Abstract

We propose a method for estimating the stiffness of bio-specimens by measuring their linear retardance properties under applied stress. For this purpose, we employ an epi-illumination Mueller matrix microscope and show the procedures for its calibration. We provide experimental results demonstrating how to apply Mueller matrix data to elastography, using chicken liver and chicken heart as biological samples. Finally, we show how the histograms of linear retardance images can be used to distinguish between specimens and quantify the discrimination accuracy.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
  3. E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
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  4. S. J. Kirkpatrick, R. K. Wang, and D. D. Duncan, “OCT-based elastography for large and small deformations,” Opt. Express 14, 11585–11597 (2006).
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  6. C. Sun, B. Standish, and V. X. D. Yang, “Optical coherence elastography: current status and future applications,” J. Biomed. Opt. 16, 043001 (2011).
    [Crossref] [PubMed]
  7. D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
    [Crossref]
  8. C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
    [Crossref] [PubMed]
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    [Crossref]
  10. D. J. Maitland and J. T. Walsh, “Quantitative measurements of linear birefringence during heating of native collagen,” Lasers Surg. Med. 20, 310–318 (1997).
    [Crossref] [PubMed]
  11. B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
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    [Crossref]
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    [Crossref] [PubMed]
  16. D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
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    [Crossref]
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    [Crossref]
  20. J. Qi, H. He, H. Ma, and D. S. Elson, “Extended polar decomposition method of Mueller matrices for turbid media in reflection geometry,” Opt. Lett. 42, 4048–4051 (2017).
    [Crossref] [PubMed]
  21. http://sakuma.ecomas.jp/theme.html . Accessed April 30, 2019.

2018 (1)

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

2017 (1)

2015 (1)

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

2014 (2)

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

O. Arteaga, M. Baldris, J. Anto, A. Canillas, E. Pascual, and E. Bertran, “Mueller matrix microscope with a dual continuous rotating compensator setup and digital demodulation,” Appl. Opt. 53, 2236–2245 (2014).
[Crossref] [PubMed]

2011 (1)

C. Sun, B. Standish, and V. X. D. Yang, “Optical coherence elastography: current status and future applications,” J. Biomed. Opt. 16, 043001 (2011).
[Crossref] [PubMed]

2009 (1)

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

2008 (1)

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

2006 (1)

2001 (2)

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

K. T. den Boer, T. de Jong, and J. Dankelman, “Problems with laparoscopic instruments: opinions of experts,” J. Laparoendosc. Adv. Surg. Tech. 11, 149–155 (2001).
[Crossref]

1998 (1)

1997 (1)

D. J. Maitland and J. T. Walsh, “Quantitative measurements of linear birefringence during heating of native collagen,” Lasers Surg. Med. 20, 310–318 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (1)

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

1992 (1)

1990 (1)

D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” JOSA A 7, 693–700 (1990).
[Crossref]

1988 (1)

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

1978 (1)

Anastasiadou, M.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Anto, J.

Arteaga, O.

Asaoka, Y.

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

Azzam, R. M. A.

Baldris, M.

Bertran, E.

Buchta, D.

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

Canillas, A.

Chang, J.

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

Chipman, R. A.

S. Y. Lu and R. A. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13, 1106–1113 (1996).
[Crossref]

D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” JOSA A 7, 693–700 (1990).
[Crossref]

Claus, D.

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

Clement, D.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Cohen, H.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Dankelman, J.

K. T. den Boer, T. de Jong, and J. Dankelman, “Problems with laparoscopic instruments: opinions of experts,” J. Laparoendosc. Adv. Surg. Tech. 11, 149–155 (2001).
[Crossref]

de Boer, J. F.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

de Jong, T.

K. T. den Boer, T. de Jong, and J. Dankelman, “Problems with laparoscopic instruments: opinions of experts,” J. Laparoendosc. Adv. Surg. Tech. 11, 149–155 (2001).
[Crossref]

De Martino, A.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

den Boer, K. T.

K. T. den Boer, T. de Jong, and J. Dankelman, “Problems with laparoscopic instruments: opinions of experts,” J. Laparoendosc. Adv. Surg. Tech. 11, 149–155 (2001).
[Crossref]

Dreyfuss, J.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Du, E.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

Duncan, D. D.

Ehman, R.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Elson, D. S.

Ghosh, N.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

Goldstein, D. H.

D. H. Goldstein, “Mueller matrix dual-rotating retarder polarimeter,” Appl. Opt. 31, 6676–6683 (1992).
[Crossref] [PubMed]

D. H. Goldstein and R. A. Chipman, “Error analysis of a Mueller matrix polarimeter,” JOSA A 7, 693–700 (1990).
[Crossref]

Greenleaf, J.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Guo, Y.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

Gupta, P. K.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

He, C.

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

He, H.

J. Qi, H. He, H. Ma, and D. S. Elson, “Extended polar decomposition method of Mueller matrices for turbid media in reflection geometry,” Opt. Lett. 42, 4048–4051 (2017).
[Crossref] [PubMed]

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

He, Y.

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

Huynh, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Itoh, K.

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

Kirkpatrick, S. J.

Laude-Boulesteix, B.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Li, X.

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

Liege, F.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Liu, S.

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

Lomas, D.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Lu, S. Y.

Ma, H.

J. Qi, H. He, H. Ma, and D. S. Elson, “Extended polar decomposition method of Mueller matrices for turbid media in reflection geometry,” Opt. Lett. 42, 4048–4051 (2017).
[Crossref] [PubMed]

C. He, H. He, X. Li, J. Chang, Y. Wang, S. Liu, N. Zeng, Y. He, and H. Ma, “Quantitatively differentiating microstructures of tissues by frequency distributions of Mueller matrix images,” J. Biomed. Opt. 20, 105009 (2015).
[Crossref] [PubMed]

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

Maitland, D. J.

D. J. Maitland and J. T. Walsh, “Quantitative measurements of linear birefringence during heating of native collagen,” Lasers Surg. Med. 20, 310–318 (1997).
[Crossref] [PubMed]

Manduca, A.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Manhas, S.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

Muthupillai, R.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Nazac, A.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Nelson, J. S.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

Osten, W.

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

Park, B. H.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

Pascual, E.

Patel, H. S.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

Pedrini, G.

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

Qi, J.

Quang, N.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Rossman, P.

R. Muthupillai, D. Lomas, P. Rossman, J. Greenleaf, A. Manduca, and R. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995).
[Crossref] [PubMed]

Saxer, C.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

Schmitt, J. M.

Schwartz, L.

M. Anastasiadou, A. De Martino, D. Clement, F. Liege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi C 5, 1423–1426 (2008).
[Crossref]

Serbes, H.

D. Buchta, H. Serbes, D. Claus, G. Pedrini, and W. Osten, “Soft tissue elastography via shearing interferometry,” J. Med. Imag. 5, 046001 (2018).
[Crossref]

Soeda, S.

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

Srinivas, S. M.

B. H. Park, C. Saxer, S. M. Srinivas, J. S. Nelson, and J. F. de Boer, “In vivo burn depth determination by high-speed fiber-based polarization sensitive optical coherence tomography,” J. Biomed. Opt. 6, 474–479 (2001).
[Crossref] [PubMed]

Standish, B.

C. Sun, B. Standish, and V. X. D. Yang, “Optical coherence elastography: current status and future applications,” J. Biomed. Opt. 16, 043001 (2011).
[Crossref] [PubMed]

Sun, C.

C. Sun, B. Standish, and V. X. D. Yang, “Optical coherence elastography: current status and future applications,” J. Biomed. Opt. 16, 043001 (2011).
[Crossref] [PubMed]

Sun, M.

E. Du, H. He, N. Zeng, M. Sun, Y. Guo, J. Wu, S. Liu, and H. Ma, “Mueller matrix polarimetry for differentiating characteristic features of cancerous tissues,” J. Biomed. Opt. 19, 076013 (2014).
[Crossref]

Swami, M. K.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

Tohno, E.

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

Ueno, E.

E. Ueno, E. Tohno, S. Soeda, Y. Asaoka, and K. Itoh, “Dynamic tests in real-time breast echography,” Ultrasound Med. Biol. 14, 53–57 (1988).
[Crossref] [PubMed]

Uppal, A.

S. Manhas, M. K. Swami, H. S. Patel, A. Uppal, N. Ghosh, and P. K. Gupta, “Polarized diffuse reflectance measurements on cancerous and noncancerous tissues,” J. Biophoton. 2, 581–587 (2009).
[Crossref]

Walsh, J. T.

D. J. Maitland and J. T. Walsh, “Quantitative measurements of linear birefringence during heating of native collagen,” Lasers Surg. Med. 20, 310–318 (1997).
[Crossref] [PubMed]

Wang, R. K.

Wang, Y.

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http://sakuma.ecomas.jp/theme.html . Accessed April 30, 2019.

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Figures (11)

Fig. 1
Fig. 1 Schematic diagram of experimental setup of epi-illumination Mueller matrix microscope used for elastographic measurement. LP: linear polarizer, QWP: quarter wave plate is used in the polarization state generator and polarization state analyzer. Rotation angles of QWP1 and QWP2 are θ(t) and 5θ(t) respectively.
Fig. 2
Fig. 2 (a) Measurement of the spatially resolved normalized Mueller matrix MS(x, y) of a mirror at normal incidence. All of the Mueller matrix elements are normalized by element m00. (b) The standard deviation images of the measured Mueller matrices after five measurements. Each image contains 1360×1024 pixels.
Fig. 3
Fig. 3 Calculated diattenuation magnitude and orientation from the measured Mueller matrix of a rotating polarizer.
Fig. 4
Fig. 4 Calculated values of linear retardance magnitude and orientation from the measured Mueller matrix images of a waveplate rotated to different orientation angles.
Fig. 5
Fig. 5 Pictures of the biological samples: (a) chicken heart and (b) chicken liver. During measurement, the samples were each cut in a rectangular shape of 10 mm×20 mm cross-section and 1.2 mm thickness. (c) Diagram of mounting system to produce stress in the sample. The samples are stressed horizontally in the laboratory reference frame.
Fig. 6
Fig. 6 Linear retardance images of rubber material for different amount of measured strain. Strain values are given in red. The mechanical thickness of the rubber material is 1.5 mm.
Fig. 7
Fig. 7 Spatial histograms of linear retardance and fitted Gaussians for the rubber material for different strain amounts.
Fig. 8
Fig. 8 Stress and linear retardance of the rubber material as a function of the applied strain.
Fig. 9
Fig. 9 Measured linear retardance images after polar decomposition of measured Mueller matrix images of chicken liver and chicken heart for different values of strain produced. All the images are shown in the same scale of linear retardance from 0°–100°.
Fig. 10
Fig. 10 (a) Stress-strain plot (b) retardance-strain plot of chicken liver and chicken heart.
Fig. 11
Fig. 11 Spatial histograms and fitted Gaussian curves for the spatial distribution of linear retardance of chicken heart and liver at strain of 0.2.

Tables (2)

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Table 1 Mueller matrices of beam splitter in transmission and reflection mode.

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Table 2 Comparison of Young’s modulus, stress-optic modulus, and stress-retardance sensitivity coefficient for differentiation of the samples used in the present study.

Equations (14)

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S out = [ S 0 S 1 S 2 S 3 ] T = P 2 ( 5 ) R 2 ( 2 , 5 θ + 4 ) M mirror R 1 ( 1 , θ + 3 ) P 1 ( 0 ° ) S in ,
M mirror = ( 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 ) .
3 = 1 4 tan 1 ( b 10 a 10 ) 1 4 tan 1 ( b 12 a 12 ) ,
4 = 3 4 tan 1 ( b 12 a 12 ) 3 4 tan 1 ( b 10 a 10 ) 1 2 tan 1 ( b 2 a 2 ) 1 2 tan 1 ( b 6 a 6 ) ,
5 = 1 2 tan 1 ( b 12 a 12 ) 1 2 tan 1 ( b 10 a 10 ) 1 2 tan 1 ( b 2 a 2 ) ,
1 = sin 1 { a 12 cos ( 4 4 2 5 ) a 10 cos ( 4 4 + 4 3 2 5 ) a 12 cos ( 4 4 2 5 ) + a 10 cos ( 4 4 + 4 3 2 5 ) } ,
2 = sin 1 { a 12 cos ( 4 3 + 2 5 ) a 2 cos ( 4 4 + 4 3 2 5 ) a 12 cos ( 4 3 + 2 5 ) + a 2 cos ( 4 4 + 4 3 2 5 ) } .
M measured = M BST M S M BSR .
M S = M BST 1 M measured M BSR 1 .
Δ = 2 π n y n x λ d = 2 π G σ y σ x λ d ,
Δ = 2 π G σ d / λ .
σ = E .
Δ = 2 π G E d λ = R ,
E = a R .