Abstract

The index of refraction n of the many mammalian tissues is an important but somewhat neglected optical constant. Archival and oral papers have quoted the use of values of n for tissue generally ranging from 1.35 to 1.55. However, these values are frequently without experimental basis. They have arbitrarily used values near that of water, which is a major component of mammalian tissue, or have calculated a theoretical n from the weighted elemental composition of tissue. Since these values have not been precise and little information is available on specific indices for each tissue, a study was undertaken to develop a simple, rapid, and reliable method for the experimental determination of n. This was done using the ubiquitous quartz optical fiber. By substituting the usual cladding found on commercial quartz optics by the tissue in question and utilizing the principle of internal reflection, the value of n for the specific tissue can be calculated. This is done by utilizing the known indices for air and quartz and measuring the angle of the emergent cone of light from the output of the optical fiber. A number of indices for mammalian tissue (bovine, porcine, canine, and human) have been determined at 632.8 nm. With few exceptions, for tissues at this wavelength, n was in the 1.38–1.41 range. The species type did not appear to be a factor. Bovine muscle showed normal dispersion characteristics through the visible wavelengths. The denaturation of tissue was shown to alter significantly the refractive index.

© 1989 Optical Society of America

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References

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  1. W. G. Driscoll, Ed., Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 10.
  2. M. S. Meyer, G. L. Eesley, “Optical Fiber Refractometer,” Rev. Sci. Instrum. 58, 2047–2048 (1987).
    [CrossRef]
  3. T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
    [CrossRef]
  4. T. Takeo, H. Hattori, “Optical Fiber Sensor for Measuring Refractive Index,” Jpn. J. Appl. Phys. 21, 1509–1512 (1982).
    [CrossRef]
  5. A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
    [CrossRef]
  6. W. Leupachur, A. Penzkofer, “Refractive-Index Measurement of Absorbing Condensed Media,” Appl. Opt. 23, 1554–1557 (1984).
    [CrossRef]
  7. Y. Lu, A. Penzkofer, “Optical Constants Measurements of Strongly Absorbing Media,” Appl. Opt. 25, 221–225 (1986).
    [CrossRef] [PubMed]
  8. W. Allan, Fibre Optics (Plenum, London, 1979), p. 8.
  9. R. Tiedeken, Fibre Optics and Its Applications (Focal Press, London, 1972), p. 21.
  10. Ref. 8, p. 196.
  11. Ref. 8, p. 197.
  12. W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 13–6.
  13. W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), pp. 13–21.
  14. Ref. 8, p. 28.
  15. F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 524.
  16. Ref. 8, p. 10.
  17. Ref. 8, p. 19.
  18. N. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), pp. 780–782.
  19. Ref. 15, p. 476.
  20. S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from A Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
    [CrossRef]
  21. S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).
  22. J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

1987

M. S. Meyer, G. L. Eesley, “Optical Fiber Refractometer,” Rev. Sci. Instrum. 58, 2047–2048 (1987).
[CrossRef]

S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).

1986

1985

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

1984

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

W. Leupachur, A. Penzkofer, “Refractive-Index Measurement of Absorbing Condensed Media,” Appl. Opt. 23, 1554–1557 (1984).
[CrossRef]

1982

T. Takeo, H. Hattori, “Optical Fiber Sensor for Measuring Refractive Index,” Jpn. J. Appl. Phys. 21, 1509–1512 (1982).
[CrossRef]

1979

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from A Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Allan, W.

W. Allan, Fibre Optics (Plenum, London, 1979), p. 8.

Alter, C.

S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).

Anderson, R.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Eesley, G. L.

M. S. Meyer, G. L. Eesley, “Optical Fiber Refractometer,” Rev. Sci. Instrum. 58, 2047–2048 (1987).
[CrossRef]

Goyal, I. C.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Graham, M. D.

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from A Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Hattori, H.

T. Takeo, H. Hattori, “Optical Fiber Sensor for Measuring Refractive Index,” Jpn. J. Appl. Phys. 21, 1509–1512 (1982).
[CrossRef]

Jacques, S.

S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).

Jenkins, F.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 524.

Kumar, A.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Lange, N.

N. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), pp. 780–782.

Leupachur, W.

Lu, Y.

Mendis, F. V. C.

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

Meyer, M. S.

M. S. Meyer, G. L. Eesley, “Optical Fiber Refractometer,” Rev. Sci. Instrum. 58, 2047–2048 (1987).
[CrossRef]

Pal, G. P.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Parrish, J.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Penzkofer, A.

Pitts, D.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Prahl, S.

S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).

Sharma, A. D.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Siegmund, W.

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 13–6.

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), pp. 13–21.

Subbrahmanyarm, T. V. B.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Takatani, S.

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from A Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Takeo, T.

T. Takeo, H. Hattori, “Optical Fiber Sensor for Measuring Refractive Index,” Jpn. J. Appl. Phys. 21, 1509–1512 (1982).
[CrossRef]

Teo, S. K.

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

Thung, T. T.

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

Thyagarajan, K.

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

Tiedeken, R.

R. Tiedeken, Fibre Optics and Its Applications (Focal Press, London, 1972), p. 21.

Urbach, F.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

Van Sel, B.

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

White, H.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 524.

Appl. Opt.

Electron. Lett.

T. T. Thung, S. K. Teo, F. V. C. Mendis, B. Van Sel, “Refractometry Through Optical Frequency Domain Reflectometry,” Electron. Lett. 21, 613–614 (1985).
[CrossRef]

A. Kumar, T. V. B. Subbrahmanyarm, A. D. Sharma, K. Thyagarajan, G. P. Pal, I. C. Goyal, “Novel Refractometer Using a Tapered Fiber Optic,” Electron. Lett. 20, 534–535 (1984).
[CrossRef]

IEEE Trans. Biomed. Eng.

S. Takatani, M. D. Graham, “Theoretical Analysis of Diffuse Reflectance from A Two-Layer Tissue Model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[CrossRef]

Jpn. J. Appl. Phys.

T. Takeo, H. Hattori, “Optical Fiber Sensor for Measuring Refractive Index,” Jpn. J. Appl. Phys. 21, 1509–1512 (1982).
[CrossRef]

Lasers Life Sci.

S. Jacques, C. Alter, S. Prahl, “Angular Dependence of HeNe Laser Light Scattering by Human Dermis,” Lasers Life Sci. 1, 309–333 (1987).

Rev. Sci. Instrum.

M. S. Meyer, G. L. Eesley, “Optical Fiber Refractometer,” Rev. Sci. Instrum. 58, 2047–2048 (1987).
[CrossRef]

Other

W. G. Driscoll, Ed., Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 10.

J. Parrish, R. Anderson, F. Urbach, D. Pitts, UVA (Plenum, New York, 1978), p. 63.

W. Allan, Fibre Optics (Plenum, London, 1979), p. 8.

R. Tiedeken, Fibre Optics and Its Applications (Focal Press, London, 1972), p. 21.

Ref. 8, p. 196.

Ref. 8, p. 197.

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), p. 13–6.

W. Siegmund, “Fiber Optics,” in Handbook of Optics, W. Driscoll, W. Vaughn, Eds. (McGraw-Hill, New York, 1978), pp. 13–21.

Ref. 8, p. 28.

F. Jenkins, H. White, Fundamentals of Optics (McGraw-Hill, New York, 1976), p. 524.

Ref. 8, p. 10.

Ref. 8, p. 19.

N. Lange, Handbook of Chemistry (McGraw-Hill, New York, 1967), pp. 780–782.

Ref. 15, p. 476.

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Figures (7)

Fig. 1
Fig. 1

Schematic of experimental setup for determining index of refraction. A bare quartz fiber is placed in a cladding of substance to be measured. The angular light output distribution is measured, and the index is determined from mathematical laws relating to refractive indices.

Fig. 2
Fig. 2

Example of the output distribution of light through a fiber optic using the setup from Fig. 1. Here human blood is used as the fiber cladding. It is evident that the distribution shows no sharp cutoff but instead assumes an approximately Gaussian form.

Fig. 3
Fig. 3

Light output distribution for a sample of kidney tissue. The value of θ at (peak intensity)/e2 used in expression (1) obtained for this kidney tissue gives an index value of 1.38 for this sample.

Fig. 4
Fig. 4

Output angle of light from the fiber optic depends on the index of refraction of the cladding as well as the core and surrounding medium. With a quartz core, the output angle in air is shown for several indices associated with biological materials such as water (n x = 1.330), muscle (n x = 1.400), and lipid (n x = 1.45). The range of angle shown provides the measurement system with good sensitivity.

Fig. 5
Fig. 5

Index of refraction values of seventeen samples of bovine striated muscle. Samples represent tissue from individual animals. The average, 1.412, is indicated by the horizontal line. The standard deviation was 0.006.

Fig. 6
Fig. 6

Index of refraction values obtained from four species and various tissues. The values represent averages of between three and seven trials. The human tissue values represent one to two trials.

Fig. 7
Fig. 7

Dispersion curves from two samples of bovine muscle tissue. The samples are denoted by the two symbol types. The downward trend in index is typical of many substances.

Tables (2)

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Table I Effects of Homogenization on the Determination of n

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Table II Effect of Coagulation on Index of Egg White

Equations (3)

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n s = SQR { n q 2 [ n 0 sin ( θ ) ] 2 } ,
N 2 a 2 π 2 ( n 1 2 n 2 2 ) / λ 2 ,
P 2 / P = 4 N 1 / 2 / 3 ,

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