Abstract

This paper proposes a low-cost snapshot quantitative phase imaging approach. The setup is simple and adds only a printed film to a conventional microscope. The phase of a sample is regarded as an additional aberration of the optical imaging system. And the image captured through a phase object is modeled as the distorted version of a projected pattern. An optimization algorithm is utilized to recover the phase information via distortion estimation. We demonstrate our method on various samples such as a micro-lens array, IMR90 cells and the dynamic evaporation process of a water drop, and our approach has a capability of real-time phase imaging for highly dynamic phenomenon using a traditional microscope.

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

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References

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  1. F. Zernike, “Das phasenkontrastverfahren bei der mikroskopischen beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).
  2. G. Nomarski, “Nouveau dispositif pour lobservation en contraste de phase differentiel,” J. Phys. Radium 16, S88 (1955).
  3. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717 (2007).
    [Crossref] [PubMed]
  4. K. Stout and L. Blunt, Three-Dimensional Surface Topography (Elsevier, 2000).
  5. G. Popescu, Quantitative Phase Imaging of Cells and Tissues (McGraw Hill Professional, 2011).
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    [Crossref]
  9. Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19, 1016–1026 (2011).
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    [Crossref] [PubMed]
  14. L. Waller, S. S. Kou, C. J. Sheppard, and G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18, 22817–22825 (2010).
    [Crossref] [PubMed]
  15. Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
    [Crossref]
  16. C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38, 3538–3541 (2013).
    [Crossref] [PubMed]
  17. J. Wu, X. Lin, Y. Liu, J. Suo, and Q. Dai, “Coded aperture pair for quantitative phase imaging,” Opt. Lett. 39, 5776–5779 (2014).
    [Crossref] [PubMed]
  18. S. R. P. Pavani, A. R. Libertun, S. V. King, and C. J. Cogswell, “Quantitative structured-illumination phase microscopy,” Appl. Opt. 47, 15–24 (2008).
    [Crossref]
  19. M. Zhang, “The code for snapshot quantitative phase microscopy with a printed film,” GitHub (2018). [retrieved 28 Jun. 2018], https://github.com/zmj1203/Snapshot-quantitative-phase-microscopy-with-a-printed-film .
  20. T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.
  21. T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011).
    [Crossref]
  22. C. Liu, “Beyond pixels: Exploring new representations and applications for motion analysis,” Ph.D. thesis, MIT, Cambridge, MA, USA (2009).
  23. A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field,” in “European Conference on Computer Vision,” (Springer, 2006), pp. 578–591.
  24. A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in “IEEE International Conference on Computer Vision,” (IEEE, 2005), pp. 174–181.
  25. C. Zuo, Q. Chen, and A. Asundi, “Boundary-artifact-free phase retrieval with the transport of intensity equation: fast solution with use of discrete cosine transform,” Opt. Express 22, 9220–9244 (2014).
    [Crossref] [PubMed]

2017 (1)

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
[Crossref]

2014 (3)

2013 (1)

2012 (2)

2011 (2)

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19, 1016–1026 (2011).
[Crossref] [PubMed]

T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011).
[Crossref]

2010 (1)

2009 (1)

2008 (1)

2007 (1)

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

2005 (1)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[Crossref]

1983 (1)

1955 (1)

G. Nomarski, “Nouveau dispositif pour lobservation en contraste de phase differentiel,” J. Phys. Radium 16, S88 (1955).

1935 (1)

F. Zernike, “Das phasenkontrastverfahren bei der mikroskopischen beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Agrawal, A.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in “IEEE International Conference on Computer Vision,” (IEEE, 2005), pp. 174–181.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field,” in “European Conference on Computer Vision,” (Springer, 2006), pp. 578–591.

Asundi, A.

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[Crossref]

Badizadegan, K.

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

Barbastathis, G.

Blunt, L.

K. Stout and L. Blunt, Three-Dimensional Surface Topography (Elsevier, 2000).

Brox, T.

T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011).
[Crossref]

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.

Bruhn, A.

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.

Chellappa, R.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in “IEEE International Conference on Computer Vision,” (IEEE, 2005), pp. 174–181.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field,” in “European Conference on Computer Vision,” (Springer, 2006), pp. 578–591.

Chen, M.

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
[Crossref]

Chen, Q.

Choi, W.

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

Cogswell, C. J.

Dai, Q.

Dasari, R. R.

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

Ding, H.

Fang-Yen, C.

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

Feld, M. S.

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

Gillette, M. U.

Groot, M. L.

Kim, M. K.

King, S. V.

Kou, S. S.

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[Crossref]

Libertun, A. R.

Lin, X.

Liu, C.

C. Liu, “Beyond pixels: Exploring new representations and applications for motion analysis,” Ph.D. thesis, MIT, Cambridge, MA, USA (2009).

Liu, Y.

Lo, C.-M.

Lue, N.

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

Malik, J.

T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011).
[Crossref]

Mann, C. J.

Mansvelder, H. D.

Mehta, S. B.

Millet, L.

Mir, M.

Nomarski, G.

G. Nomarski, “Nouveau dispositif pour lobservation en contraste de phase differentiel,” J. Phys. Radium 16, S88 (1955).

Oh, S.

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

Papenberg, N.

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.

Pavani, S. R. P.

Petruccelli, J. C.

Phillips, Z. F.

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
[Crossref]

Plauska, A.

Popescu, G.

Qu, W.

Raskar, R.

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field,” in “European Conference on Computer Vision,” (Springer, 2006), pp. 578–591.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in “IEEE International Conference on Computer Vision,” (IEEE, 2005), pp. 174–181.

Ridder, M. C.

Rogers, J.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[Crossref]

Sheppard, C. J.

Stout, K.

K. Stout and L. Blunt, Three-Dimensional Surface Topography (Elsevier, 2000).

Suo, J.

Teague, M. R.

Tian, L.

Unarunotai, S.

van Berge, L.

Waller, L.

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
[Crossref]

L. Waller, S. S. Kou, C. J. Sheppard, and G. Barbastathis, “Phase from chromatic aberrations,” Opt. Express 18, 22817–22825 (2010).
[Crossref] [PubMed]

Wang, Z.

Weickert, J.

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.

Witte, S.

Wu, J.

Yu, L.

Zernike, F.

F. Zernike, “Das phasenkontrastverfahren bei der mikroskopischen beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Zuo, C.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[Crossref]

Biomed. Opt. Express (1)

IEEE Trans. Pattern Anal. Mach. Intell. (1)

T. Brox and J. Malik, “Large displacement optical flow: Descriptor matching in variational motion estimation,” IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. Radium (1)

G. Nomarski, “Nouveau dispositif pour lobservation en contraste de phase differentiel,” J. Phys. Radium 16, S88 (1955).

Nat. Methods (1)

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

Opt. Express (5)

Opt. Lett. (4)

PLoS ONE (1)

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cDPC),” PLoS ONE 12, 1–14 (2017).
[Crossref]

Z. Techn. Phys. (1)

F. Zernike, “Das phasenkontrastverfahren bei der mikroskopischen beobachtung,” Z. Techn. Phys. 16, 454–457 (1935).

Other (7)

M. Zhang, “The code for snapshot quantitative phase microscopy with a printed film,” GitHub (2018). [retrieved 28 Jun. 2018], https://github.com/zmj1203/Snapshot-quantitative-phase-microscopy-with-a-printed-film .

T. Brox, A. Bruhn, N. Papenberg, and J. Weickert, “High accuracy optical flow estimation based on a theory for warping,” in “European Conference on Computer Vision,” (Springer, 2004), pp. 25–36.

K. Stout and L. Blunt, Three-Dimensional Surface Topography (Elsevier, 2000).

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

C. Liu, “Beyond pixels: Exploring new representations and applications for motion analysis,” Ph.D. thesis, MIT, Cambridge, MA, USA (2009).

A. Agrawal, R. Raskar, and R. Chellappa, “What is the range of surface reconstructions from a gradient field,” in “European Conference on Computer Vision,” (Springer, 2006), pp. 578–591.

A. Agrawal, R. Chellappa, and R. Raskar, “An algebraic approach to surface reconstruction from gradient fields,” in “IEEE International Conference on Computer Vision,” (IEEE, 2005), pp. 174–181.

Supplementary Material (2)

NameDescription
» Code 1       The code of our approach
» Visualization 1       The movie shows the dynamic evaporation process of a water drop at 33.3 frames per second (fps) by our approach. It demonstrates the good performance of our proposed method for quantitative phase imaging of highly dynamic events.

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Figures (6)

Fig. 1
Fig. 1 The basic idea (a) and framework (b) of our method as we shown in Code 1 [19]. (a) The phase information of the sample is viewed as the aberration of the optical system, which can be estimated by the distortion of a reference image. (b) The input of our approach is a real-time distorted video captured through a phase sample and a pre-captured reference image. An optimization algorithm is applied to estimate the distortions of each frame. The quantitative phase video is then recovered by surface integration.
Fig. 2
Fig. 2 Illustration of our method. (a) The schematic with and without a sample. (b) The reference image of a binary mask captured without a sample. (c) A distorted image of (b) captured through a drop of water.
Fig. 3
Fig. 3 Schematic of our system (a) and a photograph showing the prototype (b). The mask is projected to the focus plane of camera and distorted by the phase of sample.
Fig. 4
Fig. 4 The experimental results of a microlens array. (a) The reference image. (b) The distorted image captured through the microlens. (c) Reconstructed phase result by our approach. (d) The defocus image pair for TIE approach. (e) Reconstructed phase result by TIE approach in [25]. (f) Lens thickness cross-sections corresponding to the line profiles indicated in (c) and (e), respectively.
Fig. 5
Fig. 5 Experimental results for IMR90 cells. (a) The distorted image captured through the sample. (b) The fluorescence image of sample. The nucleus labeled by DAPI and F-actin labeled by Alexafluor 532 are shown in blue and green, respectively. (c) Reconstructed phase image by our approach. (d) The defocus image pair for TIE approach. (e) Reconstructed phase result by TIE approach in [25].
Fig. 6
Fig. 6 Experimental results for the evaporation process of a water-drop (see Visualization 1). (a) Distorted images of the evaporating water drop at different time points. (b) The corresponding reconstructed phase images at different time points.

Equations (24)

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U 0 ( x , y , 0 ) = m , n U 0 ( x , y , 0 ; m , n ) = m , n U 0 ( x , y , 0 ) rect ( x d m , y d n ) ,
U 0 ( x , y , 0 ; m , n ) A 0 ( m d , n d , 0 ) exp [ j ϕ 0 ( m d , n d , 0 ) ] rect ( x d , m , y d n ) ,
F 0 ( f x , f y , Δ z ; m , n ) = H ( f x , f y ; Δ z ) F 0 ( f x , f y , 0 ; m , n ) ,
U 1 ( x , y , Δ z ; m , n ) = U 0 ( x , y , Δ z ; m , n ) exp [ j ϕ ( x , y ) ] ,
U 1 ( x , y , Δ z ; m , n ) U 0 ( x , y , Δ z ; m , n ) exp [ j ( A x + B y + C ) ] ,
A = ϕ ( x , y ) x | x = m d , y = n d , B = ϕ ( x , y ) y | x = m d , y = n d .
F 1 ( f x , f y , Δ z ; m , n ) = exp ( j C ) H ( f x A 2 π , f y B 2 π ; Δ z ) F 0 ( f x A 2 π , f y B 2 π ; 0 ; m , n ) ,
F 1 ( f x , f y , 0 ; m , n ) = H ( f x , f y ; Δ z ) F 1 ( f x , f y , Δ z ; m , n ) ,
H ( f x A 2 π , f y B 2 π ; Δ z ) = exp [ j Δ z 2 k ( A 2 + B 2 ) ] exp [ j λ Δ z ( A f x + B f y ) ] H ( f x , f y ; Δ z ) ,
F 1 ( f x , f y , 0 ; m , n ) = exp { j [ Δ z 2 k ( A 2 + B 2 ) + C ] } exp [ j λ Δ z ( A f x + B f y ) ] F 0 ( f x A 2 π , f y B 2 π , 0 ; m , n ) .
U 0 ( x , y , 0 ; m , n ) = U 1 ( x Δ z k A , y Δ z k B , 0 ; m , n ) exp { j [ A x + B y + C Δ z 2 k ( A 2 + B 2 ) ] } .
U 0 ( x , y , 0 ) U 1 ( x Δ z k ϕ ( x , y ) x , y Δ z k ϕ ( x , y ) y , 0 ) exp ( j { ϕ ( x , y ) Δ z 2 k [ ( ϕ ( x , y ) x ) 2 + ( ϕ ( x , y ) y ) 2 ] } ) .
I 0 ( x , y ) = I 1 ( x + u ( x , y ) , y + v ( x , y ) ) ,
{ u ( x , y ) = Δ z k ϕ ( x , y ) x v ( x , y ) = Δ z k ϕ ( x , y ) y .
min w J ( w ( x , t ) ) = min w ( E d ( w ( x , t ) ) + α E m ( w ( x , t ) ) ) .
E d ( w ( x , t ) ) = t = 1 T Ω ψ ( | I 1 ( x + w ( x , t ) ) I 0 ( x ) | 2 + γ | I 1 ( x + w ( x , t ) ) I 0 ( x ) | 2 ) d x ,
E m ( w ( x , t ) ) = t = 1 T Ω ψ ( u ( x , t ) 2 2 + v ( x , t ) 2 2 ) d x ,
U 0 ( x , y , Δ z ; m , n ) = U 0 ( m d , n d , 0 ) U rec ( x m d , y n d , Δ z ) .
U rec ( x , y ) = exp ( j k Δ z ) 2 j { [ C ( ξ 2 ) C ( ξ 1 ) ] + j [ S ( ξ 2 ) S ( ξ 1 ) ] } { [ C ( η 2 ) C ( η 1 ) ] + j [ S ( η 2 ) S ( η 1 ) ] } .
{ ξ 1 = k π Δ z ( d 2 + x ) , ξ 2 = k π Δ z ( d 2 x ) η 1 = k π Δ z ( d 2 + y ) , η 2 = k π Δ z ( d 2 y ) .
| U 0 ( x , y , Δ z ; m , n ) | = 1 2 A 0 ( m d , n d , 0 ) [ C ( ξ 2 ) C ( ξ 1 ) ] 2 + [ S ( ξ 2 ) S ( ξ 1 ) ] 2 [ C ( η 2 ) C ( η 1 ) ] 2 + [ S ( η 2 ) S ( η 1 ) ] 2 .
| U 0 ( x , y , Δ z ; m , n ) | ε , ( x , y ) { ( x , y ) | | x m d | d , | y n d | d } ,
U 0 ( f x , f y , Δ z ; m , n ) U 0 ( f x , f y , Δ z ; m , n ) rect ( x m d d , y n d d ) .
Δ x ϕ ( x ) = k Δ z β w ,

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