Abstract

We present an imaging procedure that simultaneously optimizes a camera’s resolution and retrieves a sample’s phase over a sequence of snapshots. The technique, termed overlapped Fourier coding (OFC), first digitally pans a small aperture across a camera’s pupil plane with a spatial light modulator. At each aperture location, a unique image is acquired. The OFC algorithm then fuses these low-resolution images into a full-resolution estimate of the complex optical field incident upon the detector. Simultaneously, the algorithm utilizes redundancies within the acquired dataset to computationally estimate and remove unknown optical aberrations and system misalignments via simulated annealing. The result is an imaging system that can computationally overcome its optical imperfections to offer enhanced resolution, at the expense of taking multiple snapshots over time.

© 2014 Optical Society of America

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2014 (5)

2013 (9)

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

R. Gao, G. Pedrini, and W. Osten, “Phase retrieval with resolution enhancement by using structured illumination,” Opt. Lett. 38, 5204–5207 (2013).
[Crossref] [PubMed]

M. P. Lee, G. M. Gibson, R. Bowman, S. Bernet, M. Ritsch-Marte, D. B. Phillips, and M. J. Padgett, “A multi-modal stereo microscope based on a spatial light modulator,” Opt. Express 21, 16541–16551 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nature Photon. 7, 739–745 (2013).
[Crossref]

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

S. Quirin, D. S. Peterka, and R. Yuste, “Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging,” Opt. Express 21(13), 16007–16021 (2013).
[Crossref] [PubMed]

M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21(21), 25418–25439 (2013).
[Crossref] [PubMed]

A. Tripathi, I. McNulty, and O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22, 1452–1466 (2013).
[Crossref]

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

2012 (2)

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]

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37, 1094–1096 (2012).
[Crossref] [PubMed]

2010 (3)

L. Camacho, V. Mico, Z. Zalevsky, and J. Garcia, “Quantitative phase microscopy using defocusing by means of a spatial light modulator,” Opt. Express 18, 6755–6766 (2010).
[Crossref] [PubMed]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104(R) (2010).
[Crossref]

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

2009 (4)

2008 (5)

R. Fiolka, M. Beck, and A. Stemmer, “Structured illumination in total internal reflection fluorescence microscopy using a spatial light modulator,” Opt. Lett. 33(14), 1629–1631 (2008).
[Crossref] [PubMed]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
[Crossref]

2006 (1)

S. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Sig. Proc. Mag. 23(3), 32–45 (2006).
[Crossref]

2004 (2)

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

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

2003 (2)

1996 (1)

1994 (1)

1992 (1)

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 10721085 (1992).
[Crossref]

1989 (1)

A. W. Lohmann, “Scaling laws for lens systems,” Appl. Optics 28, 4996–4998 (1989).
[Crossref]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

1982 (1)

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

1968 (1)

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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Agard, D. A.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Alexandrov, S. A.

Andalman, A.

Bando, Y.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

Beck, M.

Bernet, S.

Bhaduri, B.

Bian, Z.

Bowman, R.

Broxton, M.

Brueck, S. R. J.

Bunk, O.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Camacho, L.

Campos, J.

Chen, H.

C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
[Crossref]

Chhun, B. B.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Chowdhury, S.

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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Cohen, N.

David, C.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Debevec, P. E.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” In Proc. SIGGRAPH 97, ACM SIGGRAPH/Addison Wesley Computer Graphics Proceedings, Annual Conference Series, 369–378 (1997).

Deisseroth, K.

Dierolf, M.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Dong, S.

Dorsch, R. G.

Elser, V.

Estape, M

Faulkner, H. M. L.

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

Fernandez, E.

Ferreira, C.

Fienup, J. R.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 10721085 (1992).
[Crossref]

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

Fiolka, R.

Gao, R.

Garcia, J.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Gibson, G. M.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gray, J.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Griffis, E. R.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Grosenick, L.

Guo, K.

Gustafsson, M. G.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Gustafsson, M. G. L.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

Gutzler, T.

Hanser, B. M.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Hillman, T. R.

Horstmeyer, R.

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]

Iemmi, C.

Izatt, J.

Jefimovs, K.

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

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Johnson, I.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Johnson, R. B.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals: Second Edition (Elsevier and SPIE, 2010).

Kewish, C. M.

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

Kingslake, R.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals: Second Edition (Elsevier and SPIE, 2010).

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[Crossref] [PubMed]

Kner, P.

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
[Crossref] [PubMed]

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]

Kuznetsova, Y.

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Lee, D. J.

Lee, M. P.

Levoy, M.

Liang, C.

C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
[Crossref]

Lin, T.

C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
[Crossref]

Liu, C.

C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
[Crossref]

Lizana, A.

Lohmann, A. W.

Mahajan, V. N.

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]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1562 (2009).
[Crossref] [PubMed]

Malik, J.

P. E. Debevec and J. Malik, “Recovering high dynamic range radiance maps from photographs,” In Proc. SIGGRAPH 97, ACM SIGGRAPH/Addison Wesley Computer Graphics Proceedings, Annual Conference Series, 369–378 (1997).

Marquez, A.

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Martin, N.

Marwah, K.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

McNulty, I.

A. Tripathi, I. McNulty, and O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22, 1452–1466 (2013).
[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,” Nature Phys. 4, 394–398 (2008).
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Menzel, A.

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[Crossref]

Mico, V.

Mir, M.

Moreno, I.

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S. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Sig. Proc. Mag. 23(3), 32–45 (2006).
[Crossref]

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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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Osten, W.

Ou, X.

Padgett, M. J.

Paxman, R. G.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 10721085 (1992).
[Crossref]

Pedrini, G.

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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Peterka, D. S.

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,” Nature Phys. 4, 394–398 (2008).
[Crossref]

Pfeiffer, F.

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Pham, H.

Phillips, D. B.

Popescu, G.

Quirin, S.

Raskar, R.

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

Renker, D.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

Ritsch-Marte, M.

Rodenburg, J. 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. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104(R) (2010).
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A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1562 (2009).
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H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
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Sampson, D. D.

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).
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S. Sarder and A. Nehorai, “Deconvolution methods for 3-D fluorescence microscopy images,” IEEE Sig. Proc. Mag. 23(3), 32–45 (2006).
[Crossref]

Schlichting, I.

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

Schulz, T. J.

R. G. Paxman, T. J. Schulz, and J. R. Fienup, “Joint estimation of object and aberrations by using phase diversity,” J. Opt. Soc. Am. A 9(7), 10721085 (1992).
[Crossref]

Schwarz, C. J.

Sedat, J. W.

B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

Shiradkar, R.

Shpyrko, O. G.

Stemmer, A.

Thibault, P.

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

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

K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
[Crossref]

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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,” Nature Phys. 4, 394–398 (2008).
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C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
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Yang, C.

Yang, S.

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Yzuel, M. J.

Zalevsky, Z.

Zhang, F.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104(R) (2010).
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Zheng, G.

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C. Liang, T. Lin, B. Wong, C. Liu, and H. Chen, “Programmable aperture photography: multiplexed light field acquisition,” ACM Trans. Graph. 27(3), 55 (2008).
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K. Marwah, G. Wetzstein, Y. Bando, and R. Raskar, “Compressive light field photography using overcomplete dictionaries and optimized projections,” ACM Trans. Graph. 32(4), 46 (2013).
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B. M. Hanser, M. G. Gustafsson, D. A. Agard, and J. W. Sedat, “Phase-retrieved pupil functions in wide-field fluorescence microscopy,” J. Microsc. 216(1), 32–48 (2004).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (3)

Nat. Methods (1)

P. Kner, B. B. Chhun, E. R. Griffis, L. Winoto, and M. G. L. Gustafsson, “Super-resolution video microscopy of live cells by structured illumination,” Nat. Methods 6(5), 339–342 (2009).
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Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
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Nature Photon. (1)

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Nature Phys. (1)

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[Crossref]

New J. Phys. (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von Koning, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
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X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
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M. Broxton, L. Grosenick, S. Yang, N. Cohen, A. Andalman, K. Deisseroth, and M. Levoy, “Wave optics theory and 3-D deconvolution for the light field microscope,” Opt. Express 21(21), 25418–25439 (2013).
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S. Quirin, D. S. Peterka, and R. Yuste, “Instantaneous three-dimensional sensing using spatial light modulator illumination with extended depth of field imaging,” Opt. Express 21(13), 16007–16021 (2013).
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A. Tripathi, I. McNulty, and O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22, 1452–1466 (2013).
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D. J. Lee and A. M. Weiner, “Optical phase imaging using a synthetic aperture phase retrieval technique,” Opt. Express 22, 9380–9394 (2014).
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S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22, 13586–13599 (2014).
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R. Horstmeyer and C. Yang, “A phase space model of Fourier ptychographic microscopy,” Opt. Express 22, 338–358 (2014).
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Opt. Lett. (5)

Phys. Rev. B (1)

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82, 121104(R) (2010).
[Crossref]

Phys. Rev. Lett. (2)

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[Crossref] [PubMed]

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

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
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Ultramicroscopy (3)

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

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[Crossref]

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Figures (10)

Fig. 1
Fig. 1

Outline of the OFC procedure. (a) We place a transmissive SLM in the Fourier plane of a 4f system to digitally create different sub-aperture functions. (b) We capture a sequence of aberrated images while the SLM displays a sub-aperture shifted to a unique location between each snapshot. (c) We computationally transform the captured image set into a high-resolution amplitude and phase map, as well as an estimation of the camera’s low-order aberrations.

Fig. 2
Fig. 2

One stage of the basic OFC algorithm. For each window position Wj, a segment of the spectrum estimate Ŝ0(kx, ky) is extracted (corresponding to the jth position of the SLM’s shifting sub-aperture). In the spatial domain, the amplitude associated with this windowed spectrum is constrained with the measured image Ij(x, y) to form p′(x, y). Example detected images are in (d), where we measure the simulation’s spatial frequency “cutoff” at Group 0, Element 4. The result is Fourier transformed back to the aperture plane, where it is used to update the spectrum estimate, Ŝ0(kx, ky).

Fig. 3
Fig. 3

OFC simulations for an aberration-free noisy imaging system. (a) Air force resolution “target” amplitude and phase (top) and the corresponding OFC reconstruction (bottom), including 2% noise. Note this simulated sample’s slowly-varying phase is poorly reconstructed. We box the reconstruction’s spatial frequency cutoff (Group 1, Element 5). (b) A blood smear “target” sample’s phase is reconstructed with much higher (10X) fidelity than in (a), again including 2% noise. For both simulated samples, reconstruction error grows linearly with system noise while the OFC algorithm continues to converge.

Fig. 4
Fig. 4

Schematic of the OFC algorithm with simulated annealing (SA-OFC). We use the same phase retrieval loop outlined in Fig. 2 with three additions. First, an estimate of the system’s aberrations at the Fourier plane Aj is now multiplied with the spectrum estimate Ŝ at each loop. Second, SA is used to compare T different perturbed versions of the jth windowed spectrum with the jth intensity measurement. Third, the error-minimizing aberration perturbation A j t min and corresponding sample estimate ψ j t min are identified with Eq. (9), which then update Aj+1 and Ŝj+1 via Eq. (10)Eq. (11).

Fig. 5
Fig. 5

Simulation results of the SA-OFC algorithm. (a) Without simulated annealing, OFC cannot combine a set of aberrated sub-images into an accurate full-resolution complex field estimate. The induced defocus aberration is show to right. (b) The annealing OFC algorithm accurately recovers both the sample’s amplitude and phase and the 4f setup’s aberration map Aq(kx, ky). Here, q = 20. (c)–(d) Example low-resolution sub-aperture images, for comparison.

Fig. 6
Fig. 6

(a) SA-OFC is error reducing (blue) and exhibits much lower error than the regular OFC algorithm (red) in the presence of aberrations (assuming defocus d = 200). The ideal case of performing SA-OFC with an a-priori known aberration initialized and enforced each iteration is plotted in green. (b) As the aberration size increases, SA-OFC, OFC and the ideal case all slowly decrease in MSE performance. SA-OFC exhibits an aberration recovery mean-square error Δd scaling roughly as 10–15% of d, which may be improved with additional fine-tuning of annealing parameters.

Fig. 7
Fig. 7

SA-OFC removes geometric distortions. (a) SLM sub-aperture centers at the Fourier plane (blue dots) may be distorted by optical misalignments to unknown positions. During algorithm iteration, each estimated center is randomly perturbed by vector (δx, δy) as we generate and compare trial images to measured data. (b) Ground-truth sub-aperture centers for Fig. 5’s simulation are here radially offset to simulate a Fourier plane displaced by 100 μm axially. The actual center of each displaced sub-aperture is marked with an ‘x’. Initializing each sub-aperture center on an assumed rectilinear grid (blue dots), the simulated annealing process draws these estimates close to the actual centers after 10 iterations. (c) Error decreases with iteration similar to Fig. 6(a).

Fig. 8
Fig. 8

Experimental results from an OFC setup. We first image an Air Force resolution target to test the algorithm’s spatial resolution performance. (a) A single sub-aperture image exhibits low spatial resolution. (b) The OFC algorithm without annealing recovers a sharper image, but still contains artifacts. (c) The SA-OFC algorithm further improves the output field sq(x, y)’s spatial resolution (see text for algorithm parameters), as highlighted by traces in (d).

Fig. 9
Fig. 9

(a) Aberration map recovered simultaneously with Fig. 8(c)’s image. (b) Geometric misalignments of our 4f setup’s Fourier plane also simultaneously recovered by the SAOFC algorithm. Average shifts for each row/column are plotted on the side/top. (c) Plot demonstrating the algorithm’s error reduction with iteration. After 10 iterations, SA-OFC’s NMSE is 3 times lower than the direct OFC algorithm without annealing.

Fig. 10
Fig. 10

SA-OFC for quantitative phase. (a) Recovered phase map of 5 microspheres with aberration correction. (b) Line trace through one sphere demonstrates quantitative accuracy. (c) Example captured images. (d) Simultaneously recovered aberration map exhibits a similar structure as Fig. 9(a), as expected for the same optical setup. (e) Phase map recovered by the OFC algorithm without simulated annealing, where low-order aberrations clearly impact the fidelity of the reconstructed phase map.

Equations (13)

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W j ( k x c x j , k y c y j ) = { 1 , | k x | 2 and | k y | 2 b , otherwise ,
I j ( x , y ) = | [ W j ( k x , k y ) S ^ ( k x , k y ) ) ] | 2 ,
p j ( x , y ) = I j ( x , y ) p j ( x , y ) | p j ( x , y ) | .
S ^ 0 ( k x c j x , k y c j y ) = { P ^ j ( k x c j x , k y c j y ) , | k x | 2 and | k y | 2 S ^ 0 ( k x c j x , k y c j y ) , otherwise .
E q = x y ( | s q ( x , y ) | | U ( x , y ) | ) 2 / N ,
A ( k x , k y ) = e ( i d ( k x 2 + k y 2 ) ) ,
A j t ( k x , k y ) = A j ( k x , k y ) e ( i Δ t ( k x 2 + k y 2 ) ) ,
ψ j t ( x , y ) = [ W j ( k x , k y ) Ψ ^ j t ( k x , k y ) ] ,
t min = argmin t ( x y ( | ψ j t ( x , y ) | I j ( x , y ) ) 2 ) .
A j + 1 ( k x , k y ) = A j t min ( k x , k y )
S ^ j + 1 ( 0 ) = S ^ j ( 0 ) + A j * | A j | ( Ψ ^ j Ψ ^ j ) .
W j t ( k x c j x δ x t , k y c j y δ y t ) = { 1 , | k x | δ a t 2 and | k y | δ a t 2 b , otherwise ,
ψ j t ( x , y ) = [ W j t ( k x , k y ) S ^ j ( k x , k y ) ] ,

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