Abstract

Fourier ptychography (FP) is an imaging technique that applies angular diversity functions for high-resolution complex image recovery. The FP recovery routine switches between two working domains: the spectral and spatial domains. In this paper, we investigate the spectral-spatial data redundancy requirement of the FP recovery process. We report a sparsely sampled FP scheme by exploring the sampling interplay between these two domains. We demonstrate the use of the reported scheme for bypassing the high-dynamic-range combination step in the original FP recovery routine. As such, it is able to shorten the acquisition time of the FP platform by ~50%. As a special case of the sparsely sample FP, we also discuss a sub-sampled scheme and demonstrate its application in solving the pixel aliasing problem plagued in the original FP algorithm. We validate the reported schemes with both simulations and experiments. This paper provides insights for the development of the FP approach.

© 2014 Optical Society of America

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2013 (6)

2012 (3)

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
[CrossRef] [PubMed]

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

2011 (4)

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (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]

2010 (2)

2009 (1)

2008 (4)

2007 (2)

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Sig. Proc. Mag. 24(4), 118–121 (2007).
[CrossRef]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

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 (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]

1987 (1)

1982 (2)

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

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

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).

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]

Antebi, Y.

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (2011).
[CrossRef] [PubMed]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Baraniuk, R. G.

R. G. Baraniuk, “Compressive sensing [lecture notes],” IEEE Sig. Proc. Mag. 24(4), 118–121 (2007).
[CrossRef]

Barbastathis, G.

Barsi, C.

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]

Bian, Z.

Bishara, W.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Bunk, O.

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]

Choi, W.

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Dasari, R. R.

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (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]

Di, J.

Dierolf, M.

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.

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]

Elowitz, M. B.

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (2011).
[CrossRef] [PubMed]

Elser, V.

Fan, Q.

Fang-Yen, C.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

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]

Feld, M. S.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Feng, S.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Fienup, J. R.

Fixler, D.

Fleischer, J. W.

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).

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.

Hewish, A.

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

Hillman, T. R.

Holbrow, C. J.

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

Horstmeyer, R.

Humphry, M.

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

Humphry, M. J.

Hurst, A.

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

Isikman, S. O.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Jiang, H.

Kolner, C.

Kou, S. S.

Kraus, B.

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

Kutz, J. N.

Lau, R.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Lee, S. A.

S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
[CrossRef] [PubMed]

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (2011).
[CrossRef] [PubMed]

Lu, C.-H.

Lue, N.

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Maiden, A.

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

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).
[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]

Mavandadi, S.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Menzel, A.

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]

Mico, V.

Mukherjee, N.

S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
[CrossRef] [PubMed]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

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).
[CrossRef]

Ozcan, A.

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

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.

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

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

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]

Ryle, M.

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

Sampson, D. D.

Sheppard, C. J. R.

Sun, W.

Sung, Y.

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

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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]

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.

Williams, M. O.

Yang, C.

G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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X. Ou, R. Horstmeyer, C. Yang, G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
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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]

S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
[CrossRef] [PubMed]

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (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]

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Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

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S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
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Zhang, P.

Zhao, J.

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X. Ou, R. Horstmeyer, C. Yang, G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
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G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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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).
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S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
[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).
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G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (2011).
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J. Biomed. Opt. (1)

C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, M. S. Feld, “Video-rate tomographic phase microscopy,” J. Biomed. Opt. 16, 011005 (2011).

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

Lab Chip (1)

S. A. Lee, G. Zheng, N. Mukherjee, C. Yang, “On-chip continuous monitoring of motile microorganisms on an ePetri platform,” Lab Chip 12(13), 2385–2390 (2012).
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M. Humphry, B. Kraus, A. Hurst, A. Maiden, J. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).

Nat. Methods (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
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G. Zheng, R. Horstmeyer, C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
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Phys. Rev. A (1)

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]

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S. A. Alexandrov, T. R. Hillman, T. Gutzler, D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97(16), 168102 (2006).
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PLoS ONE (1)

Y. Sung, W. Choi, N. Lue, R. R. Dasari, Z. Yaqoob, “Stain-free quantification of chromosomes in live cells using regularized tomographic phase microscopy,” PLoS ONE 7(11), e49502 (2012).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

G. Zheng, S. A. Lee, Y. Antebi, M. B. Elowitz, C. Yang, “The ePetri dish, an on-chip cell imaging platform based on subpixel perspective sweeping microscopy (SPSM),” Proc. Natl. Acad. Sci. U.S.A. 108(41), 16889–16894 (2011).
[CrossRef] [PubMed]

S. O. Isikman, W. Bishara, S. Mavandadi, F. W. Yu, S. Feng, R. Lau, A. Ozcan, “Lens-free optical tomographic microscope with a large imaging volume on a chip,” Proc. Natl. Acad. Sci. U.S.A. 108(18), 7296–7301 (2011).
[CrossRef] [PubMed]

Science (1)

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]

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Figures (8)

Fig. 1
Fig. 1

FP reconstructions with different spectrum overlapping percentages. (a1)-(a2) Input high-resolution intensity and phase profiles of the simulated complex sample. (b)-(d) FP reconstructions with different spectrum overlapping percentages in the Fourier domain. (e) The RMS errors of the FP reconstructions versus the spectrum overlapping percentages. (a1) is copyrighted by MIT; we use it with permission.

Fig. 2
Fig. 2

FP reconstructions with different empty pixel percentages in the spatial domains. (a)-(c) FP reconstructions with 10%, 60%, and 90% empty pixels. (d) The RMS error of the FP reconstructions versus the empty pixel percentage.

Fig. 3
Fig. 3

The joint spectral-spatial sampling requirement of the FP recovery process. The RMS metric is plotted as a function of the spectrum overlapping percentage. Different curves represent cases with different empty pixel percentages. The FP convergence region is enclosed by the dark dash line.

Fig. 4
Fig. 4

(a1-a2) The overexposed raw images of a blood smear sample. (b1-b2) The corresponding HDR images of (a1) and (a2). Two exposure times were used in the HDR combination process. (c1-c2) The sparsely sampled masks by binarizing the overexposed raw images (a1) and (a2).

Fig. 5
Fig. 5

(a) The raw image of a blood smear sample. The FP reconstructions without (b) and with (c) the HDR combination process. (d) The reconstructions using the sparsely sampled FP scheme. (b1)-(c1) The recovered high-resolution intensity images. (b2)-(d2) The recovered high-resolution phase images.

Fig. 6
Fig. 6

(a) Pixel aliasing problem due to a large pixel size in the spatial domain. (b) The sub-sampled scheme by dividing one original pixel into 4 sub-pixels. The effective pixel size is only half of the original pixel size. At each iteration, only 1 out of 4 sub-pixels is updated by the measurement. The other 3 are kept unchanged.

Fig. 7
Fig. 7

Simulation of the sub-sampled FP scheme. (a) Raw intensity image with the pixel size larger than the Nyquist limit. (b1-b2) The FP reconstructions using the sub-sampled scheme. (b3) The recovered spectrum of (b1) and (b2). (c1-c2) The FP reconstructions without using the sub-sampled scheme. (c3) The recovered spectrum of (c1) and (c2).

Fig. 8
Fig. 8

Experimental validation of the sub-sampled FP scheme. (a) Raw intensity image with a pixel size (4.125 µm) larger than the Nyquist limit (3.15 µm). (b1) The FP reconstruction using the sub-sampled scheme. The linewidth of group 9 element 3 is 0.78 µm. (b2) The recovered spectrum of (b1). (c1) The FP reconstruction without using the sub-sampled scheme. The image quality is significantly degraded by the pixel aliasing problem. (c2) The recovered spectrum of (c1).

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