Abstract

Differential phase contrast microscopy (DPC) provides high-resolution quantitative phase distribution of thin transparent samples under multi-axis asymmetric illuminations. Typically, illumination in DPC microscopic systems is designed with two-axis half-circle amplitude patterns, which, however, result in a non-isotropic phase contrast transfer function (PTF). Efforts have been made to achieve isotropic DPC by replacing the conventional half-circle illumination aperture with radially asymmetric patterns with three-axis illumination or gradient amplitude patterns with two-axis illumination. Nevertheless, the underlying theoretical mechanism of isotropic PTF has not been explored, and thus, the optimal illumination scheme cannot be determined. Furthermore, the frequency responses of the PTFs under these engineered illuminations have not been fully optimized, leading to suboptimal phase contrast and signal-to-noise ratio for phase reconstruction. In this paper, we provide a rigorous theoretical analysis about the necessary and sufficient conditions for DPC to achieve isotropic PTF. In addition, we derive the optimal illumination scheme to maximize the frequency response for both low and high frequencies (from 0 to 2NAobj) and meanwhile achieve perfectly isotropic PTF with only two-axis intensity measurements. We present the derivation, implementation, simulation, and experimental results demonstrating the superiority of our method over existing illumination schemes in both the phase reconstruction accuracy and noise-robustness.

© 2019 Chinese Laser Press

Full Article  |  PDF Article
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References

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2018 (9)

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

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophoton. 11, e201700364 (2018).
[Crossref]

Y.-Z. Lin, K.-Y. Huang, and Y. Luo, “Quantitative differential phase contrast imaging at high resolution with radially asymmetric illumination,” Opt. Lett. 43, 2973–2976 (2018).
[Crossref]

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, 3365–3368 (2018).
[Crossref]

Y. Fan, J. Sun, Q. Chen, J. Zhang, and C. Zuo, “Wide-field anti-aliased quantitative differential phase contrast microscopy,” Opt. Express 26, 25129–25146 (2018).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

M. Kellman, M. Chen, Z. F. Phillips, M. Lustig, and L. Waller, “Motion-resolved quantitative phase imaging,” Biomed. Opt. Express 9, 5456–5466 (2018).
[Crossref]

A. Robey and V. Ganapati, “Optimal physical preprocessing for example-based super-resolution,” Opt. Express 26, 31333–31350 (2018).
[Crossref]

M. Chen, Z. F. Phillips, and L. Waller, “Quantitative differential phase contrast (DPC) microscopy with computational aberration correction,” Opt. Express 26, 32888–32899 (2018).
[Crossref]

2017 (4)

W. Lee, D. Jung, S. Ryu, and C. Joo, “Single-exposure quantitative phase imaging in color-coded LED microscopy,” Opt. Express 25, 8398–8411 (2017).
[Crossref]

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, e0171228 (2017).
[Crossref]

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

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
[Crossref]

2016 (6)

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).
[Crossref]

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

C. J. Sheppard, S. Roth, R. Heintzmann, M. Castello, G. Vicidomini, R. Chen, X. Chen, and A. Diaspro, “Interpretation of the optical transfer function: significance for image scanning microscopy,” Opt. Express 24, 27280–27287 (2016).
[Crossref]

2015 (2)

2014 (3)

2013 (6)

2010 (1)

2009 (1)

2008 (2)

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52–A61 (2008).
[Crossref]

G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics,” Methods Cell Biol. 90, 87–115 (2008).
[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. Phys. 2, 258–261 (2006).
[Crossref]

2005 (2)

1999 (1)

1998 (1)

1985 (1)

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

1984 (2)

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

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

1983 (1)

1976 (1)

H. Rose, “Nonstandard imaging methods in electron microscopy,” Ultramicroscopy 2, 251–267 (1976).
[Crossref]

Asundi, A.

Barbastathis, G.

Barty, A.

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problem in Imaging (CRC Press, 1998).

Bevilacqua, F.

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problem in Imaging (CRC Press, 1998).

Bostan, E.

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging (to be published).

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. Phys. 2, 258–261 (2006).
[Crossref]

Castello, M.

Chen, H.-H.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophoton. 11, e201700364 (2018).
[Crossref]

Chen, M.

Chen, Q.

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

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, 3365–3368 (2018).
[Crossref]

Y. Fan, J. Sun, Q. Chen, J. Zhang, and C. Zuo, “Wide-field anti-aliased quantitative differential phase contrast microscopy,” Opt. Express 26, 25129–25146 (2018).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
[Crossref]

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

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).
[Crossref]

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

C. Zuo, Q. Chen, Y. Yu, and A. Asundi, “Transport-of-intensity phase imaging using Savitzky–Golay differentiation filter-theory and applications,” Opt. Express 21, 5346–5362 (2013).
[Crossref]

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

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38, 3538–3541 (2013).
[Crossref]

Chen, R.

Chen, X.

Colomb, T.

Cuche, E.

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. Phys. 2, 258–261 (2006).
[Crossref]

Depeursinge, C.

Diaspro, A.

Emery, Y.

Fan, Y.

Feng, S.

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

Ganapati, V.

Hamilton, D.

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

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

Heintzmann, R.

Horstmeyer, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

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

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

Hu, Y.

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

Huang, K.-Y.

Jang, S.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Joo, C.

Jung, D.

Kachar, B.

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

Kellman, M.

M. Kellman, M. Chen, Z. F. Phillips, M. Lustig, and L. Waller, “Motion-resolved quantitative phase imaging,” Biomed. Opt. Express 9, 5456–5466 (2018).
[Crossref]

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging (to be published).

Kemper, B.

Kim, K.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Kim, M. K.

Kim, U.

Kim, Y.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Kou, S. S.

Lee, D.

Lee, W.

Li, J.

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
[Crossref]

Li, X.

Lin, Y.-Z.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophoton. 11, e201700364 (2018).
[Crossref]

Y.-Z. Lin, K.-Y. Huang, and Y. Luo, “Quantitative differential phase contrast imaging at high resolution with radially asymmetric illumination,” Opt. Lett. 43, 2973–2976 (2018).
[Crossref]

Lo, C.-M.

Luo, Y.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophoton. 11, e201700364 (2018).
[Crossref]

Y.-Z. Lin, K.-Y. Huang, and Y. Luo, “Quantitative differential phase contrast imaging at high resolution with radially asymmetric illumination,” Opt. Lett. 43, 2973–2976 (2018).
[Crossref]

Lustig, M.

Magistretti, P. J.

Mann, C. J.

Marquet, P.

Mehta, S. B.

Nugent, K.

Ou, X.

Paganin, D.

Pan, X.

Park, H.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Park, Y.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Petruccelli, J. C.

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. Phys. 2, 258–261 (2006).
[Crossref]

Phillips, Z. F.

Popescu, G.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

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

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw Hill Professional, 2011).

Qu, W.

Ramchandran, K.

Rappaz, B.

Repina, N.

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging (to be published).

Roberts, A.

Robey, A.

Rose, H.

H. Rose, “Nonstandard imaging methods in electron microscopy,” Ultramicroscopy 2, 251–267 (1976).
[Crossref]

Roth, S.

Ryu, S.

Sheppard, C.

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

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

Sheppard, C. J.

Shim, H.

Y. Kim, H. Shim, K. Kim, H. Park, S. Jang, and Y. Park, “Profiling individual human red blood cells using common-path diffraction optical tomography,” Sci. Rep. 4, 6659 (2014).
[Crossref]

Sun, J.

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

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, 3365–3368 (2018).
[Crossref]

Y. Fan, J. Sun, Q. Chen, J. Zhang, and C. Zuo, “Wide-field anti-aliased quantitative differential phase contrast microscopy,” Opt. Express 26, 25129–25146 (2018).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
[Crossref]

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

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

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

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).
[Crossref]

Teague, M. R.

Tian, L.

Vicidomini, G.

von Bally, G.

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[Crossref]

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).
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L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
[Crossref]

L. Tian, J. Wang, and L. Waller, “3d differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39, 1326–1329 (2014).
[Crossref]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. Sheppard, “Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).
[Crossref]

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging (to be published).

Wang, J.

Weitkamp, T.

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[Crossref]

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[Crossref]

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R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

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

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

Yu, L.

Yu, Y.

Zhang, J.

Zhang, L.

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

Zhang, M.

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

Zhang, Y.

Zheng, G.

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

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

Zuo, C.

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

Y. Fan, J. Sun, Q. Chen, J. Zhang, and C. Zuo, “Wide-field anti-aliased quantitative differential phase contrast microscopy,” Opt. Express 26, 25129–25146 (2018).
[Crossref]

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, 3365–3368 (2018).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
[Crossref]

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

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Efficient positional misalignment correction method for Fourier ptychographic microscopy,” Biomed. Opt. Express 7, 1336–1350 (2016).
[Crossref]

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

C. Zuo, Q. Chen, Y. Yu, and A. Asundi, “Transport-of-intensity phase imaging using Savitzky–Golay differentiation filter-theory and applications,” Opt. Express 21, 5346–5362 (2013).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38, 3538–3541 (2013).
[Crossref]

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

Appl. Opt. (1)

Biomed. Opt. Express (4)

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

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

J. Opt. Soc. Am. (1)

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Nat. Photonics (2)

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

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nat. Photonics 10, 68–71 (2016).
[Crossref]

Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
[Crossref]

Opt. Express (12)

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23, 11394–11403 (2015).
[Crossref]

C. Zuo, Q. Chen, Y. Yu, and A. Asundi, “Transport-of-intensity phase imaging using Savitzky–Golay differentiation filter-theory and applications,” Opt. Express 21, 5346–5362 (2013).
[Crossref]

C. J. Mann, L. Yu, C.-M. Lo, and M. K. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13, 8693–8698 (2005).
[Crossref]

J. C. Petruccelli, L. Tian, and G. Barbastathis, “The transport of intensity equation for optical path length recovery using partially coherent illumination,” Opt. Express 21, 14430–14441 (2013).
[Crossref]

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

J. Li, Q. Chen, J. Sun, J. Zhang, X. Pan, and C. Zuo, “Optimal illumination pattern for transport-of-intensity quantitative phase microscopy,” Opt. Express 26, 27599–27614 (2018).
[Crossref]

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

A. Robey and V. Ganapati, “Optimal physical preprocessing for example-based super-resolution,” Opt. Express 26, 31333–31350 (2018).
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[Crossref]

M. Chen, Z. F. Phillips, and L. Waller, “Quantitative differential phase contrast (DPC) microscopy with computational aberration correction,” Opt. Express 26, 32888–32899 (2018).
[Crossref]

Y. Fan, J. Sun, Q. Chen, J. Zhang, and C. Zuo, “Wide-field anti-aliased quantitative differential phase contrast microscopy,” Opt. Express 26, 25129–25146 (2018).
[Crossref]

Opt. Lasers Eng. (2)

C. Zuo, J. Sun, S. Feng, Y. Hu, and Q. Chen, “Programmable colored illumination microscopy (PCIM): a practical and flexible optical staining approach for microscopic contrast enhancement,” Opt. Lasers Eng. 78, 35–47 (2016).
[Crossref]

C. Zuo, J. Sun, S. Feng, M. Zhang, and Q. Chen, “Programmable aperture microscopy: a computational method for multi-modal phase contrast and light field imaging,” Opt. Lasers Eng. 80, 24–31 (2016).
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X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38, 4845–4848 (2013).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38, 3538–3541 (2013).
[Crossref]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. Sheppard, “Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010).
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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, 3365–3368 (2018).
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Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, e0171228 (2017).
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Sci. Rep. (4)

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

J. Sun, C. Zuo, L. Zhang, and Q. Chen, “Resolution-enhanced Fourier ptychographic microscopy based on high-numerical-aperture illuminations,” Sci. Rep. 7, 1187 (2017).
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C. Zuo, J. Sun, J. Li, J. Zhang, A. Asundi, and Q. Chen, “High-resolution transport-of-intensity quantitative phase microscopy with annular illumination,” Sci. Rep. 7, 7654 (2017).
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Supplementary Material (1)

NameDescription
» Visualization 1       Quantitative phase images of the human cervical adenocarcinoma epithelial (HeLa) cell division process over the course of 5 hours

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Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the integral for PTF along the left–right axis in the polar coordinate system. (a) The radius ρ of the point Q is in the range of NA obj ρ 2 NA obj . (b) The radius ρ of the point Q is in the range of 0 ρ < NA obj .
Fig. 2.
Fig. 2. PTF and C ( ρ , θ ) with four illumination patterns. (a1)–(a4) Four illumination patterns. (b1)–(b4) PTFs along the left–right axis. (c1)–(c4) C ( ρ , θ ) with two-axis illumination. (d) Quantitative curves of C ( ρ , θ ) along the black straight line under the four illumination patterns. (e1)–(e3) Quantitative curves of C ( ρ , θ ) under the four illumination patterns on three radii.
Fig. 3.
Fig. 3. Simulation results with different regularization parameters under four illumination patterns. (a) Original phase image. (b) Diffraction limit phase image of DPC ( 2 NA obj ). (c1)–(c4), (d1)–(d4) Phase results with regularization parameters of 0 and 0.2. (e) Phase values along three small circles corresponding to different spatial frequencies evenly distributed from 0 to 2 NA obj . (f) Phase values along a small circle of the same radius in (d1)–(d4) under four illumination patterns.
Fig. 4.
Fig. 4. Phase reconstruction results of a phase resolution target QPT TM . (a) A bright-field image. (b) A zoom-in of the interest region of the bright-field image. (c) Phase reconstruction result under the half-circular uniform illumination pattern. (d) Phase reconstruction result under the optimal illumination scheme. (d) Phase values along three small circles evenly distributed from 0 to 2 NA obj under the optimal illumination pattern. (e) Phase values along a small circle of the same radius in (c), (d) under the half-circular uniform illumination pattern and optimal illumination pattern.
Fig. 5.
Fig. 5. Phase reconstruction results of HeLa cells under the optimal illumination scheme. (a) Full-field-of-view phase distribution. (b), (c) Phase maps of two selected zooms. (d) Phase results at different time points.
Fig. 6.
Fig. 6. Schematic diagram of the integral for PTF along the left–right axis illumination in the polar coordinate system. (a) The radius ρ of the point Q is in the range of NA obj ρ 2 NA obj . (b) The radius ρ of the point Q is in the range of 0 ρ < NA obj .
Fig. 7.
Fig. 7. PTF and C ( ρ , θ ) with a different L ( ρ ) function. (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C ( ρ , θ ) with two-axis illumination. (d) Quantitative curves of C ( ρ , θ ) along the black line.
Fig. 8.
Fig. 8. PTF and C ( ρ , θ ) with different thickness of the annulus (three σ ). (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C ( ρ , θ ) with two-axis illumination. (d) Quantitative curves of C ( ρ , θ ) along the black line.
Fig. 9.
Fig. 9. PTF and C ( ρ , θ ) with a different n . (a1)–(a3) Illumination patterns. (b1)–(b3) PTFs along the left–right axis. (c1)–(c3) C ( ρ , θ ) with two-axis illumination. (d) Quantitative curves of C ( ρ , θ ) along the black line.
Fig. 10.
Fig. 10. Simulation results of the optimal illumination scheme with different aberration levels. (a1)–(f1) Pupil with different aberration levels. (a2)–(f2) Reconstruction phase. (g) Quantitative curves of the reconstruction phase.

Equations (17)

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I j ( u ) = S ( u j ) δ ( u ) | P ( u j ) | 2 S ( u j ) A ( u ) [ P * ( u j ) P ( u + u j ) + P ( u j ) P * ( u u j ) ] + i S ( u j ) Φ ( u ) [ P * ( u j ) P ( u + u j ) P ( u j ) P * ( u u j ) ] ,
PTF l r ( u ) = S l r ( u j ) [ P * ( u j ) P ( u + u j ) P ( u j ) P * ( u u j ) ] d 2 u j | S l r ( u j ) | | P ( u j ) | 2 d 2 u j .
ϕ ( r ) = F 1 { i [ PTF i * ( u ) · I i DPC ( u ) ] i | PTF i * ( u ) | 2 + β } ,
S l r ( ρ , θ ) = L ( ρ ) M ( θ ) , S u d ( ρ , θ ) = L ( ρ ) N ( θ ) .
M ( θ ) = n = 1 a n cos ( n θ ) , N ( θ ) = n = 1 b n sin ( n θ ) .
PTF l r ( ρ , θ ) = { 2 ρ NA obj NA obj θ α θ + α S l r ( ξ , ε ) d ε d ξ 0 NA obj 0 2 π | S l r ( ξ , ε ) | d ε d ξ NA obj ρ 2 NA obj 2 NA obj ρ NA obj θ α θ + α S l r ( ξ , ε ) d ε d ξ 0 NA obj 0 2 π | S l r ( ξ , ε ) | d ε d ξ 0 ρ < NA obj .
S l r ( ρ , θ ) = L ( ρ ) cos ( n θ ) S u d ( ρ , θ ) = L ( ρ ) sin ( n θ ) ( n = 1 , 3 , 5 , ) .
S l r ( ρ , θ ) = δ ( ρ NA obj ) cos θ , S u d ( ρ , θ ) = δ ( ρ NA obj ) sin θ .
PTF l r ( ρ , θ ) = sin α cos θ , PTF u d ( ρ , θ ) = sin α sin θ .
C ( ρ , θ ) = 1 ρ 2 4 NA obj 2 .
S l r ( ρ , θ ) = L ( ρ ) n = 1 a n cos ( n θ ) , S u d ( ρ , θ ) = L ( ρ ) n = 1 b n sin ( n θ ) ,
PTF l r ( ρ , θ ) = { 2 ρ NA obj NA obj θ α θ + α S l r ( ξ , ε ) d ε d ξ 0 NA obj 0 2 π | S l r ( ξ , ε ) | d ε d ξ NA obj ρ 2 NA obj 2 NA obj ρ NA obj θ α θ + α S l r ( ξ , ε ) d ε d ξ 0 NA obj 0 2 π | S l r ( ξ , ε ) | d ε d ξ 0 ρ < NA obj .
PTF l r ( ρ , θ ) = { n = 1 a n cos ( n θ ) ρ NA obj NA obj L ( ξ ) sin ( n α ) d ξ n n = 1 a n 0 NA obj L ( ξ ) d ξ NA obj ρ 2 NA obj n = 1 a n cos ( n θ ) NA obj ρ NA obj L ( ξ ) sin ( n α ) d ξ n n = 1 a n 0 NA obj L ( ξ ) d ξ 0 ρ < NA obj , PTF u d ( ρ , θ ) = { n = 1 b n s i n ( n θ ) ρ NA obj NA obj L ( ξ ) sin ( n α ) d ξ n n = 1 b n 0 NA obj L ( ξ ) d ξ NA obj ρ 2 NA obj n = 1 b n s i n ( n θ ) NA obj ρ NA obj L ( ξ ) sin ( n α ) d ξ n n = 1 b n 0 NA obj L ( ξ ) d ξ 0 ρ < NA obj .
S l r ( ρ , θ ) = L ( ρ ) cos ( n θ ) S u d ( ρ , θ ) = L ( ρ ) sin ( n θ ) ( n = 1 , 3 , 5 , ) .
PTF l r ( ρ , θ ) = { cos ( n θ ) ρ NA obj NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ NA obj ρ 2 NA obj cos ( n θ ) NA obj ρ NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ 0 ρ < NA obj , PTF u d ( ρ , θ ) = { sin ( n θ ) ρ NA obj NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ NA obj ρ 2 NA obj sin ( n θ ) NA obj ρ NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ 0 ρ < NA obj .
M ( ρ ) = { ρ NA obj NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ NA obj ρ 2 NA obj NA obj ρ NA obj L ( ξ ) sin ( n α ) d ξ n 0 NA obj L ( ξ ) d ξ 0 ρ < NA obj ,
C ( ρ , θ ) = M ( ρ ) 2 .

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