Abstract

We first specialize multiple-scattering theory for uncorrelated distributions of large, low-refracting, absorbing particles to similarly and randomly aligned spheroids. The theory takes into account back-scattering interface effects, but neglects the smaller coherent reflection effects. Then we illustrate how the results can be used in optical diagnostics on suspensions of cells for biomedical purposes. We consider the isolation of molecular absorption coefficients for transmission and reflection oximetry on whole blood, scattering-shifted absorption extrema, cell-membrane fragilometry and the effects of osmotic swelling, and some asymmetrical scattering effects for optical monitoring of cell alignment in fluid-transport processes. In measurements on thin samples at wavelengths corresponding to relatively small absorption, pronounced minima in transmission and maxima in reflection have been observed for suspensions about half-full of cells; we discuss simple approximations that indicate the essentials of the phenomena.

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  1. V. Twersky, J. Math. Phys. 3, 724 (1962); J. Opt. Soc. Am. 52, 145 (1962).
  2. V. Twersky, Am. Math. Soc. Appl. Math. 16, 84 (1964); in Electromagnetic Scattering, edited by R. L. Rowell and R. S. Stein (Gordon and Breach, New York, 1968), p. 579; in Turbulence of Fluids and Plasmas, edited by J. Fox (Polytechnic Press, Brooklyn, N. Y., 1969), p. 143.
  3. C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965); IEEE Trans. AP–15, 99 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP–15, 118 (1967); J. E. Burke, T. H. Kays, J. L. Kulp, and V. Twersky, Appl. Opt. 7, 2392 (1968).
  4. V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).
  5. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), particularly pp. 175, 93.
  6. A. Guinier, X-Ray Diffraction (Freeman, San Francisco, 1963).
  7. Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).
  8. K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).
  9. E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).
  10. G. A. Millikan, Rev. Sci. Instr. 13, 434 (1942); W. G. Ziljstra, A Manual of Reflection Oximetry (Van Gorcum, Assen, Netherlands, 1958). M. L. Polanyi and R. M. Hehir, Rev. Sci. Instr. 33, 1050 (1962). N. S. Kapany and N. Silbertrust, Nature 204, 138 (1964); D. C. Harrison, N. S. Kapany, H. A. Miller, N. Silbertrust, W. L. Henry, and R. P. Drake, Am. Heart J. 71, 766 (1966).
  11. N. M. Anderson and P. S. Sekelj, Phys. Med. Biol. 12, 173 and 185 (1967).
  12. Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).
  13. K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).
  14. R. Barer, J. Opt. Soc. Am. 47, 545 (1957); Science 121, 709 (1955); G. F. Lothian and P. C. Lewis, Nature 178, 1342 (1956); P. Latimer, Archiv. Biochem. and Biophys. 119, 580 (1967); P. Latimer and C. A. Holmes Eubanks, Archiv. Biochem. and Biophys. 98, 274 (1962); R. A. MacRae, J. A. McClure, and P. Latimer, J. Opt. Soc. Am. 51, 1366 (1961); plus papers cited in these.
  15. E. Ponder, Hemolysis and Related Phenomena (Greene and Stratton, New York, 1948).
  16. D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).
  17. M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).
  18. W. E. Love, J. Cellular Comp. Physiol. 44, 291 (1954).
  19. For the sphere, the value [equation] obtained from Eqs. (39) or (42) indicates the correct order of the next term (which we neglect), but the numerical factor is wrong because we used 1—sin2θ cos2,φ≍1 in Eq. (37); see Rayleigh's more complete result Ref. 7 for arbitrary Ka. Similarly, our estimate of σ′ of Eq. (46) is 1.61 times too large; see Ref. 5, p. 90. Since the function σ′ enters the multiple-scattering forms as an over-large simplification of the required function, we use such estimates merely to indicate which isolated scatterer parameters are involved.

Anderson, N. M.

N. M. Anderson and P. S. Sekelj, Phys. Med. Biol. 12, 173 and 185 (1967).

Barer, R.

R. Barer, J. Opt. Soc. Am. 47, 545 (1957); Science 121, 709 (1955); G. F. Lothian and P. C. Lewis, Nature 178, 1342 (1956); P. Latimer, Archiv. Biochem. and Biophys. 119, 580 (1967); P. Latimer and C. A. Holmes Eubanks, Archiv. Biochem. and Biophys. 98, 274 (1962); R. A. MacRae, J. A. McClure, and P. Latimer, J. Opt. Soc. Am. 51, 1366 (1961); plus papers cited in these.

Beard, C. I.

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965); IEEE Trans. AP–15, 99 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP–15, 118 (1967); J. E. Burke, T. H. Kays, J. L. Kulp, and V. Twersky, Appl. Opt. 7, 2392 (1968).

Briscoe, W. A.

Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).

Brown, W. J.

M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).

Cournand, A.

Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).

Danon, D.

D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).

Elam, J. O.

K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).

Elam, W. N.

K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).

Enson, Y.

Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).

Frei, E. H.

D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).

Frei, Y. F.

D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).

Gordon, A.

E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).

Graf, K.

K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).

Gross, J.

E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).

Guinier, A.

A. Guinier, X-Ray Diffraction (Freeman, San Francisco, 1963).

Jacobs, M. H.

M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).

Kays, T. H.

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965); IEEE Trans. AP–15, 99 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP–15, 118 (1967); J. E. Burke, T. H. Kays, J. L. Kulp, and V. Twersky, Appl. Opt. 7, 2392 (1968).

Kimmelman, L. J.

M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).

Kramer, K.

K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).

K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).

Lipkin, Y.

D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).

Loewinger, E.

E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).

Love, W. E.

W. E. Love, J. Cellular Comp. Physiol. 44, 291 (1954).

Millikan, G. A.

G. A. Millikan, Rev. Sci. Instr. 13, 434 (1942); W. G. Ziljstra, A Manual of Reflection Oximetry (Van Gorcum, Assen, Netherlands, 1958). M. L. Polanyi and R. M. Hehir, Rev. Sci. Instr. 33, 1050 (1962). N. S. Kapany and N. Silbertrust, Nature 204, 138 (1964); D. C. Harrison, N. S. Kapany, H. A. Miller, N. Silbertrust, W. L. Henry, and R. P. Drake, Am. Heart J. 71, 766 (1966).

Overbeck, W.

K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).

Polanyi, M. L.

Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).

Ponder, E.

E. Ponder, Hemolysis and Related Phenomena (Greene and Stratton, New York, 1948).

Rayleigh, Lord

Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).

Saxton, G. A.

K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).

Sekelj, P. S.

N. M. Anderson and P. S. Sekelj, Phys. Med. Biol. 12, 173 and 185 (1967).

Stewart, D. R.

M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).

Twersky, V.

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965); IEEE Trans. AP–15, 99 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP–15, 118 (1967); J. E. Burke, T. H. Kays, J. L. Kulp, and V. Twersky, Appl. Opt. 7, 2392 (1968).

V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).

V. Twersky, Am. Math. Soc. Appl. Math. 16, 84 (1964); in Electromagnetic Scattering, edited by R. L. Rowell and R. S. Stein (Gordon and Breach, New York, 1968), p. 579; in Turbulence of Fluids and Plasmas, edited by J. Fox (Polytechnic Press, Brooklyn, N. Y., 1969), p. 143.

V. Twersky, J. Math. Phys. 3, 724 (1962); J. Opt. Soc. Am. 52, 145 (1962).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), particularly pp. 175, 93.

Weinreb, A.

E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).

Zaun, H.

K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).

Other (19)

V. Twersky, J. Math. Phys. 3, 724 (1962); J. Opt. Soc. Am. 52, 145 (1962).

V. Twersky, Am. Math. Soc. Appl. Math. 16, 84 (1964); in Electromagnetic Scattering, edited by R. L. Rowell and R. S. Stein (Gordon and Breach, New York, 1968), p. 579; in Turbulence of Fluids and Plasmas, edited by J. Fox (Polytechnic Press, Brooklyn, N. Y., 1969), p. 143.

C. I. Beard, T. H. Kays, and V. Twersky, Appl. Opt. 4, 1299 (1965); IEEE Trans. AP–15, 99 (1967); S. W. Hawley, T. H. Kays, and V. Twersky, IEEE Trans. AP–15, 118 (1967); J. E. Burke, T. H. Kays, J. L. Kulp, and V. Twersky, Appl. Opt. 7, 2392 (1968).

V. Twersky, J. Opt. Soc. Am. 60, 908 (1970).

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957), particularly pp. 175, 93.

A. Guinier, X-Ray Diffraction (Freeman, San Francisco, 1963).

Lord Rayleigh, Proc. Roy. Soc. (London) A90, 219 (1914).

K. Kramer, J. O. Elam, G. A. Saxton, and W. N. Elam, Am. J. Physiol. 165, 229 (1951).

E. Loewinger, A. Gordon, A. Weinreb, and J. Gross, J. Appl. Physiol. 19, 1179 (1964).

G. A. Millikan, Rev. Sci. Instr. 13, 434 (1942); W. G. Ziljstra, A Manual of Reflection Oximetry (Van Gorcum, Assen, Netherlands, 1958). M. L. Polanyi and R. M. Hehir, Rev. Sci. Instr. 33, 1050 (1962). N. S. Kapany and N. Silbertrust, Nature 204, 138 (1964); D. C. Harrison, N. S. Kapany, H. A. Miller, N. Silbertrust, W. L. Henry, and R. P. Drake, Am. Heart J. 71, 766 (1966).

N. M. Anderson and P. S. Sekelj, Phys. Med. Biol. 12, 173 and 185 (1967).

Y. Enson, W. A. Briscoe, M. L. Polanyi, and A. Cournand, J. Appl. Physiol. 17, 552 (1962).

K. Kramer, K. Graf, W. Overbeck, and H. Zaun, Pflüg. Arch. Physiol. 262, 285 (1956).

R. Barer, J. Opt. Soc. Am. 47, 545 (1957); Science 121, 709 (1955); G. F. Lothian and P. C. Lewis, Nature 178, 1342 (1956); P. Latimer, Archiv. Biochem. and Biophys. 119, 580 (1967); P. Latimer and C. A. Holmes Eubanks, Archiv. Biochem. and Biophys. 98, 274 (1962); R. A. MacRae, J. A. McClure, and P. Latimer, J. Opt. Soc. Am. 51, 1366 (1961); plus papers cited in these.

E. Ponder, Hemolysis and Related Phenomena (Greene and Stratton, New York, 1948).

D. Danon, E. H. Frei, Y. F. Frei, and Y. Lipkin, IEEE Trans. BME–10, 24 (1963).

M. H. Jacobs, D. R. Stewart, W. J. Brown, and L. J. Kimmelman, Am. J. Med. Sci. 217, 47 (1949).

W. E. Love, J. Cellular Comp. Physiol. 44, 291 (1954).

For the sphere, the value [equation] obtained from Eqs. (39) or (42) indicates the correct order of the next term (which we neglect), but the numerical factor is wrong because we used 1—sin2θ cos2,φ≍1 in Eq. (37); see Rayleigh's more complete result Ref. 7 for arbitrary Ka. Similarly, our estimate of σ′ of Eq. (46) is 1.61 times too large; see Ref. 5, p. 90. Since the function σ′ enters the multiple-scattering forms as an over-large simplification of the required function, we use such estimates merely to indicate which isolated scatterer parameters are involved.

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