Abstract

We realized a phase retrieval technique using terahertz (THz) radiation as an alternative to THz digital holography, named THz ptychography. Ptychography has been used in x-ray imaging as a groundbreaking improvement of conventional coherent diffraction imaging. Here we show that ptychography can be performed at THz frequencies too. We reconstructed an amplitude and a phase object with both simulated and real data. Lateral resolution accounts to <2λ, while depth variations as low as λ/30 can be assessed.

© 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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2017 (4)

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

C. Wang, Z. Xu, H. Liu, Y. Wang, J. Wang, and R. Tai, Appl. Opt. 56, 2099 (2017).
[Crossref]

L. Valzania, P. Zolliker, and E. Hack, Opt. Express 25, 11038 (2017).
[Crossref]

2015 (2)

2014 (3)

2012 (3)

K. Xue, Q. Li, Y.-D. Li, and Q. Wang, Opt. Lett. 37, 3228 (2012).
[Crossref]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

2011 (2)

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

2009 (1)

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

2008 (4)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, Opt. Express 16, 7264 (2008).
[Crossref]

2006 (1)

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006).

1969 (1)

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).
[Crossref]

Adams, D. E.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, Optica 1, 39 (2014).
[Crossref]

Aeppli, G.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Allain, M.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Bevis, C.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Boreman, G.

G. Boreman, Modulation Transfer Function in Optical and Electro-optical Systems (SPIE, 2001).

Brügmann, M.

Bunk, O.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Capello, L.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Carbone, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Chamard, V.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Chen, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Cooke, D. G.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Diaz, A.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Dierolf, M.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Dinapoli, R.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Feurer, T.

Fienup, J. R.

Gallmann, L.

Galloway, B. R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Gardner, D. F.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, Optica 1, 39 (2014).
[Crossref]

Godard, P.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

Guizar-Sicairos, M.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, Opt. Express 16, 7264 (2008).
[Crossref]

Hack, E.

Holler, M.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

Hoppe, W.

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).
[Crossref]

Huang, H.

Humphry, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Jeon, S.-G.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006).

Jepsen, P. U.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Jin, Y.-S.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006).

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Kapteyn, H. C.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, Optica 1, 39 (2014).
[Crossref]

Karl, R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Keller, U.

Kim, G.-J.

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006).

Koch, M.

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Kraus, B.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Latychevskaia, T.

Lee, Y.-S.

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009), Vol. 170.

Li, Q.

Li, Y.-D.

Li, Z.

Liu, H.

Lucchini, M.

Ludwig, A.

Maiden, A.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Maiden, A. M.

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

Mancini, G. F.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Mastropietro, F.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Menzel, A.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Metzger, T.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Müller, E.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Murnane, M. M.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, Optica 1, 39 (2014).
[Crossref]

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Porter, C. L.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Raabe, J.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Rodenburg, J.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Rodenburg, J. M.

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (2008).
[Crossref]

Rong, L.

Sarahan, M.

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

Seaberg, M. D.

Shanblatt, E. R.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, Optica 1, 39 (2014).
[Crossref]

Stangl, J.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Tai, R.

Tanksalvala, M.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Tsai, E. H.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Valzania, L.

Vila-Comamala, J.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

Wang, C.

Wang, D.

Wang, J.

Wang, Q.

Wang, Y.

Xu, Z.

Xue, K.

Zhang, B.

Zhang, X.

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Zhou, X.

Zolliker, P.

Acta Crystallogr. A (1)

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).
[Crossref]

Adv. Imaging Electron Phys. (1)

J. M. Rodenburg, Adv. Imaging Electron Phys. 150, 87 (2008).
[Crossref]

Appl. Opt. (1)

J. Korean Phys. Soc. (1)

Y.-S. Jin, G.-J. Kim, and S.-G. Jeon, J. Korean Phys. Soc. 49, 513 (2006).

Laser Photon. Rev. (1)

P. U. Jepsen, D. G. Cooke, and M. Koch, Laser Photon. Rev. 5, 124 (2011).
[Crossref]

Nat. Commun. (1)

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. Metzger, J. Stangl, and V. Chamard, Nat. Commun. 2, 568 (2011).
[Crossref]

Nat. Photonics (1)

D. F. Gardner, M. Tanksalvala, E. R. Shanblatt, X. Zhang, B. R. Galloway, C. L. Porter, R. Karl, C. Bevis, D. E. Adams, H. C. Kapteyn, M. M. Murnane, and G. F. Mancini, Nat. Photonics 11, 259 (2017).
[Crossref]

Nature (1)

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, Nature 543, 402 (2017).
[Crossref]

Opt. Express (6)

Opt. Lett. (1)

Optica (1)

Phys. Rev. B (1)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, and A. Menzel, Phys. Rev. B 86, 100103 (2012).
[Crossref]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[Crossref]

Ultramicroscopy (3)

A. M. Maiden and J. M. Rodenburg, Ultramicroscopy 109, 1256 (2009).
[Crossref]

A. Maiden, M. Humphry, M. Sarahan, B. Kraus, and J. Rodenburg, Ultramicroscopy 120, 64 (2012).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, Ultramicroscopy 108, 481 (2008).
[Crossref]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

G. Boreman, Modulation Transfer Function in Optical and Electro-optical Systems (SPIE, 2001).

Y.-S. Lee, Principles of Terahertz Science and Technology (Springer, 2009), Vol. 170.

Supplementary Material (1)

NameDescription
» Visualization 1       Excerpt from the ptychographic reconstruction of a phase object.

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Figures (2)

Fig. 1.
Fig. 1. Schematic experimental setup for transmission ptychography.
Fig. 2.
Fig. 2. Ptychographic reconstruction of an amplitude object (label 1) and a phase object (label 2). (a) Simulated object transmission function, with the relative position of the probe in three examples of the scan. Corresponding diffraction patterns obtained from the (b), (d), (f) simulated and (c), (e), (g) real object. Simulated reconstructed (h) amplitude and (j) phase. Experimentally reconstructed (i) amplitude and (k) phase. Insets show the probe (top, amplitude; bottom, phase; left, simulation; right, experiment). All phase distributions share the same phase scale, shown in (a2).

Tables (1)

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Table 1. Depth and Reconstructed Phase of the Phase Object Measured with an Optical Microscope (Second and Third Columns, Respectively) and Measured with THz Ptychography (Fourth Column) a

Equations (7)

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ψ k ( x ) = p k ( x ) o k ( x x k ) .
Ψ k ( u ) = P d [ ψ k ( x ) ] ( u ) ,
Ψ k ( u ) = I k ( u ) exp { i [ Ψ k ( u ) ] } ,
ψ k ( x ) = P d 1 [ Ψ k ( u ) ] ( x ) .
o k + 1 ( x ) = o k ( x ) + α U k o ( x + x k ) [ ψ k ( x + x k ) ψ k ( x + x k ) ] , p k + 1 ( x ) = p k ( x ) + β U k p ( x x k ) [ ψ k ( x ) ψ k ( x ) ] ,
U k o ( x ) p k * ( x ) max | p k ( x ) | 2 ; U k p ( x ) o k * ( x ) max | o k ( x ) | 2 ,
E k = 1 D u | I k ( u ) | Ψ k ( u ) | | 2 / k = 1 D u I k ( u ) .

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