Abstract

Illumination-based differential phase contrast (DPC) is a phase imaging method that uses a pair of images with asymmetric illumination patterns. Distinct from coherent techniques, DPC relies on spatially partially coherent light, providing 2× better lateral resolution, better optical sectioning and immunity to speckle noise. In this paper, we derive the 2D weak object transfer function (WOTF) and develop a quantitative phase reconstruction method that is robust to noise. The effect of spatial coherence is studied experimentally, and multiple-angle DPC is shown to provide improved frequency coverage for more stable phase recovery. Our method uses an LED array microscope to achieve real-time (10 Hz) quantitative phase imaging with in vitro live cell samples.

© 2015 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  18. 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).
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  19. X. Ou, G. Zheng, and C. Yang, “Embedded pupil function recovery for Fourier ptychographic microscopy,” Opt. Express 22, 4960–4972 (2014).
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    [Crossref]
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    [Crossref]
  22. H. Rose, “Nonstandard imaging methods in electron microscopy,” Ultramicroscopy 2, 251–267 (1977).
    [Crossref] [PubMed]
  23. B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
    [Crossref] [PubMed]
  24. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).
    [Crossref]
  25. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
    [Crossref]
  26. C. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” J. Mod. Opt. 24, 1051–1073 (1977).
  27. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
    [Crossref]

2015 (1)

2014 (5)

2013 (1)

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

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)

2009 (1)

2007 (1)

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[Crossref] [PubMed]

2004 (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 (3)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

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)

1977 (2)

C. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” J. Mod. Opt. 24, 1051–1073 (1977).

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

1953 (1)

H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[Crossref]

1942 (1)

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

Barbastathis, G.

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
[Crossref]

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).
[Crossref]

Choudhury, A.

C. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” J. Mod. Opt. 24, 1051–1073 (1977).

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]

Coté, D.

Daradich, A.

Davison, I.

Depeursinge, C.

Feser, M.

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[Crossref] [PubMed]

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]

Gasecka, A.

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]

Hopkins, H.

H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[Crossref]

Hornberger, B.

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[Crossref] [PubMed]

Horstmeyer, R.

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

Jacobsen, C.

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[Crossref] [PubMed]

Kachar, B.

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

Kolner, C.

Kou, S. S.

Li, X.

Liu, S.

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref] [PubMed]

Marquet, P.

Mehta, S. B.

Mertz, J.

J. Mertz, A. Gasecka, A. Daradich, I. Davison, and D. Coté, “Phase-gradient contrast in thick tissue with a scanning microscope,” Biomed. Opt. Express 5, 407–416 (2014).
[Crossref] [PubMed]

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]

Ou, X.

Popescu, G.

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

Ramchandran, K.

Rose, H.

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

Sheppard, C.

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]

C. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” J. Mod. Opt. 24, 1051–1073 (1977).

Sheppard, C. J.

Sheppard, C. J. R.

Streibl, N.

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

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Teague, M. R.

Tian, L.

Vest, C. M.

C. M. Vest, Holographic Interferometry, (John Wiley and Sons, Inc., 1979).

Waller, L.

Wang, J.

Wilson, T.

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

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).
[Crossref]

Yang, C.

Zernike, F.

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

Zheng, G.

Biomed. Opt. Express (2)

J. Biomed. Opt. (1)

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19, 106002 (2014).
[Crossref] [PubMed]

J. Microsc. (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]

J. Mod. Opt. (1)

C. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” J. Mod. Opt. 24, 1051–1073 (1977).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Nat. Methods (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]

Nat. Photonics (1)

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

Opt. Commun. (1)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Optica (1)

Physica (1)

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

Proc. R. Soc. London, Ser. A (1)

H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London, Ser. A 217, 408–432 (1953).
[Crossref]

Science (1)

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

Ultramicroscopy (2)

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

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission x-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[Crossref] [PubMed]

Other (4)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, 1999).
[Crossref]

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
[Crossref]

C. M. Vest, Holographic Interferometry, (John Wiley and Sons, Inc., 1979).

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

Supplementary Material (2)

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Figures (5)

Fig. 1
Fig. 1

Top: The LED array microscope places a programmable source sufficiently far from the sample to be in Fourier space. Bottom: Intensity images taken with the top and bottom halves of the LEDs on demonstrate strong phase contrast (HeLa cell, 20× 0.4 NA). The typical brightfield image (incoherence parameter = 1), is generated by the sum of the two half-circle images and contains no phase contrast. The differential phase contrast (DPC) image is the normalized difference of the two half-circle images.

Fig. 2
Fig. 2

The 2D WOTF phase transfer function of DPC does not exactly match the first derivative approximation that is generally used. Here we compare transfer functions from WOTF model (Column 1) with the derivative model (Column 2). Both recover spatial frequencies out to twice the NA of the objective (black and red dashed circles are spatial frequencies NA/λ and 2NA/λ, respectively). However, our inverse transfer function compensates for damping of high frequencies, so small details are better recovered. Quantitative phase (Row 3) is reconstructed using data from Fig. 1 with regularization (α = 10−3).

Fig. 3
Fig. 3

Multi-axis DPC phase reconstructions (HeLa cells) eliminate artifacts due to missing frequencies along the axis of asymmetry. (Left) Single-axis DPC with Top-Bottom source asymmetry results in missing vertical features (yellow boxes), while Left-Right source asymmetry results in missing horizontal features (red boxes). (Right) Combining 2-axis or 12-axis data results in improved phase recovery, due to better coverage of spatial frequencies. As more angles are added, up to 12, the transfer function changes only marginally. (Bottom row) The 12-axis phase result is used as a best estimate of true phase, in order to show the errors incurred when using fewer angles.

Fig. 4
Fig. 4

Quantitative phase imaging at 10 Hz with 0.8 NA. The 2-axis DPC images are taken with a 20× 0.4 NA objective by repeating top, bottom, left and right half-circle illumination at 40Hz. Real-time sub-cellular dynamics can be visualized in the accompanying videos for both (Top) unstained neural progenitor cells (NPC) after five days of differentiation ( Media 1), and (Bottom) unstained MCF10A human breast basal epithelial cell ( Media 2).

Fig. 5
Fig. 5

DPC requires illumination from high angles for good phase recovery at all spatial frequencies. As the illumination NA increases (measured by the coherence parameter σ), both low spatial frequency and high spatial frequency phase information are better captured. When we use a half-circle source with σ ≤ 1, spatial frequencies below (1 − σ)NAobj/λ and above (1 + σ)NAobj/λ are missing. Thus, DPC only achieves resolution corresponding to twice the NA of the objective when σ ≥ 1. Interestingly, DPC with half-annular sources provides improved contrast for low spatial frequencies, maintaining the maximum 2NA bandlimit without sacrificing high spatial frequency response.

Equations (14)

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I ( r c ) = | [ q ( r ) o ( r ) exp ( i 2 π r u ) d 2 r ] P ( u ) exp ( i 2 π u r c ) d 2 u | 2 ,
I ( r c ) = | [ q ( r ) o ( r ) exp ( i 2 π r u ) d 2 r ] P ( u ) exp ( i 2 π u r c ) d 2 u | 2 d 2 u .
q ( r ) = S ( u ) exp ( i 2 π u r ) .
o ( r ) o * ( r ) 1 [ μ ( r ) + μ ( r ) ] + i [ ϕ ( r ) ϕ ( r ) ] .
I ˜ ( u ) = B δ ( u ) + H abs ( u ) μ ˜ ( u ) + H ph ( u ) ϕ ˜ ( u ) ,
B = S ( u ) | P ( u ) | 2 d 2 u .
H abs ( u ) = [ S ( u ) P * ( u ) P ( u + u ) d 2 u + S ( u ) P * ( u ) P ( u u ) d 2 u ] ,
H ph ( u ) = i [ S ( u ) P * ( u ) P ( u + u ) d 2 u S ( u ) P * ( u ) P ( u u ) d 2 u ] .
I DPC ( r c ) = I T ( r c ) I B ( r c ) I T ( r c ) + I B ( r c ) ,
H abs DPC ( u ) = 0 ,
I ˜ DPC ( u ) = H ( u ) ϕ ˜ ( u ) ,
min j | I ˜ DPC , j ( u ) H j ( u ) ϕ ˜ ( u ) | 2 + α | ϕ ˜ ( u ) | 2 ,
ϕ tik ( r ) = 1 { j H j * ( u ) I ˜ DPC , j ( u ) j | H j ( u ) | 2 + α } ,
H tik ( u ) = H 0 * ( u ) / ( | H 0 ( u ) | 2 + α ) ,

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