Abstract

Fourier ptychography (FP) is a recently developed imaging approach that bypasses the resolution limit defined by the lens’ aperture. In current FP imaging platforms, systematic noise sources come from the intensity fluctuation of multiple LED elements and the pupil aberrations of the employed optics. These system uncertainties can significantly degrade the reconstruction quality and limit the achievable resolution, imposing a restriction on the effectiveness of the FP approach. In this paper, we report an optimization procedure that performs adaptive system correction for Fourier ptychographic imaging. Similar to the techniques used in phase retrieval, the reported procedure involves the evaluation of an image-quality metric at each iteration step, followed by the estimation of an improved system correction. This optimization process is repeated until the image-quality metric is maximized. As a demonstration, we used this process to correct for illumination intensity fluctuation, to compensate for pupil aberration of the optics, and to recover several unknown system parameters. The reported adaptive correction scheme may improve the robustness of Fourier ptychographic imaging by factoring out system imperfections and uncertainties.

© 2013 Optical Society of America

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2013 (5)

2012 (3)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and 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, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

2011 (2)

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

A. E. Tippie, A. Kumar, and J. R. Fienup, “High-resolution synthetic-aperture digital holography with digital phase and pupil correction,” Opt. Express19(13), 12027–12038 (2011).
[CrossRef] [PubMed]

2010 (3)

2009 (1)

2008 (5)

2007 (1)

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

2006 (2)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett.97(16), 168102 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. García-Martínez, and J. García, “Synthetic aperture superresolution with multiple off-axis holograms,” J. Opt. Soc. Am. A23(12), 3162–3170 (2006).
[CrossRef] [PubMed]

2004 (1)

H. M. L. Faulkner and 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)

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

2001 (1)

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

1995 (1)

P. Nellist, B. McCallum, and J. Rodenburg, “Resolution beyond the'information limit'in transmission electron microscopy,” Nature374, 630–632 (1995).

1993 (1)

1982 (1)

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

1969 (1)

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Alexandrov, S. A.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett.35(8), 1136–1138 (2010).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett.97(16), 168102 (2006).
[CrossRef] [PubMed]

Allen, L.

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

Audet, C.

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

Balic, M.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Bao, P.

Bean, R.

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Berenguer, F.

Bowers, C. W.

Brueck, S. R.

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Chen, B.

Cote, R. J.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Datar, R.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dean, B. H.

Dennis, J. E.

C. Audet and J. E. Dennis., “Analysis of generalized pattern searches,” SIAM J. Optim.13(3), 889–903 (2002).
[CrossRef]

Di, J.

Diaz, A.

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Elser, V.

Fan, Q.

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(2), 023903 (2004).
[CrossRef] [PubMed]

Fienup, J. R.

García, J.

García-Martínez, P.

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Gonsalves, R. A.

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

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Granero, L.

Guizar-Sicairos, M.

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(10), 7264–7278 (2008).
[CrossRef] [PubMed]

Gutzler, T.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett.35(8), 1136–1138 (2010).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett.97(16), 168102 (2006).
[CrossRef] [PubMed]

Hillman, T. R.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett.35(8), 1136–1138 (2010).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett.97(16), 168102 (2006).
[CrossRef] [PubMed]

Hoppe, W.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

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,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

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

Jiang, H.

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and 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, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

Kumar, A.

Kuznetsova, Y.

Lin, H.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Liu, J.-Q.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Maiden, A. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and 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, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

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

McCallum, B.

P. Nellist, B. McCallum, and J. Rodenburg, “Resolution beyond the'information limit'in transmission electron microscopy,” Nature374, 630–632 (1995).

Menzel, A.

Mico, V.

Micó, V.

Miller, J. J.

Nellist, P.

P. Nellist, B. McCallum, and J. Rodenburg, “Resolution beyond the'information limit'in transmission electron microscopy,” Nature374, 630–632 (1995).

Osten, W.

Ou, X.

Oxley, M.

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

Pedrini, G.

Peterson, I.

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Robinson, I. K.

Rodenburg, J.

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys.150, 87–184 (2008).
[CrossRef]

P. Nellist, B. McCallum, and J. Rodenburg, “Resolution beyond the'information limit'in transmission electron microscopy,” Nature374, 630–632 (1995).

Rodenburg, J. M.

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. Express21(11), 13592–13606 (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,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

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

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

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett.93(2), 023903 (2004).
[CrossRef] [PubMed]

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Sampson, D. D.

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Coherent aperture-synthesis, wide-field, high-resolution holographic microscopy of biological tissue,” Opt. Lett.35(8), 1136–1138 (2010).
[CrossRef] [PubMed]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture fourier holographic optical microscopy,” Phys. Rev. Lett.97(16), 168102 (2006).
[CrossRef] [PubMed]

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,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

Schwarz, C. J.

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Shenfield, A.

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

Strube, G.

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Sun, W.

Tai, Y.-C.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Thibault, P.

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Thurman, S. T.

Tippie, A. E.

Vila-Comamala, J.

Yang, C.

Zalevsky, Z.

Zhang, F.

Zhang, P.

Zhao, J.

Zheng, G.

Zheng, S.

S. Zheng, H. Lin, J.-Q. Liu, M. Balic, R. Datar, R. J. Cote, and Y.-C. Tai, “Membrane microfilter device for selective capture, electrolysis and genomic analysis of human circulating tumor cells,” J. Chromatogr. A1162(2), 154–161 (2007).
[CrossRef] [PubMed]

Acta Crystallogr. A (1)

W. Hoppe and G. Strube, “Diffraction in inhomogeneous primary wave fields. 2. Optical experiments for phase determination of lattice interferences,” Acta Crystallogr. A25, 502–507 (1969).
[CrossRef]

Adv. Imaging Electron Phys. (1)

J. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imaging Electron Phys.150, 87–184 (2008).
[CrossRef]

Appl. Opt. (3)

J. Appl. Phys. (1)

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

J. Chromatogr. A (1)

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Figures (9)

Fig. 1
Fig. 1

The flow chart of the adaptive Fourier ptychographic algorithm for intensity correction.

Fig. 2
Fig. 2

FP reconstructions with illumination uncertainty. (a1)-(a2) Input high-resolution intensity and phase profiles of the simulated complex sample. (b)-(e) FP reconstructions with different level of illumination fluctuations. Cameraman image © Massachusetts Institute of Technology. Used with permission.

Fig. 3
Fig. 3

Comparison of FP reconstructions with (a) and without (b) intensity correction. (c) The RMS error of the reconstruction versus different levels of intensity drift. Cameraman image © Massachusetts Institute of Technology. Used with permission.

Fig. 4
Fig. 4

Robustness of the reported scheme under different conditions. (a) The RMS errors of the reconstructions under extreme intensity drift. The large RMS for extreme LED intensity fluctuation may simply due to the nonlinear nature of the optimization process (b) The RMS errors of the reconstructions with different amount of additive noises.

Fig. 5
Fig. 5

Experimental validation of the reported intensity correcting scheme. (a) The low-resolution raw data of the pathology slide, with a pixel size of 2.75 µm. The reconstructed intensity (b1) and phase (b2) images without using the intensity correcting routine. The reconstructed intensity (c1) and phase (c2) images using the intensity correcting routine. 10 iterations were used in the iterative recovery process.

Fig. 6
Fig. 6

Second order pupil function recovery through optimization of the convergence index. (a) Raw data of the sample. (b) The FP reconstruction with (b) and without (c) the adaptive correction scheme. (d) The recovered pupil function.

Fig. 7
Fig. 7

Adaptive pupil correction for biological samples. (a) The raw data of a blood smear. The high-resolution recovered intensity (b1) and phase (b2) images using the adaptive correction scheme. The high-resolution recovered intensity (c1) and phase (c2) images without using the adaptive correction scheme.

Fig. 8
Fig. 8

Sample position recovery through optimization of the convergence index. (a), (b) FP reconstructions using different defocused distances. (c) The FP convergence index as a function of defocused distances.

Fig. 9
Fig. 9

LED position and central wavelength recovery through the adaptive correction scheme.

Equations (1)

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Convergence index= i mean( I mi ) x,y  abs( I li I mi ) ,

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