Abstract

Differential phase contrast (DPC) microscopy is a popular methodology to recover quantitative phase information of thin transparent samples under multi-axis asymmetric illumination patterns. Based on spatially partially coherent illuminations, DPC provides high-quality, speckle-free 3D reconstructions with lateral resolution up to twice the coherent diffraction limit, under the precondition that the pixel size of the imaging sensor is small enough to prevent spatial aliasing/undersampling. However, microscope cameras are in general designed to have a large pixel size so that the intensity information transmitted by the optical system cannot be adequately sampled or digitized. On the other hand, using an image sensor with a smaller pixel size or adding a magnification camera adapter to the camera can resolve the undersampling at the expense of a reduced field of view (FOV). To solve this tradeoff, we introduce a new variation of quantitative DPC approach, termed anti-aliased DPC (AADPC), which uses several aliased intensity images under asymmetric illuminations to recover wide-field aliasing-free phase images. Besides, phase transfer functions under different illumination patterns in DPC are analyzed to design an illumination scheme with better phase transfer characteristics. AADPC starts from an initial phase estimate obtained by a DPC-like deconvolution based on the system's weak phase transfer function under discrete half-annular illumination. Then the obtained initial phase map is further refined by the iterative de-multiplexing algorithm to overcome pixel-aliasing and improve the imaging resolution. The data redundancy requirement as well as the optimal illumination scheme of AADPC are analyzed and discussed based on several simulations, suggesting that the spatial undersampling can be mitigated through the iterative algorithm that uses only 4 images, yielding a nearly 4-fold increase in the space-bandwidth product (SBP) compared to the conventional DPC approach. We experimentally verify that AADPC can achieve a half-pitch imaging resolution of 345 nm, corresponding to 1.88× of the theoretical Nyquist-Shannon sampling resolution limit imposed by the sensor pixel size. The high-speed, high-throughput quantitative phase imaging capabilities of AADPC are also demonstrated by imaging HeLa cells mitosis in vitro, achieving a full-pitch lateral resolution of 665 nm across a wide FOV of 1.77mm2 at 25 fps.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

J. Sun, C. Zuo, J. Zhang, Y. Fan, and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8(1), 7669 (2018).
[Crossref] [PubMed]

J. Sun, Q. Chen, J. Zhang, Y. Fan, and C. Zuo., “Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography,” Opt. Lett. 43(14), 3365–3368 (2018).
[Crossref] [PubMed]

2017 (3)

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy, ” Sci. Reports,  7(1), 11777 (2017).
[Crossref]

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Reports 7(1), 1187 (2017).
[Crossref]

2016 (4)

2015 (1)

2014 (4)

2013 (3)

2012 (1)

T. N. Ford, K. K. Chu, and J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

2009 (1)

2008 (1)

G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods Cell Biol. 90, 87–115 (2008).
[Crossref]

2007 (2)

E. Glory and R. F. Murphy, “Automated subcellular location determination and high-throughput microscopy,” Dev. Cell 12(1), 7–16 (2007).
[Crossref] [PubMed]

V. Starkuviene and R. Pepperkok, “The potential of highcontent high-throughput microscopy in drug discovery,” Br. Journal pharmacology 152(1), 62–71 (2007).
[Crossref]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Physics 2, 258 (2006).
[Crossref]

2005 (2)

2004 (2)

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

1999 (1)

1998 (1)

1985 (2)

N. Streibl, “Three-dimensional imaging by a microscope,” J. Opt. Soc. Am. A 2, 121–127 (1985).
[Crossref]

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[Crossref] [PubMed]

1984 (2)

D. Hamilton, C. Sheppard, and T. Wilson, “Improved imaging of phase gradients in scanning optical microscopy,” J. Microscopy 135, 275–286 (1984).
[Crossref]

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microscopy 133, 27–39 (1984).
[Crossref]

1977 (1)

H. Rose, “Nonstandard imaging methods in electron microscopy,” Ultramicroscopy 2, 251–267 (1977).
[Crossref] [PubMed]

1942 (1)

F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects,” Physica 9, 686–698 (1942).
[Crossref]

Allman, B.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

Asundi, A.

Asundi., A.

Barbastathis, G.

Barty, A.

Bellair, C.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

Bertero, Mario

Mario Bertero and Patrizia Boccacci., Introduction to Inverse Problems in Imaging (CRC Press, 1998).
[Crossref]

Bevilacqua, F.

Bian, Z.

Bishara, W.

Boccacci., Patrizia

Mario Bertero and Patrizia Boccacci., Introduction to Inverse Problems in Imaging (CRC Press, 1998).
[Crossref]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Physics 2, 258 (2006).
[Crossref]

Castello, M.

Chen, Q.

J. Sun, Q. Chen, J. Zhang, Y. Fan, and C. Zuo., “Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography,” Opt. Lett. 43(14), 3365–3368 (2018).
[Crossref] [PubMed]

J. Sun, C. Zuo, J. Zhang, Y. Fan, and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8(1), 7669 (2018).
[Crossref] [PubMed]

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Reports 7(1), 1187 (2017).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy, ” Sci. Reports,  7(1), 11777 (2017).
[Crossref]

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space, ” Opt. Express 24(14), 15765–15781 (2016).
[Crossref] [PubMed]

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18) 20724–20744 (2016).
[Crossref] [PubMed]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “High-speed transport-of-intensity phase microscopy with an electrically tunable lens,” Opt. Express 21(20), 24060–24075 (2013).
[Crossref] [PubMed]

C. Zuo, Q. Chen, W. Qu, and A. Asundi., “Phase aberration compensation in digital holographic microscopy based on principal component analysis,” Opt. Lett. 38(10) 1724–1726 (2013).
[Crossref] [PubMed]

Chen, R.

Chen, X.

Chu, K. K.

T. N. Ford, K. K. Chu, and J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[Crossref] [PubMed]

Colomb, T.

Coskun, A.

Cuche, E.

Cuche, Etienne

Curl, C.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Physics 2, 258 (2006).
[Crossref]

Delbridge, L.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

Depeursinge, C.

Diaspro, A.

Dong, S.

Emery, Y.

Fan, Y.

J. Sun, Q. Chen, J. Zhang, Y. Fan, and C. Zuo., “Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography,” Opt. Lett. 43(14), 3365–3368 (2018).
[Crossref] [PubMed]

J. Sun, C. Zuo, J. Zhang, Y. Fan, and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8(1), 7669 (2018).
[Crossref] [PubMed]

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

Faulkner, H. M.

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Feizi, A.

W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning, ” Light 5(4), e16060 (2016).
[Crossref]

Ford, T. N.

T. N. Ford, K. K. Chu, and J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[Crossref] [PubMed]

Glory, E.

E. Glory and R. F. Murphy, “Automated subcellular location determination and high-throughput microscopy,” Dev. Cell 12(1), 7–16 (2007).
[Crossref] [PubMed]

Göröcs, Z.

W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning, ” Light 5(4), e16060 (2016).
[Crossref]

Hamilton, D.

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microscopy 133, 27–39 (1984).
[Crossref]

D. Hamilton, C. Sheppard, and T. Wilson, “Improved imaging of phase gradients in scanning optical microscopy,” J. Microscopy 135, 275–286 (1984).
[Crossref]

Harris, P.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

Heintzmann, R.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, highresolution fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Kachar, B.

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[Crossref] [PubMed]

Kim, M. K.

Kolner, C.

Kou, S. S.

Li, J.

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy, ” Sci. Reports,  7(1), 11777 (2017).
[Crossref]

Li, X.

Lo, C.-M.

Luo, W.

W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning, ” Light 5(4), e16060 (2016).
[Crossref]

Magistretti, P. J.

Mann, C. J.

Marquet, P.

Mehta, S. B.

Mertz, J.

T. N. Ford, K. K. Chu, and J. Mertz, “Phase-gradient microscopy in thick tissue with oblique back-illumination,” Nat. Methods 9, 1195–1197 (2012).
[Crossref] [PubMed]

Murphy, R. F.

E. Glory and R. F. Murphy, “Automated subcellular location determination and high-throughput microscopy,” Dev. Cell 12(1), 7–16 (2007).
[Crossref] [PubMed]

Nanda, P.

Nugent, K.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

Nugent, K. A.

Ozcan, A.

W. Luo, Y. Zhang, A. Feizi, Z. Göröcs, and A. Ozcan, “Pixel super-resolution using wavelength scanning, ” Light 5(4), e16060 (2016).
[Crossref]

W. Bishara, T. Su, A. Coskun, and 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]

Paganin, D.

Pepperkok, R.

V. Starkuviene and R. Pepperkok, “The potential of highcontent high-throughput microscopy in drug discovery,” Br. Journal pharmacology 152(1), 62–71 (2007).
[Crossref]

Pfeiffer, F.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Physics 2, 258 (2006).
[Crossref]

Popescu, G.

G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods Cell Biol. 90, 87–115 (2008).
[Crossref]

Qu, W.

Ramchandran, K.

Rappaz, B.

Roberts, A.

C. Bellair, C. Curl, B. Allman, P. Harris, A. Roberts, L. Delbridge, and K. Nugent, “Quantitative phase amplitude microscopy IV: imaging thick specimens,” J. Microscopy,  214(6), 62–69 (2004).
[Crossref]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[Crossref]

Rodenburg, J. M.

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[Crossref]

Rose, H.

H. Rose, “Nonstandard imaging methods in electron microscopy,” Ultramicroscopy 2, 251–267 (1977).
[Crossref] [PubMed]

Roth, S.

Sheppard, C.

D. Hamilton, C. Sheppard, and T. Wilson, “Improved imaging of phase gradients in scanning optical microscopy,” J. Microscopy 135, 275–286 (1984).
[Crossref]

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microscopy 133, 27–39 (1984).
[Crossref]

Sheppard, C. J.

Sheppard, C.J

Shiradkar, R.

Starkuviene, V.

V. Starkuviene and R. Pepperkok, “The potential of highcontent high-throughput microscopy in drug discovery,” Br. Journal pharmacology 152(1), 62–71 (2007).
[Crossref]

Streibl, N.

Su, T.

Sun, J.

J. Sun, Q. Chen, J. Zhang, Y. Fan, and C. Zuo., “Single-shot quantitative phase microscopy based on color-multiplexed Fourier ptychography,” Opt. Lett. 43(14), 3365–3368 (2018).
[Crossref] [PubMed]

J. Sun, C. Zuo, J. Zhang, Y. Fan, and Q. Chen, “High-speed Fourier ptychographic microscopy based on programmable annular illuminations,” Sci. Rep. 8(1), 7669 (2018).
[Crossref] [PubMed]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy, ” Sci. Reports,  7(1), 11777 (2017).
[Crossref]

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Reports 7(1), 1187 (2017).
[Crossref]

Y. Fan, J. Sun, Q. Chen, M. Wang, and C. Zuo, “Adaptive denoising method for Fourier ptychographic microscopy,” Opt. Commun. 404, 23–31 (2017).
[Crossref]

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18) 20724–20744 (2016).
[Crossref] [PubMed]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space, ” Opt. Express 24(14), 15765–15781 (2016).
[Crossref] [PubMed]

Tian, L.

Vicidomini, G.

Waller, L.

Wang, J.

Wang, M.

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Supplementary Material (1)

NameDescription
» Visualization 1       Phase reconstruction results on HeLa cells. (a) Large-SBP Phase reconstruction result; (b),(c) Phase of two selected zoom-ins regions;

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Figures (9)

Fig. 1
Fig. 1 Effect of pixel aliasing on DPC reconstruction. (a1), (a2), (b1), (b2) are PTFs of DPC in the cases of pixel aliasing and without pixel aliasing; (c) Ideal image with 2NAobj resolution; (d) phase reconstruction result with pixel aliasing.
Fig. 2
Fig. 2 PTF with half-circle illumination, continuous half-annular illumination, and discrete half-annular illumination. (a1)–(a3) are PTFs under single LED at different angles; (b1)–(b3) PTFs under half-circle illumination, continuous half-annular illumination and discrete half-annular illumination; (c1)–(c3) Quantitative curves of PTFs corresponding to each illumination pattern.
Fig. 3
Fig. 3 Phase reconstruction results with noise under half-circle illumination, continuous half-annular illumination, and discrete half-annular illumination. (a1)–(a3) Phase reconstruction results with noise; (b1)–(b3) Phase reconstruction results with regularization parameters α = 0.05.
Fig. 4
Fig. 4 Image acquisition process of the AADPC method. (a) and (b) are uniform intensity illumination scheme and uniform intensity image IB; (c1)–(c3) LED illumination patterns of AADPC method; (d1)–(d3) Captured images.
Fig. 5
Fig. 5 Algorithm flowchart of AADPC.
Fig. 6
Fig. 6 Phase reconstruction results under different number of LEDs (N). (a1)–(a5) The LED illumination patterns under different N; (b1)–(b5) Phase reconstruction results with different N; (c1)–(c5) Partial enlarged images of (b1)–(b5); (d1)–(d5) HR spectrum under different N.
Fig. 7
Fig. 7 Phase reconstruction results under different number of captured images. (a)–(e) Phase reconstruction results obtained by reducing different number of captured images under different N values; (f) and (g) are RMSE curves; (h1)–(h3) are phase reconstruction results with 4 images under different N.
Fig. 8
Fig. 8 Phase reconstruction results on Quantitative Phase Microscopy Target (QPTTM). (a) and (b) are observed results under the bright field; (c),(d) Phase reconstruction results with half-circular DPC; (e),(f) Phase reconstruction results with AADPC.
Fig. 9
Fig. 9 Phase reconstruction results on HeLa cells (Visualization 1). (a) Large-SBP Phase reconstruction result; (b),(c) Phase of two selected zoom-ins regions; (d1)–(d5) Phase reconstruction results on different time scales.

Equations (10)

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W j ( u ) = L ( u j ) [ δ ( u u j ) + i Φ ( u u j ) ] P ( u )
I j ( u ) = W j ( u ) W j * ( u ) = L ( u j ) δ ( u ) | P ( u j ) | 2 + i L ( u j ) Φ ( u ) [ P * ( u j ) P ( u + u j ) P ( u j ) P * ( u u j ) ]
I ( u ) = B δ ( u ) + i Φ ( u ) PTF ( u )
B = L ( u j ) | P ( u j ) | 2 d 2 u j
PTF ( u ) = L ( u j ) [ P * ( u j ) P ( u + u j ) P ( u j ) P * ( u u j ) ] d 2 u j .
I lr DPC = I l I r I l + I r .
( I l I r ) = i Φ ( u ) [ PTF l ( u ) PTF r ( u ) ] , ( I l + I r ) = ( B l + B r ) δ ( u ) .
I lr DPC ( u ) = i Φ ( u ) PTF lr ( u ) B l + B r .
PTF lr DPC ( u ) = L l ( u j ) [ P * ( u j ) P ( u + u j ) P ( u j ) P * ( u u j ) ] d 2 u j L l ( u j ) | P ( u j ) | 2 d 2 u j .
ϕ ( r ) = 1 { i [ PTF i DPC * ( u ) I i DPC ( u ) ] i | PTF i D P C * ( u ) | 2 + α } .

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