Abstract

By using the cross-section theorem an approximation formula is derived for the scattering of light in the forward direction. It is valid for spherical aerosols if the radius of the particles is larger than the wavelength of the incident light.

© 1962 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957).
  2. R. Penndorf and B. Goldberg, Tables of Light Scattering Functions (unpublished manuscript, 1953).
  3. Here and in the following equations, the prime indicates that the parameters are based on the validity of Eq. (8).
  4. R. Penndorf, J. Opt. Soc. Am. 47, 1010 (1957).
    [CrossRef]
  5. M. Kerker, J. Opt. Soc. Am. 45, 1081 (1955).
    [CrossRef]
  6. R. Penndorf, J. Phys. Chem. 62, 1537 (1958).
    [CrossRef]
  7. M. Kerker and E. Matijevic, J. Opt. Soc. Am. 51, 87 (1961).
    [CrossRef]

1961 (1)

1958 (1)

R. Penndorf, J. Phys. Chem. 62, 1537 (1958).
[CrossRef]

1957 (1)

1955 (1)

Goldberg, B.

R. Penndorf and B. Goldberg, Tables of Light Scattering Functions (unpublished manuscript, 1953).

Kerker, M.

Matijevic, E.

Penndorf, R.

R. Penndorf, J. Phys. Chem. 62, 1537 (1958).
[CrossRef]

R. Penndorf, J. Opt. Soc. Am. 47, 1010 (1957).
[CrossRef]

R. Penndorf and B. Goldberg, Tables of Light Scattering Functions (unpublished manuscript, 1953).

van de Hulst, H. C.

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

J. Opt. Soc. Am. (3)

J. Phys. Chem. (1)

R. Penndorf, J. Phys. Chem. 62, 1537 (1958).
[CrossRef]

Other (3)

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

R. Penndorf and B. Goldberg, Tables of Light Scattering Functions (unpublished manuscript, 1953).

Here and in the following equations, the prime indicates that the parameters are based on the validity of Eq. (8).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Phase function p M and approximated phase function p M for n = 1.33. The curve for p M is based on computations using the exact Mie theory [Eq. (3)]. The curve for p M has been computed using Eq. (5). The curves agree very well.

Fig. 2
Fig. 2

Angular scattering coefficient iθ, Rayleigh approximation iθR, and phase functions p M and p M for n = 2.0. The curve for p M (solid line) is based on computations using the exact Mie theory [Eq. (3)]. The curve for p M has been computed using Eq. (5) and K ¯, where K is based on approximations.

Tables (2)

Tables Icon

Table I Examples of the amplitudes (ReS,) ImS and i1 and i1 for n = 1.33.

Tables Icon

Table II Error of the approximate phase function p M in percent for n = 1.33 computed from ( p M p M ) / p M.

Equations (16)

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

i 1 = | S 1 | 2 = | 1 ( 2 m + 1 ) ( a m π m + b m τ m ) | 2 , i 2 = | S 2 | 2 = | 1 ( 2 m + 1 ) ( a m τ m + b m π m ) | 2 ,
S 1 = 1 ( 2 m + 1 ) [ π m Re ( a m ) + τ m Re ( b m ) + i π m Im ( a m ) + i τ m Im ( b m ) ] .
i θ = ( i 1 + i 2 ) / 2 π α 2 ,
p M = 2 ( i 1 + i 2 ) / α 2 K .
σ = π r 2 K ( e ) = ( 4 π / k 2 ) Re S { 0 } = ( λ 2 / π ) Re S { 0 } .
p M { α } = 1 4 α 2 K ,
S { 0 } = Re S { 0 } + i Im S { 0 } .
π m = τ m = 1 2 .
| Re S { 0 } | | Im S { 0 } | .
S 1 = Re S { 0 } .
i 1 = i 2 = | Re S 1 { 0 } | 2 = | Re S 2 { 0 } | 2 .
1 4 α 2 K = Re S { 0 } .
i 1 = i 2 = ( 1 4 α 2 K ) 2 .
i θ = α 2 K 2 / 16 π ,
p M = 1 4 α 2 K .
lim α p M = 1 2 α 2