Abstract

Extinction, scattering, and absorption efficiency factors for a concentric sphere of a nonlight absorbing nucleus (m = 1.5) and an absorbing shell (m = 1.95 − 0.66i) were calculated based on the theory of Aden and Kerker. For small size parameters (ν < 1), the magnitude of the extinction efficiency factor is markedly affected by the shell thickness. An approximating equation, based on the Rayleigh light scattering equation, is presented which relates the increase of the extinction efficiency factor of an absorbing sphere over the extinction efficiency factor of a nonabsorbing sphere to the pertinent variables (refractive index and size parameter).

© 1967 Optical Society of America

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References

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  1. A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
    [CrossRef]
  2. G. Mie, Ann. Physik 30, 377 (1908).
    [CrossRef]
  3. W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
    [CrossRef] [PubMed]
  4. W. Kerker, J. P. Kratohvil, E. Matijevič, J. Opt. Soc. Am. 52, 551 (1962).
    [CrossRef]
  5. R. W. Fenn, H. Oser, Appl. Opt. 4, 1504 (1965).
    [CrossRef]
  6. B. M. Herman, L. J. Battan, J. Meteorol. 18, 468 (1961).
    [CrossRef]
  7. J. R. Hodkinson, J. Opt. Soc. Am. 54, 846 (1964).
    [CrossRef]
  8. H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

1965 (2)

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

R. W. Fenn, H. Oser, Appl. Opt. 4, 1504 (1965).
[CrossRef]

1964 (1)

1962 (1)

1961 (1)

B. M. Herman, L. J. Battan, J. Meteorol. 18, 468 (1961).
[CrossRef]

1951 (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

1908 (1)

G. Mie, Ann. Physik 30, 377 (1908).
[CrossRef]

Aden, A. L.

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Battan, L. J.

B. M. Herman, L. J. Battan, J. Meteorol. 18, 468 (1961).
[CrossRef]

Espenscheid, W. F.

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

Fenn, R. W.

Herman, B. M.

B. M. Herman, L. J. Battan, J. Meteorol. 18, 468 (1961).
[CrossRef]

Hodkinson, J. R.

Kerker, M.

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

Kerker, W.

Kratohvil, J. P.

Matijevic, E.

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

W. Kerker, J. P. Kratohvil, E. Matijevič, J. Opt. Soc. Am. 52, 551 (1962).
[CrossRef]

Mie, G.

G. Mie, Ann. Physik 30, 377 (1908).
[CrossRef]

Oser, H.

Van de Hulst, H. C.

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

Willis, E.

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

Ann. Physik (1)

G. Mie, Ann. Physik 30, 377 (1908).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

A. L. Aden, M. Kerker, J. Appl. Phys. 22, 1242 (1951).
[CrossRef]

J. Colloid Sci. (1)

W. F. Espenscheid, E. Willis, E. Matijevič, M. Kerker, J. Colloid Sci. 20, 501 (1965).
[CrossRef] [PubMed]

J. Meteorol. (1)

B. M. Herman, L. J. Battan, J. Meteorol. 18, 468 (1961).
[CrossRef]

J. Opt. Soc. Am. (2)

Other (1)

H. C. Van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).

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Figures (5)

Fig. 1
Fig. 1

Concentric sphere parameters.

Fig. 2
Fig. 2

Extinction, scattering, and absorption efficiency factors as a function of shell size parameter at nucleus shell size ratios of (a) 1.0, (b) 0.99, (c) 0.5, and (d) 0.0.

Fig. 3
Fig. 3

Graph showing effect of absorbing shell thickness of concentric sphere on the extinction efficiency factor.

Fig. 4
Fig. 4

Graph showing effect of absorbing shell thickness of concentric sphere on the scattering efficiency factor.

Fig. 5
Fig. 5

Comparison of absorbing sphere and nonabsorbing sphere efficiency factors.

Tables (1)

Tables Icon

Table I Concentric Sphere Classifications by Refractive Index

Equations (7)

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Q E = ( 2 / ν 2 ) t = 1 ( 2 t + 1 ) Re ( a t + b t ) , Q S = ( 2 / ν 2 ) t = 1 ( 2 t + 1 ) ( a t 2 + b t 2 ) , Q A = Q E - Q S .
a t = H 1 η t ( 1 ) ( ν ) + H 2 Z t ( 1 ) ( ν ) H 1 η t ( 3 ) ( ν ) + H 2 Z t ( 3 ) ( ν ) , b t = H 3 Z t ( 1 ) ( ν ) + H 4 η t ( 1 ) ( ν ) H 3 Z t ( 3 ) ( ν ) + H 4 η t ( 3 ) ( ν ) ,
H 1 = m 2 2 G 1 + m 1 m 2 G 2 , H 2 = m 2 G 3 + m 1 G 4 , H 3 = m 2 2 G 4 + m 1 m 2 G 3 , H 4 = m 2 G 2 + m 1 G 1 ,
G 1 = η t ( 1 ) ( m 1 α ) [ Z t ( 3 ) ( m 2 α ) Z t ( 1 ) ( m 2 ν ) - Z t ( 1 ) ( m 2 α ) Z t ( 3 ) ( m 2 ν ) ] , G 2 = Z t ( 1 ) ( m 1 α ) [ η t ( 1 ) ( m 2 α ) Z t ( 3 ) ( m 2 ν ) - η t ( 3 ) ( m 2 α ) Z t ( 1 ) ( m 2 ν ) ] , G 3 = η t ( 1 ) ( m 1 α ) [ Z t ( 1 ) ( m 2 α ) η t ( 3 ) ( m 2 ν ) - Z t ( 3 ) ( m 2 α ) η t ( 1 ) ( m 2 ν ) ] , G 4 = Z t ( 1 ) ( m 1 α ) [ η t ( 1 ) ( m 2 ν ) η t ( 3 ) ( m 2 α ) - η t ( 1 ) ( m 2 α ) η t ( 3 ) ( m 2 ν ) ] .
Q E = α 4 Re [ 8 3 ( m 2 - 1 m 2 + 2 ) 2 ] - 4 α Im [ m 2 - 1 m 2 + 2 ] , Q S = α 4 8 3 | m 2 - 1 m 2 + 2 | 2 .
Q E Q E ( k = 0 ) = α 4 Re { 8 / 3 [ ( m 2 - 1 ) / ( m 2 + 2 ) ] 2 - 4 α Im [ ( m 2 - 1 ) / ( m 2 + 2 ) ] α 4 Re { 8 / 3 [ ( m 2 - 1 ) / ( m 2 + 2 ) ] 2 } .
[ Q E / Q E ( k = 0 ) ] = 1 + [ 9 j k F / α 3 Re ( X 2 ) ] ,

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