Abstract

The normal-incidence spectral reflectance of ice at −7° C has been measured in the range 300–5000 cm−1. A Kramers–Kronig phase-shift analysis of the measured spectral reflectance has been employed to provide values of the real and imaginary parts of the refractive index. The resulting values of these optical constants are suitable for use in Mie-theory computations of scattering by ice particles in planetary atmospheres. The optical constants of ice at −7° C are compared in detail with those of liquid water at several temperatures and with those recently determined for ice at −170° C.

© 1973 Optical Society of America

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References

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  1. W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968).
    [Crossref]
  2. W. Luck, Ber. Bunsenges. Phys. Chem. 67, 186 (1963).
  3. N. Ockmann, Adv. Phys. 7, 199 (1958); Doctoral dissertation, University of Michigan (1957).
    [Crossref]
  4. F. P. Reding, Thesis, Brown University (1951).
  5. J. J. Fox and A. E. Martin, Proc. R. Soc. A 174, 234 (1940).
    [Crossref]
  6. R. Zimmerman and G. C. Pimentel, Proc. Intern. Meeting Mol. Spectry, Bologna 2, 726 (1962).
  7. C. H. Cartwright and J. Errera, Proc. R. Soc. A 154, 138 (1936).
    [Crossref]
  8. J. E. Bertie and E. Whalley, J. Chem. Phys. 40, 1637 (1964).
    [Crossref]
  9. J. E. Bertie and E. Whalley, J. Chem. Phys. 46, 1271 (1967).
    [Crossref]
  10. M. Weingeroff, Z. Phys. 70, 104 (1931).
    [Crossref]
  11. G. Bode, Ann. Phys. (Leipz.) 30, 326 (1909).
    [Crossref]
  12. L. D. Kislovski, Opt. Spektrosk. 7, 201 (1959) [Opt. Spectrosc. 7, 311 (1959).
  13. A. J. Alkezweeny and P. V. Hobbs, J. Geophys. Res. 71, 1083 (1966).
    [Crossref]
  14. J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
    [Crossref]
  15. A. N. Rusk, D. Williams, and M. R. Querry, J. Opt. Soc. Am. 61, 895 (1971).
    [Crossref]
  16. J. Strong, Procedures in Experimental Physics (Prentice-Hall, New York, 1938), p. 376.
  17. More-detailed tabulation of results along with a more detailed analysis of uncertainties are presented in the doctoral dissertation of J. W. Schaaf, Kansas State University (1973).
  18. G. M. Hale, M. R. Querry, A. N. Rusk, and D. Williams, J. Opt. Soc. Am. 62, 1103 (1972).
    [Crossref]

1972 (1)

1971 (1)

1969 (1)

J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
[Crossref]

1968 (1)

W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

1967 (1)

J. E. Bertie and E. Whalley, J. Chem. Phys. 46, 1271 (1967).
[Crossref]

1966 (1)

A. J. Alkezweeny and P. V. Hobbs, J. Geophys. Res. 71, 1083 (1966).
[Crossref]

1964 (1)

J. E. Bertie and E. Whalley, J. Chem. Phys. 40, 1637 (1964).
[Crossref]

1963 (1)

W. Luck, Ber. Bunsenges. Phys. Chem. 67, 186 (1963).

1962 (1)

R. Zimmerman and G. C. Pimentel, Proc. Intern. Meeting Mol. Spectry, Bologna 2, 726 (1962).

1959 (1)

L. D. Kislovski, Opt. Spektrosk. 7, 201 (1959) [Opt. Spectrosc. 7, 311 (1959).

1958 (1)

N. Ockmann, Adv. Phys. 7, 199 (1958); Doctoral dissertation, University of Michigan (1957).
[Crossref]

1940 (1)

J. J. Fox and A. E. Martin, Proc. R. Soc. A 174, 234 (1940).
[Crossref]

1936 (1)

C. H. Cartwright and J. Errera, Proc. R. Soc. A 154, 138 (1936).
[Crossref]

1931 (1)

M. Weingeroff, Z. Phys. 70, 104 (1931).
[Crossref]

1909 (1)

G. Bode, Ann. Phys. (Leipz.) 30, 326 (1909).
[Crossref]

Alkezweeny, A. J.

A. J. Alkezweeny and P. V. Hobbs, J. Geophys. Res. 71, 1083 (1966).
[Crossref]

Bertie, J. E.

J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
[Crossref]

J. E. Bertie and E. Whalley, J. Chem. Phys. 46, 1271 (1967).
[Crossref]

J. E. Bertie and E. Whalley, J. Chem. Phys. 40, 1637 (1964).
[Crossref]

Bode, G.

G. Bode, Ann. Phys. (Leipz.) 30, 326 (1909).
[Crossref]

Cartwright, C. H.

C. H. Cartwright and J. Errera, Proc. R. Soc. A 154, 138 (1936).
[Crossref]

Errera, J.

C. H. Cartwright and J. Errera, Proc. R. Soc. A 154, 138 (1936).
[Crossref]

Fox, J. J.

J. J. Fox and A. E. Martin, Proc. R. Soc. A 174, 234 (1940).
[Crossref]

Hale, G. M.

Hobbs, P. V.

A. J. Alkezweeny and P. V. Hobbs, J. Geophys. Res. 71, 1083 (1966).
[Crossref]

Irvine, W. M.

W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

Kislovski, L. D.

L. D. Kislovski, Opt. Spektrosk. 7, 201 (1959) [Opt. Spectrosc. 7, 311 (1959).

Labbé, H. J.

J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
[Crossref]

Luck, W.

W. Luck, Ber. Bunsenges. Phys. Chem. 67, 186 (1963).

Martin, A. E.

J. J. Fox and A. E. Martin, Proc. R. Soc. A 174, 234 (1940).
[Crossref]

Ockmann, N.

N. Ockmann, Adv. Phys. 7, 199 (1958); Doctoral dissertation, University of Michigan (1957).
[Crossref]

Pimentel, G. C.

R. Zimmerman and G. C. Pimentel, Proc. Intern. Meeting Mol. Spectry, Bologna 2, 726 (1962).

Pollack, J. B.

W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

Querry, M. R.

Reding, F. P.

F. P. Reding, Thesis, Brown University (1951).

Rusk, A. N.

Schaaf, J. W.

More-detailed tabulation of results along with a more detailed analysis of uncertainties are presented in the doctoral dissertation of J. W. Schaaf, Kansas State University (1973).

Strong, J.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, New York, 1938), p. 376.

Weingeroff, M.

M. Weingeroff, Z. Phys. 70, 104 (1931).
[Crossref]

Whalley, E.

J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
[Crossref]

J. E. Bertie and E. Whalley, J. Chem. Phys. 46, 1271 (1967).
[Crossref]

J. E. Bertie and E. Whalley, J. Chem. Phys. 40, 1637 (1964).
[Crossref]

Williams, D.

Zimmerman, R.

R. Zimmerman and G. C. Pimentel, Proc. Intern. Meeting Mol. Spectry, Bologna 2, 726 (1962).

Adv. Phys. (1)

N. Ockmann, Adv. Phys. 7, 199 (1958); Doctoral dissertation, University of Michigan (1957).
[Crossref]

Ann. Phys. (Leipz.) (1)

G. Bode, Ann. Phys. (Leipz.) 30, 326 (1909).
[Crossref]

Ber. Bunsenges. Phys. Chem. (1)

W. Luck, Ber. Bunsenges. Phys. Chem. 67, 186 (1963).

Icarus (1)

W. M. Irvine and J. B. Pollack, Icarus 8, 324 (1968).
[Crossref]

J. Chem. Phys. (3)

J. E. Bertie and E. Whalley, J. Chem. Phys. 40, 1637 (1964).
[Crossref]

J. E. Bertie and E. Whalley, J. Chem. Phys. 46, 1271 (1967).
[Crossref]

J. E. Bertie, H. J. Labbé, and E. Whalley, J. Chem. Phys. 50, 4501 (1969).
[Crossref]

J. Geophys. Res. (1)

A. J. Alkezweeny and P. V. Hobbs, J. Geophys. Res. 71, 1083 (1966).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Spektrosk. (1)

L. D. Kislovski, Opt. Spektrosk. 7, 201 (1959) [Opt. Spectrosc. 7, 311 (1959).

Proc. Intern. Meeting Mol. Spectry, Bologna (1)

R. Zimmerman and G. C. Pimentel, Proc. Intern. Meeting Mol. Spectry, Bologna 2, 726 (1962).

Proc. R. Soc. A (2)

C. H. Cartwright and J. Errera, Proc. R. Soc. A 154, 138 (1936).
[Crossref]

J. J. Fox and A. E. Martin, Proc. R. Soc. A 174, 234 (1940).
[Crossref]

Z. Phys. (1)

M. Weingeroff, Z. Phys. 70, 104 (1931).
[Crossref]

Other (3)

F. P. Reding, Thesis, Brown University (1951).

J. Strong, Procedures in Experimental Physics (Prentice-Hall, New York, 1938), p. 376.

More-detailed tabulation of results along with a more detailed analysis of uncertainties are presented in the doctoral dissertation of J. W. Schaaf, Kansas State University (1973).

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of sample holder.

Fig. 2
Fig. 2

Normal-incidence spectral reflectance of ice at −7°C

Fig. 3
Fig. 3

Real part nr of the refractive index of ice as a function of frequency, in wave numbers.

Fig. 4
Fig. 4

Imaginary part ni of the refractive index of ice as a function of frequency, in wave numbers.

Fig. 5
Fig. 5

Comparison of present results for nr, given by the continuous curve, with values of nr listed in the Irvine–Pollack survey given by points.

Fig. 6
Fig. 6

Comparison of present results for ni, given by the continuous curve, with values of ni listed in the Irvine–Pollack survey given by points.

Tables (2)

Tables Icon

Table I Reflectivity and optical constants of ice at −7°C.

Tables Icon

Table II Band characteristics at various temperatures.

Equations (3)

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

n r = [ 1 R ] / [ 1 + R 2 R cos ϕ ] ,
n i = [ 2 R sin ϕ ] / [ 1 + R 2 R cos ϕ ] ,
ϕ ( ν 0 ) = ( 2 ν 0 / π ) P 0 ln R ( ν ) d ν ν 0 2 ν 2 ,