Abstract

We report an imaging scheme, termed aperture-scanning Fourier ptychography, for 3D refocusing and super-resolution macroscopic imaging. The reported scheme scans an aperture at the Fourier plane of an optical system and acquires the corresponding intensity images of the object. The acquired images are then synthesized in the frequency domain to recover a high-resolution complex sample wavefront; no phase information is needed in the recovery process. We demonstrate two applications of the reported scheme. In the first example, we use an aperture-scanning Fourier ptychography platform to recover the complex hologram of extended objects. The recovered hologram is then digitally propagated into different planes along the optical axis to examine the 3D structure of the object. We also demonstrate a reconstruction resolution better than the detector pixel limit (i.e., pixel super-resolution). In the second example, we develop a camera-scanning Fourier ptychography platform for super-resolution macroscopic imaging. By simply scanning the camera over different positions, we bypass the diffraction limit of the photographic lens and recover a super-resolution image of an object placed at the far field. This platform’s maximum achievable resolution is ultimately determined by the camera’s traveling range, not the aperture size of the lens. The FP scheme reported in this work may find applications in 3D object tracking, synthetic aperture imaging, remote sensing, and optical/electron/X-ray microscopy.

© 2014 Optical Society of America

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2014 (5)

2013 (8)

2012 (2)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[CrossRef] [PubMed]

A. B. Parthasarathy, K. K. Chu, T. N. Ford, J. Mertz, “Quantitative phase imaging using a partitioned detection aperture,” Opt. Lett. 37(19), 4062–4064 (2012).
[CrossRef] [PubMed]

2011 (5)

I. Iglesias, “Pyramid phase microscopy,” Opt. Lett. 36(18), 3636–3638 (2011).
[CrossRef] [PubMed]

M. Ben-Ezra, “A digital gigapixel large-format tile-scan camera,” IEEE Comput. Graph. Appl. 31(1), 49–61 (2011).
[CrossRef] [PubMed]

G. Zheng, C. Kolner, C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Opt. Lett. 36(20), 3987–3989 (2011).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. Shenfield, J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[CrossRef]

2010 (6)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

W. Bishara, T.-W. Su, A. F. Coskun, A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18(11), 11181–11191 (2010).
[CrossRef] [PubMed]

L. Waller, S. S. Kou, C. J. R. Sheppard, G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18(22), 22817–22825 (2010).
[CrossRef] [PubMed]

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

2009 (2)

2008 (4)

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
[CrossRef]

M. Guizar-Sicairos, J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47(30), 5654–5659 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (3)

2005 (1)

2004 (2)

V. Mico, Z. Zalevsky, P. Garcia-Martinez, J. Garcia, “Single-step superresolution by interferometric imaging,” Opt. Express 12(12), 2589–2596 (2004).
[CrossRef] [PubMed]

H. M. L. Faulkner, J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[CrossRef] [PubMed]

2003 (4)

2002 (1)

2001 (1)

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

1996 (1)

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
[CrossRef]

1995 (1)

J. C. Gillette, T. M. Stadtmiller, R. C. Hardie, “Aliasing reduction in staring infrared imagers utilizing subpixel techniques,” Opt. Eng. 34(11), 3130–3137 (1995).
[CrossRef]

1992 (1)

J. M. Rodenburg, R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philos. Trans. R. Soc., A 339(1655), 521–553 (1992).
[CrossRef]

1987 (1)

1982 (2)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
[CrossRef] [PubMed]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).

1981 (1)

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. 29(2), 386–391 (1981).
[CrossRef]

1978 (1)

1972 (1)

R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

1970 (1)

1969 (1)

W. Hoppe, G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[CrossRef]

1960 (1)

M. Ryle, A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc. 120, 220 (1960).

Alexandrov, S. A.

Allen, L.

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Barbastathis, G.

Barsi, C.

Bates, R. H. T.

J. M. Rodenburg, R. H. T. Bates, “The Theory of Super-Resolution Electron Microscopy Via Wigner-Distribution Deconvolution,” Philos. Trans. R. Soc., A 339(1655), 521–553 (1992).
[CrossRef]

Batey, D. J.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Ben-Ezra, M.

M. Ben-Ezra, “A digital gigapixel large-format tile-scan camera,” IEEE Comput. Graph. Appl. 31(1), 49–61 (2011).
[CrossRef] [PubMed]

Bian, Z.

Bishara, W.

Bowers, C. W.

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Chen, H. H.

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
[CrossRef]

Chu, K. K.

Chung, J.

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photon. News 25, 26–33 (2014).

Coskun, A. F.

Daneshpanah, M.

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

M. Daneshpanah, B. Javidi, “Tracking biological microorganisms in sequence of 3D holographic microscopy images,” Opt. Express 15(17), 10761–10766 (2007).
[CrossRef] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dean, B. H.

Di, J.

Dierolf, M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dong, S.

Dorsch, R. G.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
[CrossRef]

Edo, T. B.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Elser, V.

Fan, Q.

Faulkner, H. M. L.

H. M. L. Faulkner, J. M. Rodenburg, “Movable Aperture Lensless Transmission Microscopy: A Novel Phase Retrieval Algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[CrossRef] [PubMed]

Ferreira, C.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
[CrossRef]

Fienup, J. R.

Fixler, D.

Fleischer, J. W.

Ford, T. N.

Garcia, J.

García, J.

Garcia-Martinez, P.

García-Martínez, P.

Gerchberg, R.

R. Gerchberg, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237 (1972).

Gillette, J. C.

J. C. Gillette, T. M. Stadtmiller, R. C. Hardie, “Aliasing reduction in staring infrared imagers utilizing subpixel techniques,” Opt. Eng. 34(11), 3130–3137 (1995).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, “Phase retrieval by differential intensity measurements,” J. Opt. Soc. Am. A 4(1), 166–170 (1987).
[CrossRef]

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).

Guizar-Sicairos, M.

Gutzler, T.

Hardie, R. C.

J. C. Gillette, T. M. Stadtmiller, R. C. Hardie, “Aliasing reduction in staring infrared imagers utilizing subpixel techniques,” Opt. Eng. 34(11), 3130–3137 (1995).
[CrossRef]

Hewish, A.

M. Ryle, A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc. 120, 220 (1960).

Hillman, T. R.

Hoppe, W.

W. Hoppe, G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[CrossRef]

Horstmeyer, R.

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photon. News 25, 26–33 (2014).

X. Ou, R. Horstmeyer, C. Yang, G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[CrossRef] [PubMed]

G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[CrossRef]

G. Zheng, X. Ou, R. Horstmeyer, C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[CrossRef] [PubMed]

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

Humphry, M. J.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[CrossRef] [PubMed]

A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[CrossRef] [PubMed]

Iglesias, I.

Jang, J.-S.

Javidi, B.

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

Jiang, H.

Kang, M. G.

S. C. Park, M. K. Park, M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Processing Mag. 20(3), 21–36 (2003).
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Kewish, C. M.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

Kolner, C.

Kou, S. S.

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[CrossRef] [PubMed]

Kutz, J. N.

Lee, S. A.

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

Liang, C.-K.

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
[CrossRef]

Lin, T.-H.

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
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Liu, C.

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
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A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
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Lu, C.-H.

Maia, F.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
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Maiden, A. M.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
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M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
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F. Hüe, J. M. Rodenburg, A. M. Maiden, P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
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A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
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S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
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Martinez-Corral, M.

Meinel, A. B.

Mendlovic, D.

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
[CrossRef]

Menzel, A.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
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P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Mertz, J.

Mico, V.

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

Nanda, P.

Osten, W.

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

Ou, X.

Oxley, M.

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
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Ozcan, A.

Park, M. K.

S. C. Park, M. K. Park, M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Processing Mag. 20(3), 21–36 (2003).
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Park, S. C.

S. C. Park, M. K. Park, M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Processing Mag. 20(3), 21–36 (2003).
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Parthasarathy, A. B.

Pešic, Z. D.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Pfeiffer, F.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
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P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Rau, C.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Rodenburg, J. M.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
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M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
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A. Shenfield, J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
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F. Hüe, J. M. Rodenburg, A. M. Maiden, P. A. Midgley, “Extended ptychography in the transmission electron microscope: Possibilities and limitations,” Ultramicroscopy 111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
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M. Ryle, A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc. 120, 220 (1960).

Sampson, D. D.

Schaal, F.

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

Schirotzek, A.

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
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Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
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Shenfield, A.

A. Shenfield, J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[CrossRef]

Sheppard, C. J. R.

Shiradkar, R.

Stadtmiller, T. M.

J. C. Gillette, T. M. Stadtmiller, R. C. Hardie, “Aliasing reduction in staring infrared imagers utilizing subpixel techniques,” Opt. Eng. 34(11), 3130–3137 (1995).
[CrossRef]

Stern, A.

Strube, G.

W. Hoppe, G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
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Su, T.-W.

Sun, W.

Taylor, L.

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. 29(2), 386–391 (1981).
[CrossRef]

Thibault, P.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-Ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Tian, L.

von König, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

Wagner, U.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Waigh, T. A.

T. B. Edo, D. J. Batey, A. M. Maiden, C. Rau, U. Wagner, Z. D. Pešić, T. A. Waigh, J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[CrossRef]

Waller, L.

Wang, J.

Warber, M.

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

Williams, M. O.

Wong, B.-Y.

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
[CrossRef]

Wu, H.-

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
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Xiao, X.

Yang, C.

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photon. News 25, 26–33 (2014).

X. Ou, G. Zheng, C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[CrossRef] [PubMed]

G. Zheng, X. Ou, C. Yang, “0.5 gigapixel microscopy using a flatbed scanner,” Biomed. Opt. Express 5(1), 1–8 (2014).
[CrossRef] [PubMed]

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
[CrossRef]

X. Ou, R. Horstmeyer, C. Yang, G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[CrossRef] [PubMed]

G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[CrossRef]

G. Zheng, X. Ou, R. Horstmeyer, C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[CrossRef] [PubMed]

G. Zheng, C. Kolner, C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Opt. Lett. 36(20), 3987–3989 (2011).
[CrossRef] [PubMed]

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

Yang, S.

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

Zalevsky, Z.

Zhang, P.

Zhao, J.

Zheng, G.

G. Zheng, X. Ou, C. Yang, “0.5 gigapixel microscopy using a flatbed scanner,” Biomed. Opt. Express 5(1), 1–8 (2014).
[CrossRef] [PubMed]

X. Ou, G. Zheng, C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[CrossRef] [PubMed]

G. Zheng, X. Ou, R. Horstmeyer, J. Chung, C. Yang, “Fourier Ptychographic Microscopy: A Gigapixel Superscope for Biomedicine,” Opt. Photon. News 25, 26–33 (2014).

S. Dong, R. Shiradkar, P. Nanda, G. Zheng, “Spectral multiplexing and coherent-state decomposition in Fourier ptychographic imaging,” Biomed. Opt. Express 5(6), 1757–1767 (2014).
[CrossRef]

G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[CrossRef]

X. Ou, R. Horstmeyer, C. Yang, G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[CrossRef] [PubMed]

Z. Bian, S. Dong, G. Zheng, “Adaptive system correction for robust Fourier ptychographic imaging,” Opt. Express 21(26), 32400–32410 (2013).
[CrossRef] [PubMed]

G. Zheng, X. Ou, R. Horstmeyer, C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[CrossRef] [PubMed]

G. Zheng, C. Kolner, C. Yang, “Microscopy refocusing and dark-field imaging by using a simple LED array,” Opt. Lett. 36(20), 3987–3989 (2011).
[CrossRef] [PubMed]

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

Zwick, S.

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

ACM Trans. Graph. (1)

C.-K. Liang, T.-H. Lin, B.-Y. Wong, C. Liu, H. H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 1–10 (2008).
[CrossRef]

Acta Crystallogr. A (1)

W. Hoppe, G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A 25, 502–507 (1969).
[CrossRef]

Appl. Opt. (5)

Biomed. Opt. Express (2)

IEEE Comput. Graph. Appl. (1)

M. Ben-Ezra, “A digital gigapixel large-format tile-scan camera,” IEEE Comput. Graph. Appl. 31(1), 49–61 (2011).
[CrossRef] [PubMed]

IEEE Signal Processing Mag. (1)

S. C. Park, M. K. Park, M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Processing Mag. 20(3), 21–36 (2003).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

L. Taylor, “The phase retrieval problem,” IEEE Trans. Antennas Propag. 29(2), 386–391 (1981).
[CrossRef]

Inverse Probl. (1)

S. Marchesini, A. Schirotzek, C. Yang, H.- Wu, F. Maia, “Augmented projections for ptychographic imaging,” Inverse Probl. 29(11), 115009 (2013).
[CrossRef]

J. Appl. Phys. (1)

A. Shenfield, J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109(12), 124510 (2011).
[CrossRef]

J. Opt. Soc. Am. A (4)

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

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A. 13(3), 470–473 (1996).
[CrossRef]

Journalism (1)

M. Daneshpanah, S. Zwick, F. Schaal, M. Warber, B. Javidi, W. Osten, “3D Holographic Imaging and Trapping for Non-Invasive Cell Identification and Tracking,” Display Technology, Journalism 6, 490–499 (2010).

Lab Chip (1)

G. Zheng, S. A. Lee, S. Yang, C. Yang, “Sub-pixel resolving optofluidic microscope for on-chip cell imaging,” Lab Chip 10(22), 3125–3129 (2010).
[CrossRef] [PubMed]

Mon. Not. R. Astron. Soc. (1)

M. Ryle, A. Hewish, “The synthesis of large radio telescopes,” Mon. Not. R. Astron. Soc. 120, 220 (1960).

Nat. Commun. (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[CrossRef] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[CrossRef]

New J. Phys. (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12(3), 035017 (2010).
[CrossRef]

Opt. Commun. (1)

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199(1-4), 65–75 (2001).
[CrossRef]

Opt. Eng. (2)

R. A. Gonsalves, “Phase retrieval and diversity in adaptive optics,” Opt. Eng. 21, 215829 (1982).

J. C. Gillette, T. M. Stadtmiller, R. C. Hardie, “Aliasing reduction in staring infrared imagers utilizing subpixel techniques,” Opt. Eng. 34(11), 3130–3137 (1995).
[CrossRef]

Opt. Express (12)

X. Ou, G. Zheng, C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22(5), 4960–4972 (2014).
[CrossRef] [PubMed]

M. Daneshpanah, B. Javidi, “Tracking biological microorganisms in sequence of 3D holographic microscopy images,” Opt. Express 15(17), 10761–10766 (2007).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, J. García, “Superresolution optical system by common-path interferometry,” Opt. Express 14(12), 5168–5177 (2006).
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J. García, Z. Zalevsky, D. Fixler, “Synthetic aperture superresolution by speckle pattern projection,” Opt. Express 13(16), 6073–6078 (2005).
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A. Stern, B. Javidi, “3-D computational synthetic aperture integral imaging (COMPSAII),” Opt. Express 11(19), 2446–2451 (2003).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, J. Garcia, “Single-step superresolution by interferometric imaging,” Opt. Express 12(12), 2589–2596 (2004).
[CrossRef] [PubMed]

T. R. Hillman, T. Gutzler, S. A. Alexandrov, D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture Fourier holographic optical microscopy,” Opt. Express 17(10), 7873–7892 (2009).
[CrossRef] [PubMed]

G. Zheng, X. Ou, R. Horstmeyer, C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21(13), 15131–15143 (2013).
[CrossRef] [PubMed]

L. Waller, S. S. Kou, C. J. R. Sheppard, G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18(22), 22817–22825 (2010).
[CrossRef] [PubMed]

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Supplementary Material (1)

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Figures (6)

Fig. 1
Fig. 1

Scheme of aperture-scanning FP. (a) Optical setup. A circular aperture is placed at the Fourier plane of a 4f system. (b) A x-y motion stage is used to scan the circular aperture at the pupil plane. (c) The prototype setup of the reported scheme. (d) Outline of the FP recovery algorithm.

Fig. 2
Fig. 2

Pixel super-resolution demonstration using the aperture-scanning Fourier ptychographic imaging scheme. (a) The raw intensity image captured with the circular mask. The resolution is limited by the size of the circular mask. (b) The aperture-scanning FP reconstruction. The resolution is limited by the synthetic mask, which is 4 times larger than the mask used in Fig. 2(a). (c) The captured image with the circular aperture fully open. The resolution is twice of the pixel size, limited by the pixel aliasing problem.

Fig. 3
Fig. 3

Demonstration of 3D holographic refocusing using the aperture-scanning FP scheme. (a) The raw intensity image of a titled slide. (b) The aperture-scanning FP recovered intensity and phase images. The recovered sections at (c1) z = −1300 µm, (c2) z = −1000 µm, (c3) z = −700, and (c4) z = −400 µm.

Fig. 4
Fig. 4

(Media 1) Holographic refocusing of an extended 3D object. (a) The raw intensity image of a 3D object (leg of a spider). (b) The aperture-scanning FP recovered intensity and phase images. The recovered sections after digital propagation to (c1) z = −500 µm, (c2) z = −150 µm, (c3) z = + 150, and (c4) z = + 500 µm.

Fig. 5
Fig. 5

Experimental setup of the camera-scanning FP approach. (a) The sample is placed at the far field and the aperture of the camera lens naturally serves as a support constraint at the sample’s Fourier conjugate plane. By scanning the entire camera at different x-y positions, we can synthesize a larger passband in Fourier space, enabling super-resolution imaging of the object. (b)The USAF target is placed at the far field and a 2D motion stage is used to scan the entire camera assembly through the x-y plane.

Fig. 6
Fig. 6

Imaging performance of the camera-scanning FP approach. (a1) The raw image of the object directly captured by the camera. (a2) The spectrum of (a1). (b) The recovered image using the camera-scanning FP scheme. Group 2, element 4 can be clearly resolved. (b2) The recovered spectrum of (b1). The remaining artifacts of the recovered image may be due to the incorrect modeling of the aperture shape and partial coherent effects of the light source.

Equations (5)

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C L ( r 1 , r 2 )= γ 2 A( r 1 ,ω )δ( r 1 r 2 ),
C S ( r 1 ' r 2 ' ) A( r ) e 2πj λz r( r 1 ' r 2 ' ) dr= A ^ ( r ),
C I ( r 1 , r 2 )= A ^ ( r 1 ' r 2 ' )s( r 1 ' ) s * ( r 2 ' ) a ^ ( r 1 ' r 1 ) a ^ * ( r 2 ' r 2 )d r 1 ' d r 2 ' ,
I( r,x )= A ^ ( r 1 ' r 2 ' )s( r 1 ' ) s * ( r 2 ' ) a ^ ( r 1 ' r ) a ^ * ( r 2 ' r ) e ikx( r 1 ' r 2 ' ) d r 1 ' d r 2 ' ,
sin(atan(( d max w/2)/f)) sin(atan(( d max +w/2)/f)) = λ min λ max .

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