La Formation des Images (Editions de la Revue d’Optique Théorique et Instrumentale, 1952), Chap. 6.3.4, p. 91.

Mikš, A.

Monken, C. H.

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

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

Nasr, M. B.

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

Novák, J.

Ottonello, P.

L. Bazano and P. Ottonello, “Ghost imaging: open secrets and puzzles for undergraduates,” Am. J. Phys. 75, 343–351 (2007).
[CrossRef]

Padua, S.

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

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

Pittman, T. B.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[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]

Predazzi, E.

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Ribeiro, P. H. S.

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

P. H. S. Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef]

Rubin, M. H.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef]

Saleh, B. E. A.

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Salehand, B. E. A.

Sanchez-Soto, L. L.

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[CrossRef]

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Subwavelength lithography over extended areas,” Phys. Rev. A 64, 013811 (2001).
[CrossRef]

Scherzer, O.

O. Scherzer, “The theoretical resolution limit of the electron microscope,” J. Appl. Phys. 20, 20–29 (1949).
[CrossRef]

Sergienko, A. V.

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

A. F. Abouraddy, B. E. A. Salehand, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef]

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

Setl, T.

T. Shirai, H. Kellock, T. Setl, and A. T. Friberg, “Imaging through an aberrating medium with classical ghost diffraction,” J. Opt. Soc. Am. A 29, 1288–1292 (2012).
[CrossRef]

T. Shirai, T. Setl, and A. T. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801 (2011).
[CrossRef]

Shafer, D.

D. Shafer, “Optical design with only two surfaces” in Proc. SPIE 0237, 256–261 (1980).
[CrossRef]

Shapiro, J. H.

Shih, Y. H.

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[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]

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

Shirai, T.

T. Shirai, H. Kellock, T. Setl, and A. T. Friberg, “Imaging through an aberrating medium with classical ghost diffraction,” J. Opt. Soc. Am. A 29, 1288–1292 (2012).
[CrossRef]

T. Shirai, T. Setl, and A. T. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801 (2011).
[CrossRef]

Simon, D. S.

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

Soderholm, J.

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Subwavelength lithography over extended areas,” Phys. Rev. A 64, 013811 (2001).
[CrossRef]

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[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]

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

Teich, M. C.

A. F. Abouraddy, B. E. A. Salehand, A. V. Sergienko, and M. C. Teich, “Quantum holography,” Opt. Express 9, 498–505 (2001).
[CrossRef]

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

Walborn, S. P.

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1991).

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

Williams, D. B.

D. B. Williams and C. B. Carter, Transmission Electron Microscopy (Springer, 2009), Chap. 28.7.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

Zhu, S.

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

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

Adv. Opt. Photon. (1)

Am. J. Phys. (1)

L. Bazano and P. Ottonello, “Ghost imaging: open secrets and puzzles for undergraduates,” Am. J. Phys. 75, 343–351 (2007).
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Appl. Opt. (1)

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[CrossRef]

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

Opt. Express (1)

Opt. Lett. (1)

Optik (1)

B. J. Hoenders, “On the reconstruction of a weak phase-amplitude object,” Optik 35, 116–133 (1972).

Phys. Lett. (1)

D. N. Klyshko, “Combined EPR and two-slits experiments: interference of advanced waves,” Phys. Lett. 132, 299–304 (1988).
[CrossRef]

Phys. Rev. A (14)

J. Cheng, “Transfer functions in lensless ghost-imaging systems,” Phys. Rev. A 78, 043823 (2008).
[CrossRef]

D. S. Simon and A. V. Sergienko, “Odd-order aberration cancellation in correlated-photon imaging,” Phys. Rev. A 82, 023819 (2010).
[CrossRef]

T. Shirai, T. Setl, and A. T. Friberg, “Ghost imaging of phase objects with classical incoherent light,” Phys. Rev. A 84, 041801 (2011).
[CrossRef]

S. P. Walborn, M. O. T. Cunha, S. Padua, and C. H. Monken, “Double-slit quantum eraser,” Phys. Rev. A 65, 033818 (2002).
[CrossRef]

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Subwavelength lithography over extended areas,” Phys. Rev. A 64, 013811 (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]

V. Giovannetti, S. Lloyd, and L. Maccone, “Positioning and clock synchronization through entanglement,” Phys. Rev. A 65, 022309 (2002).
[CrossRef]

P. H. S. Ribeiro and G. A. Barbosa, “Direct and ghost interference in double-slit experiments with coincidence measurements,” Phys. Rev. A 54, 3489–3492 (1996).
[CrossRef]

T. B. Pittman, D. V. Strekalov, D. N. Klyshko, M. H. Rubin, A. V. Sergienko, and Y. H. Shih, “Two-photon geometric optics,” Phys. Rev. A 53, 2804–2815 (1996).
[CrossRef]

G. A. Barbosa, “Quantum images in double-slit experiments with spontaneous down-conversion light,” Phys. Rev. A 54, 4473–4478 (1996).
[CrossRef]

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

A. F. Abouraddy, M. B. Nasr, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, “Demonstration of the complementarity of one- and two-photon interference,” Phys. Rev. A 63, 063803 (2001).
[CrossRef]

B. E. A. Saleh, A. F. Abouraddy, A. V. Sergienko, and M. C. Teich, “Duality between partial coherence and partial entanglement,” Phys. Rev. A 62, 043816 (2000).
[CrossRef]

G. Brida, E. Cagliero, G. Falzetta, M. Genovese, M. Gramegna, and E. Predazzi, “Biphoton double-slit experiment,” Phys. Rev. A 68, 033803 (2003).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (6)

A. Gatti, E. Brambilla, and L. A. Lugiato, “Entangled imaging and wave-particle duality: from the microscopic to macroscopic realm,” Phys. Rev. Lett. 90, 133603 (2003).
[CrossRef]

A. Gatti, E. Brambilla, L. A. Lugiato, and M. I. Kolobov, “Quantum entangled image,” Phys. Rev. Lett. 83, 1763–1766 (1999).
[CrossRef]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, “Quantum interferometric optical lighography: exploiting entanglement to beat the diffraction limit,” Phys. Rev. Lett. 85, 2733–2736 (2000).
[CrossRef]

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

G. Bjork, L. L. Sanchez-Soto, and J. Soderholm, “Entangled-state lithography: tailoring any pattern with a single state,” Phys. Rev. Lett. 86, 4516–4519 (2001).
[CrossRef]

M. D. Angelo, M. V. Chekhova, and Y. H. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001).
[CrossRef]

Proc. SPIE (1)

D. Shafer, “Optical design with only two surfaces” in Proc. SPIE 0237, 256–261 (1980).
[CrossRef]

Other (7)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1975).

A. Maréchal, in Encyclopedia of Physics (Springer, 1956), Vol. 24, Sect. 67.

T. Lépine, http://paristech.institutoptique.fr/site.php?id=562&fileid=6761 , and http://paristech.institutoptique.fr/site.php?id=562 , (2013).

A. Maréchal, “Imagerie géométrique. Aberrations,” in Traite d’Optique Instrumentale. Section 1: La Formation des Images (Editions de la Revue d’Optique Théorique et Instrumentale, 1952), Chap. 6.3.4, p. 91.

J. W. Goodman, Statistical Optics (Wiley, 2000), Chap. 5.6.2, pp. 210–215.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, 1991).

D. B. Williams and C. B. Carter, Transmission Electron Microscopy (Springer, 2009), Chap. 28.7.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of lenses’ ghost image with thermal light.

Fig. 2.
Fig. 2.

Dependence of a single slit image on the spherical aberration Cs2 introduced by lens L2 with Δz*=0, Cs1=500λ.

Fig. 3.
Fig. 3.

Dependence of the image of a single slit on the defocus coefficient Δz2 introduced by lens L2 with Cs*=0, Δz1=3mm.

Fig. 4.
Fig. 4.

Filter function sin(χ(H,0)) versus the variable λH with a different aberration of the ghost image system.

Fig. 5.
Fig. 5.

Image of a weak phase cos object with different aberrations. (a) The spatial frequency H=0.7λ. (b) The spatial frequency H=0.1λ.

Equations (59)

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g(2)(ξ,v)=I(ξ)I(v)I(ξ)I(v)|Γ(ξ,v)|2,
Γ(v1,v2)=++E(x1,y1)E*(x2,y2)×h1(x1,y1,ξ)h2*(x2,y2,v1,v2)dx1dx2dy1dy2.
h1(x1,y1,ξ)=++1λ2b1f3H(u1,u2)exp[iπλb1(a1(x12+y12)2x1u12y1u2+d1(u12+u22))iS1(x1,y1,u1,u2)]exp[iπλf3u·ξ]du1du2
h1(x1,y1,ξ=0)=++1λ2b1f3H(u1,u2)exp[iπλb1(a1(x12+y12)2x1u12y1u2+d1(u12+u22))iS1(x1,y1,u1,u2)]du1du2,
h2(x2,y2,v1,v2)=iλb2exp[iπλb2(a2(x22+y22)2x2v12y2v2+d2(v12+v22))iS2(x2,y2,v1,v2)],
S1(x1,y1,u1,u2)=14A1R1414B1ρ14C1ϰ1212D1R12ρ12+E1R12ϰ12+F1ρ12ϰ12
ifR12=x12+y12,ρ12=u12+u22,ϰ12=x1u1+y1u2,
S2(x2,y2,v1,v2)=14A2R2414B2ρ24C2ϰ2212D2R22ρ22+E2R22ϰ22+F2ρ22ϰ22
ifR22=x22+y22,ρ22=v12+v22,ϰ22=x2v1+y2v2.
(a1b1c1d1)=(1z201)(101f11)(1z101)=(1z2f1z1+z2z1z2f11f11z1f1),
(a2b2c2d2)=(1l201)(101f21)(1l101)=(1l2f2l1+l2l1l2f21f21l1f2).
E(x1,y1)E*(x2,y2)=I0δ(x1x2)δ(y1y2).
Γ(v1,v2)=iI0λ3b1b2f3δ(x1x2)δ(y1y2)×exp[iπλb1(a1(x12+y12)2x1u12y1u2+d1(u12+u22))iS1(x1,y1,u1,u2)]×H(u1,u2)exp[+iπλb2(a2(x22+y22)2x2v12y2v2+d2(v12+v22))+iS2(x2,y2,v1,v2)]dx1dx2dy1dy2du1du2.
|Γ(v1,v2)|2=|H(u1,u2)G(u1,u2,v1,v2)du1du2|2,
G(u1,u2,v1,v2)=iI0λ3b1b2f3exp[iπλb1(a1(x2+y2)2xu12yu2+d1(u12+u22))iS1(x,y,u1,u2)+iπλb2(a2(x2+y2)2xv12yv2+d2(v12+v22))+iS2(x,y,v1,v2)]dxdy
G(3)(u1,u2;v1,v2)=G(1)(u1,u2;x,y)G(2)(x,y;v1,v2)dxdy.
G(u1,u2,v1,v2)=iI0λ3b1b2f3exp[iπλb1(a1(x2+y2)2xu12yu2+d1(u12+u22))+iπλb2(a2(x2+y2)2xv12yv2+d2(v12+v22))]dxdy.
πa2λb2πa1λb1=0.
+exp(2πiμx))dx=δ(μ)
G(u1,u2,v1,v2)=ib1I0λb2f3exp[iπd1λb1(u12+u22)+iπd1λb1(u12+u22)]δ(u1b1b2v2)δ(u2b1b2v2).
|Γ(v1,v2)|2=|b1I0λf3b2H(b1v1b2,b1v2b2)|2.
G(u1,u2,v1,v2)=iI0λ3f3f2exp[iπλf(2xu12yu2)iχ(x,y)+iπλf(2xv12yv2)]dxdy,
χ(x,y)=S1(x,y,v1,v2)S2(x,y,u1,u2)=2πλ[Cs*R44f4Δz*R22f2],R2=x2+y2.
G(v1u1,v2u2)=iI0λ3f3f2bbbbexp(iχ(x,y))exp[i2πxλf(v1u1)i2πyλf(v2u2)]dxdy.
|Γ(v1,v2)|2=|bbbbH(u1,u2)G(v1u1,v2u2)dxdydu1du2|2.
H(u1,u2)={1|u1|<a/20,others,
|Γ(v1,v2=0)|2=|iI0λ3f3f2bbbba/2a/2H(u1,u2)exp(iχ(x,y))×exp[i2πxλf(v1u1)+i2πyλfu2]dxdydu1du2|2.
|Γ(v1,v2=0)|2=|iI0λ2f3fbba/2a/2exp[i2πxu1λf]du1exp(iχ(x,0))×exp[i2πxv1λf]dx|2.
|Γ(v1,v2=0)|2=C|b/λfb/λfsin(πaxf)πxfexp(iχ(xfλf,0))exp(2πxf)dxf|2,
H(u1,u2)=exp(iϕ(u1,u2))1+iϕ(u1,u2),
Γ(v1,v2)=++(1+iϕ(u1,u2))G(u1,u2,v1,v2)du1du2.
|Γ(v1,v2)|2=++iϕ(u1,u2)G(u1,u2,v1,v2)du1du2×++G*(u1,u2,v1,v2)du1du2++iϕ(u1,u2)G*(u1,u2,v1,v2)du1du2×++G(u1,u2,v1,v2)du1du2+background,
background(v1,v2)=++G(u1,u2,v1,v2)du1du2++G*(u1,u2,v1,v2)du1du2.
++G(u1,u2,v1,v2)du1du2=++G*(u1,u2,v1,v2)du1du2.
|Γ(v1,v2)|2background(v1,v2)++G*(u1,u2,v1,v2)du1du2×[++iϕ(u1,u2){G(u1,u2,v1,v2)+G*(u1,u2,v1,v2)}du1du2].
G(u1,u2,v1,v2)+G*(u1,u2,v1,v2)=2I0λ3f3f2exp[iπλf(2xu12yu2)+iπλf(2xv12yv2)]sin(χ(x,y))dxdy.
|Γ(v1,v2)|2background(v1,v2)++G*(u1,u2,v1,v2)du1du2×0=0.
s(x,y)=sin(χ(x,y)).
Δfsch=1.2CSλ.
1,51Cs1/4λ1/4.
sin(χ(x,y))sin(2πλ[14Cs*(x2+y2)2f412Δz*(x2+y2)f2]).
|Γ(v1,v2=0)|2background(v1,v2)++G*(u1,u2,v1,v2)du1du2×2iI0λ2f3f++ϕ(u1,u2)exp[i2πxu1λf]du1exp[i2πxv1λf]sin(χ(x,0))dx.
φ(u1,u2)=Acos(2πHu1),
|Γ(v1,v2=0)|2background(v1,v2)++G*(u1,u2,v1,v2)du1du2×2iAI0λf3cos(2πHv1)sin(χ(λfH,0)).
background(v1,v2)=I02λ2f32,and++G*(u1,u2,v1,v2)du1du2=iI0λf3.
|Γ(v1,v2=0)|2C[1+2Asin(χ(H,0))cos(2πHv1)].
χ(H,0)=π2(τλ2H2)2+1.2πτλ2H2.
++G(u1,u2,v1,v2)du1du2=++G*(u1,u2,v1,v2)du1du2.
G(u1,u2,v1,v2)=iI0λ3f3f2exp[iπλb1(2xu12yu2)iχ(x,y)+iπλb2(2xv12yv2)]dxdy,
χ(x,y)=2πλ[14CsR4f412ΔzR2f2],R2=x2+y2.
++G(u1,u2,v1,v2)du1du2=iI0λf3×exp(iχ(0,0)=0)
++G*(u1,u2,v1,v2)du1du2=iI0λf3×exp(iχ(0,0)=0).
χ(x,y)=2πλ[14CsR4f412ΔzR2f2]withR2=x2+y2
χR=0,whereR=R/f.
0=χR=CsR3+RΔz,
CsR3+RΔz=0.
2π3=2πλ(14CsR412R2Δz).
Δz=1.2Csλ,
R=1.51Cs14λ14.

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