Abstract

Polarized light can reveal diagnostic information about tissue morphology. To promote easy adoption of polarization imaging techniques in the clinic it would be beneficial if they can be used with standard medical imaging instruments such as rigid endoscopes. We have characterized the polarization properties of two commercial laparoscopes and observed birefringence effects that complicate polarization imaging. Possible solutions are discussed that may be of interest to other tissue polarization imaging researchers.

© 2010 Optical Society of America

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References

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  1. R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127(7), 1000–1005 (1991).
    [Crossref] [PubMed]
  2. C. W. Sun, L. S. Lu, C. C. Yang, Y. W. Kiang, and M. J. Su, “Myocardial tissue characterization based on the time-resolved Stokes-Mueller formalism,” Opt. Express 10(23), 1347–1353 (2002).
    [PubMed]
  3. J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
    [Crossref] [PubMed]
  4. M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, “Polar decomposition of 3 x 3 Mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14(20), 9324–9337 (2006).
    [Crossref] [PubMed]
  5. M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
    [Crossref] [PubMed]
  6. V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
    [Crossref]
  7. R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
    [Crossref] [PubMed]
  8. W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
    [Crossref]
  9. R. Anderson, “Measurement of Mueller matrices,” Appl. Opt. 31(1), 11–13 (1992).
    [Crossref] [PubMed]
  10. T. Wood, S. Thiemjarus, K. Koh, D. Elson, and G. Yang, “Optimal feature selection applied to multispectral fluorescence imaging,” Medical Image Computing and Computer-Assisted Intervention MICCAI 2008 2, 222–229 (2008).
  11. S. Lu and R. Chipman, “Interpretation of Mueller matrices based on polar decomposition,” J. Opt. Soc. Am. A 13(5), 1106–1113 (1996).
    [Crossref]
  12. E. A. Oberemok and S. N. Savenkov, “Structure of deterministic Mueller matrices and their reconstruction in the method of three input polarizations,” J. Appl. Spectrosc. 70(2), 224–229 (2003).
    [Crossref]
  13. J. Morio and F. Goudail, “Influence of the order of diattenuator, retarder, and polarizer in polar decomposition of Mueller matrices,” Opt. Lett. 29(19), 2234–2236 (2004).
    [Crossref] [PubMed]
  14. P. Shukla and A. Pradhan, “Mueller decomposition images for cervical tissue: potential for discriminating normal and dysplastic states,” Opt. Express 17(3), 1600–1609 (2009).
    [Crossref] [PubMed]
  15. N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
    [Crossref] [PubMed]
  16. T. C. Wood, and D. S. Elson, “Polarization characterisation of laparoscope systems for polarization resolved tissue imaging,” in “Biomedical Optics,” (Optical Society of America, 2010), p. BTuD29.
  17. A. MacGregor, “Method for computing homogeneous liquid-crystal conoscopic figures,” J. Opt. Soc. Am. B 7(3), 337–347 (1990).
    [Crossref]

2009 (3)

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

P. Shukla and A. Pradhan, “Mueller decomposition images for cervical tissue: potential for discriminating normal and dysplastic states,” Opt. Express 17(3), 1600–1609 (2009).
[Crossref] [PubMed]

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

2006 (1)

2004 (1)

2003 (1)

E. A. Oberemok and S. N. Savenkov, “Structure of deterministic Mueller matrices and their reconstruction in the method of three input polarizations,” J. Appl. Spectrosc. 70(2), 224–229 (2003).
[Crossref]

2002 (2)

C. W. Sun, L. S. Lu, C. C. Yang, Y. W. Kiang, and M. J. Su, “Myocardial tissue characterization based on the time-resolved Stokes-Mueller formalism,” Opt. Express 10(23), 1347–1353 (2002).
[PubMed]

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

2001 (1)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

1999 (1)

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

1996 (1)

1992 (1)

1991 (1)

R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127(7), 1000–1005 (1991).
[Crossref] [PubMed]

1990 (1)

A. MacGregor, “Method for computing homogeneous liquid-crystal conoscopic figures,” J. Opt. Soc. Am. B 7(3), 337–347 (1990).
[Crossref]

1985 (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Anderson, R.

Anderson, R. R.

R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127(7), 1000–1005 (1991).
[Crossref] [PubMed]

Baba, J. S.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Backman, V.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Badizadegan, K.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Bailey, W. M.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Bickel, W. S.

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Buddhiwant, P.

Cameron, B. D.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Chipman, R.

Chung, J. R.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Coté, G. L.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Dasari, R.

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Dasari, R. R.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

DeLaughter, A. H.

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

Feld, M.

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Feld, M. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Georgakoudi, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Ghosh, N.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

M. K. Swami, S. Manhas, P. Buddhiwant, N. Ghosh, A. Uppal, and P. K. Gupta, “Polar decomposition of 3 x 3 Mueller matrix: a tool for quantitative tissue polarimetry,” Opt. Express 14(20), 9324–9337 (2006).
[Crossref] [PubMed]

Goudail, F.

Gupta, P. K.

Gurjar, R.

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Gurjar, R. S.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Itzkan, I.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Kiang, Y. W.

Li, R. K.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

Li, S. H.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

Lu, L. S.

Lu, S.

MacGregor, A.

A. MacGregor, “Method for computing homogeneous liquid-crystal conoscopic figures,” J. Opt. Soc. Am. B 7(3), 337–347 (1990).
[Crossref]

Manhas, S.

Morio, J.

Moriyama, E. H.

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

Oberemok, E. A.

E. A. Oberemok and S. N. Savenkov, “Structure of deterministic Mueller matrices and their reconstruction in the method of three input polarizations,” J. Appl. Spectrosc. 70(2), 224–229 (2003).
[Crossref]

Perelman, L.

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

Perelman, L. T.

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Pradhan, A.

Savenkov, S. N.

E. A. Oberemok and S. N. Savenkov, “Structure of deterministic Mueller matrices and their reconstruction in the method of three input polarizations,” J. Appl. Spectrosc. 70(2), 224–229 (2003).
[Crossref]

Shukla, P.

Su, M. J.

Sun, C. W.

Swami, M. K.

Uppal, A.

Vitkin, I. A.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

Weisel, R. D.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

Wilson, B. C.

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

Wood, M. F.

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

Yang, C. C.

Am. J. Phys. (1)

W. S. Bickel and W. M. Bailey, “Stokes vectors, Mueller matrices, and polarized scattered light,” Am. J. Phys. 53(5), 468–478 (1985).
[Crossref]

Appl. Opt. (1)

Arch. Dermatol. (1)

R. R. Anderson, “Polarized light examination and photography of the skin,” Arch. Dermatol. 127(7), 1000–1005 (1991).
[Crossref] [PubMed]

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

V. Backman, R. Gurjar, K. Badizadegan, I. Itzkan, R. Dasari, L. Perelman, and M. Feld, “Polarized light scattering spectroscopy for quantitative measurement of epithelial cellular structures in situ,” IEEE J. Sel. Top. Quantum Electron. 5(4), 1019–1026 (1999).
[Crossref]

J Biophotonics (1)

N. Ghosh, M. F. Wood, S. H. Li, R. D. Weisel, B. C. Wilson, R. K. Li, and I. A. Vitkin, “Mueller matrix decomposition for polarized light assessment of biological tissues,” J Biophotonics 2(3), 145–156 (2009).
[Crossref] [PubMed]

J. Appl. Spectrosc. (1)

E. A. Oberemok and S. N. Savenkov, “Structure of deterministic Mueller matrices and their reconstruction in the method of three input polarizations,” J. Appl. Spectrosc. 70(2), 224–229 (2003).
[Crossref]

J. Biomed. Opt. (2)

M. F. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[Crossref] [PubMed]

J. S. Baba, J. R. Chung, A. H. DeLaughter, B. D. Cameron, and G. L. Coté, “Development and calibration of an automated Mueller matrix polarization imaging system,” J. Biomed. Opt. 7(3), 341–349 (2002).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

A. MacGregor, “Method for computing homogeneous liquid-crystal conoscopic figures,” J. Opt. Soc. Am. B 7(3), 337–347 (1990).
[Crossref]

Nat. Med. (1)

R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7(11), 1245–1248 (2001).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Other (2)

T. C. Wood, and D. S. Elson, “Polarization characterisation of laparoscope systems for polarization resolved tissue imaging,” in “Biomedical Optics,” (Optical Society of America, 2010), p. BTuD29.

T. Wood, S. Thiemjarus, K. Koh, D. Elson, and G. Yang, “Optimal feature selection applied to multispectral fluorescence imaging,” Medical Image Computing and Computer-Assisted Intervention MICCAI 2008 2, 222–229 (2008).

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Figures (5)

Fig. 1.
Fig. 1.

The Olympus 0° forward-viewing laparoscope characterized in this experiment (top), and a schematic showing a cross section (bottom). The length is 500 mm and diameter 10 mm. The proximal end is on the left and distal tip the right. Illumination light is directed by fibre optics to the tip. Light reflected from tissue is then imaged by the objective lens, relayed via the rod lenses and then transmitted to the viewer at the eyepiece. Hard windows that can withstand sterilization cover the entrance and exit to prevent contamination. The Karl Storz laparoscope is similar in appearance.

Fig. 2.
Fig. 2.

Experimental schematic. Laser light at 600 nm is incident on a diffuser to ensure even illumination. A rotatable polarizer and removable λ/4 waveplate are used to create linear and circular polarization states. This uniform polarization is then imaged by the objective lens of the laparoscope. A rod lens system relays this image to the eyepiece, where a chosen state is passed by the analyser. Finally a lens forms the image of the viewing field on the CCD.

Fig. 3.
Fig. 3.

Measured Mueller matrices for the Olympus and Storz laparoscope (a)–(c) and a simulation for a sheet of sapphire (d). Each sub-image shows one element of the matrix across the whole field. Matrices were measured with the system illustrated in Fig. 2. The Karl Storz laparoscope patterns did not vary with the laparoscope orientation while the Olympus laparoscope did. Parts (a) & (c) recreated from [16].

Fig. 4.
Fig. 4.

The standard conoscopic geometry. Points in the image correspond to angles through the sample, usually a crystal. Any symmetry in the captured images will correspond to symmetries in the crystal lattice of the sample. These will change with the orientation of the crystal axes. By comparison with a laparoscope the exit window is equivalent to the sample.

Fig. 5.
Fig. 5.

The decomposed parameters of the Storz laparoscope (a)–(c) and the calculated retardance of a magnesium fluoride plate (d) for similar viewing angles, showing the same X-shaped patterns in both. Adapted from [16].

Equations (3)

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S = ( I Q U V ) = ( H + V H V P + M R + L ) M = ( m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 m 41 m 42 m 43 m 44 )
S 2 = M S 1
M = M Δ M ψ M D

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