Abstract

We introduce a novel coherent diffraction imaging technique based on ptychography that enables simultaneous full-field imaging of multiple, spatially separate, sample locations. This technique only requires that diffracted light from spatially separated sample sites be mutually incoherent at the detector, which can be achieved using multiple probes that are separated either by wavelength or by orthogonal polarization states. This approach enables spatially resolved polarization spectroscopy from a single ptychography scan, as well as allowing a larger field of view to be imaged without loss in spatial resolution. Further, we compare the numerical efficiency of the multi-mode ptychography algorithm with a single mode algorithm.

© 2015 Optical Society of America

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References

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2015 (1)

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 249–254 (2015).
[Crossref]

2014 (2)

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

P. Li, T. B. Edo, and J. M. Rodenburg, “Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design,” Ultramicroscopy 147, 106–113 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

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

2011 (1)

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

2010 (2)

2009 (2)

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

2008 (4)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elect. Phys. 150, 87–184 (2008).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 7076, 70760A(2008).

2001 (1)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

1997 (4)

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

C. Spielmann, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

K. Schafer and K. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[Crossref]

I. Christov, M. Murnane, and H. Kapteyn, “High-harmonic generation of attosecond pulses in the single-cycle regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

1996 (1)

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

1994 (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

1993 (1)

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

1982 (1)

1952 (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[Crossref]

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Agostini, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Auge, F.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Balcou, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Bean, R.

Becker, A.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Berenguer, F.

Breger, P.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Bunk, O.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Chang, Z.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010).
[Crossref]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Chen, B.

Christov, I.

I. Christov, M. Murnane, and H. Kapteyn, “High-harmonic generation of attosecond pulses in the single-cycle regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Clark, J. N.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Cohen, O.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Corkum, P. B.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

de Jonge, M.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Diaz, A.

Dierolf, M.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Dorney, K.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Durfee, C.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Edo, T. B.

P. Li, T. B. Edo, and J. M. Rodenburg, “Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design,” Ultramicroscopy 147, 106–113 (2014).
[Crossref] [PubMed]

Fan, T.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Fienup, J. R.

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 7076, 70760A(2008).

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

Frassetto, F.

Guizar-Sicairos, M.

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 7076, 70760A(2008).

Guo, Z.

Gychtol, P.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Hernández-garcía, C.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Hickstein, D.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Hickstein, D. D.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Hogle, C.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Hüe, F.

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

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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Ishikawa, T.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 249–254 (2015).
[Crossref]

Ivanov, M. Y.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Jaronbecker, A.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Jaron-becker, A.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Kapteyn, H.

I. Christov, M. Murnane, and H. Kapteyn, “High-harmonic generation of attosecond pulses in the single-cycle regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Kapteyn, H. C.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Kfir, O.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Knut, R.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Kulander, K.

K. Schafer and K. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[Crossref]

L Huillier, A.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Lewenstein, M.

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Li, P.

P. Li, T. B. Edo, and J. M. Rodenburg, “Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design,” Ultramicroscopy 147, 106–113 (2014).
[Crossref] [PubMed]

Liu, H.

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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

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

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

Margaret, M.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

McNulty, I.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Menzel, A.

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, 13592–606 (2013).
[Crossref] [PubMed]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Miao, J.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 249–254 (2015).
[Crossref]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Midgley, P. A.

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

Muller, H. G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Mullot, G.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Murnane, M.

I. Christov, M. Murnane, and H. Kapteyn, “High-harmonic generation of attosecond pulses in the single-cycle regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Murnane, M. M.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 249–254 (2015).
[Crossref]

Nugent, K. A.

H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Paul, P. M.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Peatross, J.

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Peele, A. G.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Peterson, I.

Pfeifer, M. A.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Pfeiffer, F.

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Plaja, L.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Poletto, L.

Popmintchev, T.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

Robinson, I. K.

Rodenburg, J. M.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

P. Li, T. B. Edo, and J. M. Rodenburg, “Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design,” Ultramicroscopy 147, 106–113 (2014).
[Crossref] [PubMed]

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, 13592–606 (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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

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

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

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elect. Phys. 150, 87–184 (2008).
[Crossref]

Rundquist, A.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[Crossref]

Schafer, K.

K. Schafer and K. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[Crossref]

Shpyrko, O.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Spielmann, C.

C. Spielmann, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

Tai, R.

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Toma, E. S.

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

Vila-Comamala, J.

Wang, H.

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

Williams, G. J.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Wu, Y.

Xu, Z.

Zhang, F.

Zhang, X.

Zhou, J.

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Zusin, D.

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

Acta Crystallogr. (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[Crossref]

Adv. Imag. Elect. Phys. (1)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elect. Phys. 150, 87–184 (2008).
[Crossref]

Appl. Opt. (3)

Nat. Photonics (1)

H. N. Chapman and K. A. Nugent, “Coherent lensless x-ray imaging,” Nat. Photonics 4, 833–839 (2010).
[Crossref]

Nat. Phys. (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Nature (2)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

Opt. Express (2)

Phys. Rev. A (1)

M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L Huillier, and P. B. Corkum, “Theory of high-harmonic generation by low-frequency laser fields,” Phys. Rev. A 49, 2117–2132 (1994).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

I. Christov, M. Murnane, and H. Kapteyn, “High-harmonic generation of attosecond pulses in the single-cycle regime,” Phys. Rev. Lett. 78, 1251–1254 (1997).
[Crossref]

J. Zhou, J. Peatross, M. Murnane, H. Kapteyn, and I. Christov, “Enhanced high-harmonic generation using 25 fs laser pulses,” Phys. Rev. Lett. 76, 752–755 (1996).
[Crossref] [PubMed]

Z. Chang, A. Rundquist, H. Wang, M. Murnane, and H. Kapteyn, “Generation of coherent soft x rays at 2.7 nm using high harmonics,” Phys. Rev. Lett. 79, 2967–2970 (1997).
[Crossref]

P. B. Corkum, “Plasma perspective on strong-field multiphoton ionization,” Phys. Rev. Lett. 71, 1994–1997 (1993).
[Crossref] [PubMed]

K. Schafer and K. Kulander, “High harmonic generation from ultrafast pump lasers,” Phys. Rev. Lett. 78, 638–641 (1997).
[Crossref]

Science (4)

P. M. Paul, E. S. Toma, P. Breger, G. Mullot, F. Auge, P. Balcou, H. G. Muller, and P. Agostini, “Observation of a train of attosecond pulses from high harmonic generation,” Science 292, 1689–1692 (2001).
[Crossref] [PubMed]

C. Spielmann, “Generation of coherent x-rays in the water window using 5-femtosecond laser pulses,” Science 278, 661–664 (1997).
[Crossref]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 249–254 (2015).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Ultramicroscopy (6)

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

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

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

P. Li, T. B. Edo, and J. M. Rodenburg, “Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design,” Ultramicroscopy 147, 106–113 (2014).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[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,” Ultramicroscopy 120, 64–72 (2012).
[Crossref] [PubMed]

Other (3)

T. Fan, P. Gychtol, R. Knut, C. Hernández-garcía, D. Hickstein, C. Hogle, D. Zusin, K. Dorney, O. Shpyrko, O. Cohen, O. Kfir, L. Plaja, A. Becker, A. Jaron-becker, M. Murnane, H. Kapteyn, and T. Popmintchev, “Bright circularly polarized soft x-ray high harmonics for x-ray magnetic circular dichroism,” in CLEO Postdeadline Papers (2015), pp. 2–3.

O. Kfir, P. Grychtol, E. Turgut, R. Knut, D. Zusin, D. Popmintchev, T. Popmintchev, H. Nembach, J. M. Shaw, A. Fleischer, H. Kapteyn, M. Murnane, and O. Cohen, “Generation of bright circularly-polarized extreme ultraviolet high harmonics for magnetic circular dichroism spectroscopy,” Arxiv preprint http://arxiv.org/abs/1401.4101v1 9, 12 (2014).

C. Hernández-garcía, D. D. Hickstein, T. Popmintchev, M. Margaret, H. C. Kapteyn, A. Becker, A. Jaronbecker, and C. Durfee, “Isolated attosecond pulses with controlled polarization,” Super Intense Laser-Atom Physics Conference (2015).

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Figures (7)

Fig. 1
Fig. 1

Experimental schematic (not to scale). Spatially filtered blue and red beams are combined using a beamsplitter and then spatially separated using a pair of diffraction gratings. Other diffraction orders from the gratings are blocked by a pinhole. The two unblocked beams are then focused onto a 1951 USAF test pattern. The diffracted light is collected using a Mightex SCN-B013-U CMOS detector after passing through a 2 cm lens.

Fig. 2
Fig. 2

Reconstructed objects for a) the red and b) the blue probe beams (scale bar is 20 μm wide). c) Imaged areas shown on the USAF test sample. The two areas are separated by 175 μm, which is the same as the separation between the probes. (b) uses the same scale as (a).

Fig. 3
Fig. 3

Amplitude of the blue beam (a) and red beam (b) extracted from ptychographic reconstruction. The sizes of the beams agree with independent measurements performed near the imaging plane. c) and d) Propagation of the blue and red beams along the propagation direction. The white dotted lines indicate the location of the reconstructed probes, while the white dashed lines indicate the imaging plane for the probes. e) and f) Probe beams at the imaging plane, propagated from the reconstructed probes. The distance between the imaging plane for the blue probe and the red probe is found to be consistent with the chromatic aberration of the imaging lens. The scale bar in (a) is 20 μm wide and is shared by (b), (e), and (f). The scale bar in (c) is 1 mm wide and is shared by (d).

Fig. 4
Fig. 4

Experimental schematic (not to scale). Two orthogonal linear polarization states of a red laser diode (λ = 656 nm) were split using a BBO crystal. Both of these beams were used simultaneously in a single ptychography scan to image two separate areas with polarization sensitivity.

Fig. 5
Fig. 5

a) Direct CCD image of the probe beams in the plane of the sample. The beams are separated into two orthogonal polarization states. The separation between the beams is 233 μm. (b–c) Reconstructed amplitude and phase of the parallel polarization (ê). (d–e) Reconstructed amplitude and phase of the perpendicular polarization (ê). The maximum value of the phase is 1.5 rad in (c) and is 2.5 rad in (e). The scale bar is 20 μm wide and (b–e) are on the same scale as (a).

Fig. 6
Fig. 6

Reconstructed object for a) the parallel (ê) polarization and b) the perpendicular (ê) polarization. These areas are group 6 and 7 on the USAF test sample. c) Location of these areas on the USAF test sample. These two areas are separated by 170 μm, which corresponds to the shift between the two probes. The scale bar is 20 μm wide. (a) and (b) share the same scale bar.

Fig. 7
Fig. 7

Simulation of reconstruction error for multi-mode ptychography (red circles) and single mode ptychography (blue diamonds) with two colors. The error is calculated between the reconstructed object and the object used to simulate the data. a) Original object (red dashed circle indicates field of view of reconstruction), b) reconstructed object from multiplexing algorithm after 5 iterations, c) reconstructed object from single mode algorithm after 5 iterations for each color, d) reconstructed object from multiplexing algorithm after 40 iterations, e) reconstructed object from single mode algorithm after 40 iterations for each color.

Equations (1)

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E = { 1 / N Σ x Ω [ | O r ( x ) | | O 0 ( x ) | ] 2 } 1 / 2

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