Abstract

Optical polarimetry is used in pharmaceutical drug testing and quality control for saccharide-containing products (juice, honey). More recently, it has been proposed as a method for noninvasive glucose sensing for diabetic patients. Sagnac interferometry is commonly used in optical gyroscopes, measuring minute Doppler shifts resulting from mechanical rotation. In this work, we demonstrate that Sagnac interferometers are also sensitive to optical rotation, or the rotation of linearly polarized light, and are therefore useful in optical polarimetry. Results from simulation and experiment show that Sagnac interferometers are advantageous in optical polarimetry as they are insensitive to net linear birefringence and alignment of polarization components.

© 2011 Optical Society of America

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References

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  1. W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
    [CrossRef] [PubMed]
  2. B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
    [CrossRef] [PubMed]
  3. W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
    [CrossRef] [PubMed]
  4. S. Pohjola, “The glucose content of aqueous humor in man,” Acta Ophthalmol. 88, 1–80 (1966).
  5. B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
    [CrossRef] [PubMed]
  6. B. D. Cameron and G. L. Coté, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
    [CrossRef] [PubMed]
  7. J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
    [CrossRef] [PubMed]
  8. Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
    [CrossRef]
  9. B. D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diabetes Technol. Ther. 8, 156–164(2006).
    [CrossRef] [PubMed]
  10. E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493(1967).
    [CrossRef]
  11. American Diabetes Association, “Diabetes Statistics,” http://www.diabetes.org/diabetes-statistics.jsp.
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    [CrossRef] [PubMed]
  13. G. J. Van Blokland and S. C. Verhelst, “Corneal polarization in the living human eye explained with a biaxial model,” J. Opt. Soc. Am. A 4, 82–90 (1987).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  19. S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
    [CrossRef]
  20. A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.
  21. D. Andreou, “A method for mixing the signal and idler beams of an OPO in CdSe at the correct polarisations,” J. Phys. E 11, 1164–1165 (1978).
    [CrossRef]
  22. D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
    [CrossRef]

2010

Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
[CrossRef]

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

2006

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
[CrossRef]

B. D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diabetes Technol. Ther. 8, 156–164(2006).
[CrossRef] [PubMed]

2004

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9, 103–115 (2004).
[CrossRef] [PubMed]

2002

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

2001

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
[CrossRef] [PubMed]

2000

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt. 5, 5–16 (2000).
[CrossRef] [PubMed]

1999

1997

B. D. Cameron and G. L. Coté, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

1987

1985

1982

P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” J. Mod. Opt. 29, 1027–1040 (1982).
[CrossRef]

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
[CrossRef] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
[CrossRef] [PubMed]

1979

W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
[CrossRef] [PubMed]

1978

D. Andreou, “A method for mixing the signal and idler beams of an OPO in CdSe at the correct polarisations,” J. Phys. E 11, 1164–1165 (1978).
[CrossRef]

1967

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493(1967).
[CrossRef]

1966

S. Pohjola, “The glucose content of aqueous humor in man,” Acta Ophthalmol. 88, 1–80 (1966).

Adams, R. L.

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
[CrossRef] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
[CrossRef] [PubMed]

Andreou, D.

D. Andreou, “A method for mixing the signal and idler beams of an OPO in CdSe at the correct polarisations,” J. Phys. E 11, 1164–1165 (1978).
[CrossRef]

Ansari, R. R.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9, 103–115 (2004).
[CrossRef] [PubMed]

Anumula, H.

B. D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diabetes Technol. Ther. 8, 156–164(2006).
[CrossRef] [PubMed]

Atchison, D. A.

D. A. Atchison and G. Smith, Optics of the Human Eye(Butterworth-Heinemann, 2000).

Baba, J. S.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
[CrossRef] [PubMed]

Bescós, J.

Böckle, S.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9, 103–115 (2004).
[CrossRef] [PubMed]

Cameron, B. D.

B. D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diabetes Technol. Ther. 8, 156–164(2006).
[CrossRef] [PubMed]

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
[CrossRef] [PubMed]

B. D. Cameron and G. L. Coté, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

Carney, L. G.

P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” J. Mod. Opt. 29, 1027–1040 (1982).
[CrossRef]

Chipman, R.

A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.

Coté, G. L.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
[CrossRef] [PubMed]

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt. 5, 5–16 (2000).
[CrossRef] [PubMed]

B. D. Cameron and G. L. Coté, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

Engerman, R.

W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
[CrossRef] [PubMed]

Escudera-Sanz, I.

Gough, D. A.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Hao, Y.

Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
[CrossRef]

Kiely, P. M.

P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” J. Mod. Opt. 29, 1027–1040 (1982).
[CrossRef]

Kumosa, L. S.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Lin, J. T.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Lucisano, J. Y.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Mahler, A. B.

A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.

March, W. F.

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
[CrossRef] [PubMed]

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
[CrossRef] [PubMed]

W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
[CrossRef] [PubMed]

Marienko, V. V.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
[CrossRef]

McNichols, R. J.

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt. 5, 5–16 (2000).
[CrossRef] [PubMed]

Navarro, R.

Oberemok, E. A.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
[CrossRef]

Pohjola, S.

S. Pohjola, “The glucose content of aqueous humor in man,” Acta Ophthalmol. 88, 1–80 (1966).

Post, E. J.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493(1967).
[CrossRef]

Rabinovitch, B.

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
[CrossRef] [PubMed]

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
[CrossRef] [PubMed]

W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
[CrossRef] [PubMed]

Routh, T. L.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Rovati, L.

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9, 103–115 (2004).
[CrossRef] [PubMed]

Santamaría, J.

Savenkov, S. N.

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
[CrossRef]

Smith, G.

P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” J. Mod. Opt. 29, 1027–1040 (1982).
[CrossRef]

D. A. Atchison and G. Smith, Optics of the Human Eye(Butterworth-Heinemann, 2000).

A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.

Smith, P.

A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.

Theru, S.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

Van Blokland, G. J.

Verhelst, S. C.

Wang, C.

Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
[CrossRef]

Xiao, Z.

Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
[CrossRef]

Acta Ophthalmol.

S. Pohjola, “The glucose content of aqueous humor in man,” Acta Ophthalmol. 88, 1–80 (1966).

Diabetes Care

B. Rabinovitch, W. F. March, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part I. Measurement of very small optical rotations,” Diabetes Care 5, 254–258 (1982).
[CrossRef] [PubMed]

W. F. March, B. Rabinovitch, and R. L. Adams, “Noninvasive glucose monitoring of the aqueous humor of the eye: part II. Animal studies and the scleral lens,” Diabetes Care 5, 259–265 (1982).
[CrossRef] [PubMed]

Diabetes Technol. Ther.

B. D. Cameron and H. Anumula, “Development of a real-time corneal birefringence compensated glucose sensing polarimeter,” Diabetes Technol. Ther. 8, 156–164(2006).
[CrossRef] [PubMed]

B. D. Cameron, J. S. Baba, and G. L. Coté, “Measurement of the glucose transport time delay between the blood and aqueous humor of the eye for the eventual development of a noninvasive glucose sensor,” Diabetes Technol. Ther. 3, 201–207 (2001).
[CrossRef] [PubMed]

IEEE Trans. Biomed. Eng.

B. D. Cameron and G. L. Coté, “Noninvasive glucose sensing utilizing a digital closed-loop polarimetric approach,” IEEE Trans. Biomed. Eng. 44, 1221–1227 (1997).
[CrossRef] [PubMed]

J. Biomed. Opt.

J. S. Baba, B. D. Cameron, S. Theru, and G. L. Coté, “Effect of temperature, pH, and corneal birefringence on polarimetric glucose monitoring in the eye,” J. Biomed. Opt. 7, 321–328(2002).
[CrossRef] [PubMed]

R. R. Ansari, S. Böckle, and L. Rovati, “New optical scheme for a polarimetric-based glucose sensor,” J. Biomed. Opt. 9, 103–115 (2004).
[CrossRef] [PubMed]

R. J. McNichols and G. L. Coté, “Optical glucose sensing in biological fluids: an overview,” J. Biomed. Opt. 5, 5–16 (2000).
[CrossRef] [PubMed]

J. Mod. Opt.

P. M. Kiely, G. Smith, and L. G. Carney, “The mean shape of the human cornea,” J. Mod. Opt. 29, 1027–1040 (1982).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. E

D. Andreou, “A method for mixing the signal and idler beams of an OPO in CdSe at the correct polarisations,” J. Phys. E 11, 1164–1165 (1978).
[CrossRef]

Ophthal. Res.

Z. Xiao, C. Wang, and Y. Hao, “The in vitro study of pressure change on corneal birefringence,” Ophthal. Res. 43, 159–168(2010).
[CrossRef]

Phys. Rev. E

S. N. Savenkov, V. V. Marienko, and E. A. Oberemok, “Generalized matrix equivalence theorem for polarization theory,” Phys. Rev. E 74, 056607 (2006).
[CrossRef]

Rev. Mod. Phys.

E. J. Post, “Sagnac effect,” Rev. Mod. Phys. 39, 475–493(1967).
[CrossRef]

Sci. Transl. Med.

D. A. Gough, L. S. Kumosa, T. L. Routh, J. T. Lin, and J. Y. Lucisano, “Function of an implanted tissue glucose sensor for more than 1 year in animals,” Sci. Transl. Med. 28, 42ra53(2010).
[CrossRef]

Trans. Am. Soc. Artif. Intern. Organs

W. F. March, R. Engerman, and B. Rabinovitch, “Optical monitor of glucose,” Trans. Am. Soc. Artif. Intern. Organs 25, 28–31 (1979).
[CrossRef] [PubMed]

Other

D. A. Atchison and G. Smith, Optics of the Human Eye(Butterworth-Heinemann, 2000).

American Diabetes Association, “Diabetes Statistics,” http://www.diabetes.org/diabetes-statistics.jsp.

A. B. Mahler, P. Smith, R. Chipman, and G. Smith, “High-accuracy spectropolarimetric imaging using photoelastic modulator cameras with low-polarization coatings,” presented at the NASA Science Technology Conference, Adelphi, Maryland, 19–21 June 2007.

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Figures (9)

Fig. 1
Fig. 1

Many models exist for the cornea, but in general it varies significantly from person to person. To cover the range of corneal shapes, three eye models are considered: (a) the Navarro eye model, or the mean eye model, (b) Extreme 1, and (c) Extreme 2. The ray path through the eye enters the cornea, traverses the aqueous humor, and exits the cornea. The ray path can either be temple (left) to nose (right) or vice versa. On the depiction of the Navarro model (a), the angle between the anterior cornea surface normal and the ray within the cornea, γ, is shown. This angle is critical for determining the apparent corneal birefringence using Van Blokland’s model.

Fig. 2
Fig. 2

In the crossed polarizer method, polarized light is continuously optically rotated by a modulating retarder. The polarization of light traversing the eye is rotated with respect to a reference beam. This difference in polarization state is detected as a difference in signal phase using an analyzer placed in front of a detector. The image of the eye shown here is openly available from the National Eye Institute (http://www.nei.nih.gov/photo/).

Fig. 3
Fig. 3

In a Sagnac interferometer, light from counterpropagating paths are combined. For a stationary interferometer with no sample, the optical paths are identical. Optical rotation, however, introduces an optical path difference between the counterpropagating beams. The modulating retarder, which continuously changes the optical rotation from 0 to 360 deg produces a cosinusoidal interference signal at the detector. An additional optical rotation from the eye results in a phase difference between the reference and sample signals. The image of the eye shown here is openly available from the National Eye Institute (http://www.nei.nih.gov/photo/).

Fig. 4
Fig. 4

Light that traveled in one direction around the system experiences an optical rotation opposite that experienced by light that traveled in the other direction.

Fig. 5
Fig. 5

Varying corneal birefringence affects the measured glucose concentration for both the (a) crossed polarizer and (b) Sagnac methods even when the corneal slow axis is fixed at 0 deg (aligned with the incident polarization state). The error bars are + / 1 standard deviation. The results are superimposed on the Clarke error grid. Regions A, B, and C are considered clinically safe, while regions D and E are considered dangerous based on the action a diabetic patient would take given the measured reading. Neither the crossed polarizer nor Sagnac results are contained with regions A, B, and C for all three eye models.

Fig. 6
Fig. 6

Varying corneal birefringence with an uncertainty in the corneal slow axis of + / 0.1 deg strongly affects the crossed polarizer results, with error bars of the order of 1000 mg / dL as shown in (a). The error bars are + / 1 standard deviation. The Sagnac results are unaffected by the orientation of the corneal slow axis as shown in (b) and are the same as those in Fig. 5b.

Fig. 7
Fig. 7

The multiwavelength algorithm for extracting the optical rotation due to glucose concentration did not perform well for the crossed polarizer method for all three eye models, even when the corneal slow axis is fixed at 0 deg as shown in (a). With the Sagnac method, however, the multiwavelength algorithm was very successful, with all the data points lying within region A, even when the corneal slow axis was randomly varied between + / 180 deg as shown in (b).

Fig. 8
Fig. 8

Varying birefringence and diattenuation with a fixed axis for both 0 deg decreases the error bars as compared to when the birefringence alone is varied for both methods for all three eye models. With calibration, the Sagnac results can be contained within regions A, B, and C.

Fig. 9
Fig. 9

The measured optical rotation was negligible with no sample present and with the linear retarder only. The measured optical rotation for quartz was 127 deg , as expected, with and without a linear retarder present.

Tables (3)

Tables Icon

Table 2 Range of Corneal Retardance Values Used in Simulation

Tables Icon

Table 3 Range of Diattenuation Values Used in Simulation

Equations (25)

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

α = [ α ] λ T × l × c ,
[ α ] λ = 6.3333 × 10 7 × λ 2.1945   deg   per   dm g / ml ,
optRot ( α ) = ( cos ( α ) sin ( α ) sin ( α ) cos ( α ) ) .
Δ n = Δ n x z sin ( θ 1 ) sin ( θ 2 ) ,
β = arctan ( Δ n x y Δ n x z ) .
X 2 + ( 1 + Q ) Z 2 2 R Z = 0.
eye = antDiattn 2 × linRtd 2 × postDiattn 2 × optRot × postDiattn 1 × linRtd 1 × antDiattn 1 .
linRtd ( Δ n L , λ , θ ) = ( cos ( π λ Δ n L ) i cos ( 2 θ ) sin ( π λ Δ n L ) i sin ( 2 θ ) sin ( π λ Δ n L ) i sin ( 2 θ ) sin ( π λ Δ n L ) cos ( π λ Δ n L ) + i cos ( 2 θ ) sin ( π λ Δ n L ) ) .
diattn ( D , T ave , θ ) = T ave ( ( 1 + D ) cos 2 ( θ ) + ( 1 D ) sin 2 ( θ ) ( 1 + D ) cos ( θ ) sin ( θ ) ( 1 D ) cos ( θ ) sin ( θ ) ( 1 + D ) cos ( θ ) sin ( θ ) ( 1 D ) cos ( θ ) sin ( θ ) ( 1 D ) cos 2 ( θ ) + ( 1 + D ) sin 2 ( θ ) ) .
crPol = analyzer × modRtd ( α mod ) × eye × polarizer,
polarizer = ( 1 0 0 0 ) ,
analyzer = ( 0 0 0 1 ) .
path   1 = bsRef × modRtd ( α mod ) × mirror × eye 1 × mirror × bsRef, path   2 = bsTrans × mirror × eye 2 × mirror × modRtd ( α mod ) × bsTrans, sagnac = path   1 + path   2 ,
mirror = ( 1 0 0 1 ) ,
eye 1 = antDiattn 2 ( θ ) × LinRtd 2 ( θ ) × postDiattn 2 ( θ ) × optRot × postDiattn 1 ( θ ) × LinRtd 1 ( θ ) × antDiattn 1 ( θ ) ,
eye 2 = antDiattn 1 ( θ ) × LinRtd 1 ( θ ) × postDiattn 1 ( θ ) × optRot × postDiattn 2 ( θ ) × LinRtd 2 ( θ ) × antDiattn 2 ( θ ) .
input = ( 1 0 ) .
linRtd ( δ ) = ( e i δ / 2 0 0 e i δ / 2 ) ,
linRtd ( δ 2 ) optRot ( α ) linRtd ( δ 1 ) = ( e i 1 2 ( δ 1 + δ 2 ) cos ( α ) e i 1 2 ( δ 1 δ 2 ) sin ( α ) e i 1 2 ( δ 1 δ 2 ) sin ( α ) e i 1 2 ( δ 1 + δ 2 ) cos ( α ) ) ,
tan ( α net ) = m 12 m 21 m 11 m 22 .
tan ( α net ) = tan ( α ) × cos ( δ 1 δ 2 2 ) cos ( δ 1 + δ 2 2 ) .
δ = 2 π λ Δ n L ,
tan ( α net ( λ ) ) = tan ( 6.3333 × 10 7 × λ 2.1945 × l × c ) × cos ( π λ ( Δ n 1 L 1 Δ n 2 L 2 ) ) cos ( π λ ( Δ n 1 L 1 + Δ n 2 L 2 ) ) .
tan ( α net ( λ ) ) 6.3333 × 10 7 × λ 2.1945 × l × c × π 180 cos ( π λ ( Δ n 1 L 1 + Δ n 2 L 2 ) ) .
6.3333 × 10 7 × λ 2.1945 × π 180 tan ( α net ( λ ) ) 1 l × c × cos ( π λ ( Δ n 1 L 1 + Δ n 2 L 2 ) ) .

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