Abstract

We developed an interferometric microscopy technique, referred to as Jones phase microscopy, capable of extracting the spatially resolved Jones polarization matrix associated with transparent and anisotropic samples. This is a generalization of quantitative phase imaging, which is recovered from one diagonal element of the measured matrix. The principle of the technique is demonstrated with measurements of a liquid crystal spatial light modulator and the potential for live cell imaging with experiments on live neurons in culture.

© 2008 Optical Society of America

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2007 (2)

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

2005 (2)

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

J. F. de Boer and T. E. Milner, J. Biomed. Opt. 7, 359 (2002).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

1998 (1)

1996 (1)

R. Oldenbourg, Nature 381, 811 (1996).
[CrossRef] [PubMed]

1992 (1)

1982 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

1966 (1)

1963 (1)

1962 (1)

1947 (1)

1946 (1)

D. Gabor, J. Inst. Electr. Eng. 93, 329 (1946).

1941 (1)

Backman, V.

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Badizadegan, K.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Best, C. A.

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Bonner, R. F.

Brock, R. S.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Brown, B. R.

Cameron, B. D.

Cote, G. L.

Cuche, E.

Dasari, R. R.

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

de Boer, J. F.

J. F. de Boer and T. E. Milner, J. Biomed. Opt. 7, 359 (2002).
[CrossRef] [PubMed]

Depeursinge, C.

Ding, H.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Feld, M. S.

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Friberg, A. T.

Gabor, D.

D. Gabor, J. Inst. Electr. Eng. 93, 329 (1946).

Gandjbakhche, A. H.

Gillette, M. U.

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gurjar, R.

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Hu, X. H.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Ikeda, T.

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

Ina, H.

Itzkan, L.

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Jacobs, K. M.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Jones, R. C.

Kattawar, G. W.

Kobayashi, S.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

Lu, J. Q.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Marquet, P.

McConnell, T. J.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Mehrubeoglu, M.

Millet, L. J.

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Milner, T. E.

J. F. de Boer and T. E. Milner, J. Biomed. Opt. 7, 359 (2002).
[CrossRef] [PubMed]

Mujat, M.

M. Mujat, “Polarimetric characterization of random electromagnetic beams and applications,” Ph.D dissertation (University of Central Florida, 2004).

Nuzzo, R. G.

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Ojeda, J. F.

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

Oldenbourg, R.

R. Oldenbourg, Nature 381, 811 (1996).
[CrossRef] [PubMed]

Perelman, L. T.

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

Pluta, M.

M. Pluta, Advanced Light Microscopy: Measuring Techniques (North Holland, 1993).

Popescu, G.

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, Opt. Lett. 30, 1165 (2005).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

G. Popescu, “Quantitative phase imaging and applications: a review,” (2007) http://light.ece.uiuc.edu/QPIreview.htm.

Rakovic, M. J.

Rastegar, S.

Schmitt, J. M.

Setala, T.

Stewart, M. E.

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Sweedler, J. V.

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Takeda, M.

Tervo, J.

Upatnieks, J.

Wang, L. V.

Wolf, E.

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 2002).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 2002).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

V. Backman, R. Gurjar, K. Badizadegan, L. Itzkan, R. R. Dasari, L. T. Perelman, and M. S. Feld, IEEE J. Sel. Top. Quantum Electron. 5, 1019 (1999).
[CrossRef]

J. Biomed. Opt. (3)

H. Ding, J. Q. Lu, R. S. Brock, T. J. McConnell, J. F. Ojeda, K. M. Jacobs, and X. H. Hu, J. Biomed. Opt. 12, 034032 (2007).
[CrossRef] [PubMed]

J. F. de Boer and T. E. Milner, J. Biomed. Opt. 7, 359 (2002).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, C. A. Best, K. Badizadegan, R. R. Dasari, and M. S. Feld, J. Biomed. Opt. 10, 060503 (2005).
[CrossRef]

J. Inst. Electr. Eng. (1)

D. Gabor, J. Inst. Electr. Eng. 93, 329 (1946).

J. Opt. Soc. Am. (5)

Lab Chip (1)

L. J. Millet, M. E. Stewart, J. V. Sweedler, R. G. Nuzzo, and M. U. Gillette, Lab Chip 7, 987 (2007).
[CrossRef] [PubMed]

Nature (1)

R. Oldenbourg, Nature 381, 811 (1996).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Other (5)

M. Mujat, “Polarimetric characterization of random electromagnetic beams and applications,” Ph.D dissertation (University of Central Florida, 2004).

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley-Interscience, 2002).

M. Pluta, Advanced Light Microscopy: Measuring Techniques (North Holland, 1993).

G. Popescu, “Quantitative phase imaging and applications: a review,” (2007) http://light.ece.uiuc.edu/QPIreview.htm.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (3)

Fig. 1
Fig. 1

Jones phase microscope: P O , P R , and P A , polarizers; C 1 , C 2 , collimating lenses; L 1 , L 2 , Fourier lens pair; BS, beam splitter; CCD, charge coupled device. Inset, polarization orientation for the four measurements. For Y 11 , P O is at 45 ° and P A is at 0 ° ; for Y 12 , P O is at 45 ° and P A is at 90 ° ; for Y 21 , P O is at 45 ° and P A is at 0 ° ; for Y 22 , P O is at 45 ° and P A is at 90 ° . P R has the same orientation as P O .

Fig. 2
Fig. 2

Amplitude and phase maps of the Jones matrix for the SLM–polarizer combination. For each subplot, left is the amplitude map (bar in arbitrary units) and right is the phase map (bar in radians). The scale bar is the same in all images. (a) J x x ; (b) J x y ; (c) J y x ; (d) J y y .

Fig. 3
Fig. 3

JPM of an individual hippocampal neuron (live) in cell culture. For each subplot, the left side is the amplitude map (bar in arbitrary units) and the right side is the phase map (bar in radians). (a) J x x ; (b) J x y ; (c) J y x ; (d) J y y .

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

I ( x ) = I R + I S ( x ) + 2 [ I R I S ( x ) ] 1 2 cos [ q x + ϕ ( x ) ] ,
J ̱ [ J x x J x y J y x J y y ] ,
E + 45 = C 1 [ 1 1 ] ,
E 45 = C 2 [ 1 1 ] ,
[ Y 11 Y 12 ] = C 1 [ J x x + J x y J y x + J y y ] ,
[ Y 21 Y 22 ] = C 2 [ J x x J x y J y x J y y ] .
[ Y 11 Y 21 Y 12 Y 22 ] = [ C 1 C 1 0 0 C 2 C 2 0 0 0 0 C 1 C 1 0 0 C 2 C 2 ] [ J x x J x y J y x J y y ] .

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