Abstract

Differential interference contrast (DIC) microscopy is an inherently qualitative phase-imaging technique. What is obtained is an image with mixed phase-gradient and amplitude information rather than a true linear mapping of actual optical path length (OPL) differences. Here we investigate an approach that combines the transport-of-intensity equation (TIE) with DIC microscopy, thus improving direct visual observation. There is little hardware modification and the computation is noniterative. Numerically solving for the propagation of light in a series of through-focus DIC images allows linear phase information in a single slice to be completely determined and restored from DIC intensity values.

© 2010 Optical Society of America

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References

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2006

2004

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

2002

2001

L. J. Allen and M. P. Oxley, Opt. Commun. 199, 65 (2001).
[CrossRef]

2000

1998

1997

D. S. C. Biggs and M. Andrews, Appl. Opt. 36, 1766 (1997).
[CrossRef] [PubMed]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

1992

C. J. Cogswell and C. J. R. Sheppard, J. Microsc. 165, 81 (1992).
[CrossRef]

1983

Allen, L. J.

L. J. Allen and M. P. Oxley, Opt. Commun. 199, 65 (2001).
[CrossRef]

Andrews, M.

Arnison, M.

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

Barty, A.

Beleggia, M.

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

Biggs, D. S. C.

Cogswell, C.

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

Cogswell, C. J.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

C. J. Cogswell and C. J. R. Sheppard, J. Microsc. 165, 81 (1992).
[CrossRef]

Hariharan, P.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

Inoue, S.

Larkin, K.

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

Larkin, K. G.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

Nugent, K. A.

Oxley, M. P.

L. J. Allen and M. P. Oxley, Opt. Commun. 199, 65 (2001).
[CrossRef]

Paganin, D.

Pluta, M.

M. Pluta, Specialized Methods, Advanced Light Microscopy (Elsevier, 1989), Vol. 2.

Preza, C.

Roberts, A.

Schofield, M. A.

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

Sheppard, C.

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

Sheppard, C. J. R.

C. J. R. Sheppard, Appl. Opt. 41, 5951 (2002).
[CrossRef] [PubMed]

C. J. Cogswell and C. J. R. Sheppard, J. Microsc. 165, 81 (1992).
[CrossRef]

Shribak, M.

Smith, N.

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

Smith, N. I.

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

Teague, M. R.

Volkov, V. V.

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

Zhu, Y.

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

Appl. Opt.

J. Microsc.

C. J. Cogswell and C. J. R. Sheppard, J. Microsc. 165, 81 (1992).
[CrossRef]

M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, J. Microsc. 214, 7 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

L. J. Allen and M. P. Oxley, Opt. Commun. 199, 65 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998).
[CrossRef]

Proc. SPIE

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, Proc. SPIE 2984, 72 (1997).
[CrossRef]

Ultramicroscopy

M. Beleggia, M. A. Schofield, V. V. Volkov, and Y. Zhu, Ultramicroscopy 102, 37 (2004).
[CrossRef] [PubMed]

Other

M. Pluta, Specialized Methods, Advanced Light Microscopy (Elsevier, 1989), Vol. 2.

Supplementary Material (1)

» Media 1: MOV (774 KB)     

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Figures (4)

Fig. 1
Fig. 1

Original DIC images of cheek cell and TI-DIC reconstruction images. (a)–(c) (left column) DIC image at bias value θ of π 4 bias and 3 pi 4 bias, respectively. (b)–(d) TI-DIC reconstruction images for (a) and (c), respectively.

Fig. 2
Fig. 2

Validating the TI-DIC process with phase-gradient information. (a) Phase-gradient image from differentiating TI-DIC image. (b) Phase-gradient image from phase-stepping DIC. The phase-gradient reconstructions are substantially the same, even though they are generated from different data sets.

Fig. 3
Fig. 3

TI-DIC fiber reconstruction. (a) Reconstructed phase profile of the fiber. (b) Same profile after histogram adjustment. (c) Fitting of the fiber profile to theoretical data.

Fig. 4
Fig. 4

DIC image of macrophage cells (left) and its reconstructed phase image (right) (Media 1).

Equations (6)

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[ I ( r ̃ , z ) ϕ ( r ̃ , z ) ] = k I ( r ̃ , z ) z ,
U A = a A ( x , y ) exp i ( ϕ A ( x + Δ , y ) θ ) ,
U B = a B ( x , y ) exp i ( ϕ B ( x Δ , y ) + θ ) .
I = | a A | 2 + | a B | 2 2 a A a B cos ( ϕ A ϕ B 2 θ ) .
k I z = ( I A ϕ A ) + ( I B ϕ B ) 2 k I A I B z cos ( ϕ A ϕ B 2 θ ) ,
k I z = 2 I 0 [ 1 cos ( 2 δ ϕ 2 θ ) ] 2 ϕ 0 .

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