Abstract

Approximation formulas are derived for small spherical aerosols (<i>r</i><λ) by using the series expansion of the exact solution (Mie theory). The first three terms of the series are given for real, complex, and infinite indices of refraction. The new formulas allow for computing the scattering and absorption coefficients for small aerosols more simply and faster than the Mie formulas. The error of our approximation formulas is determined, and it is found that the useful size range is extended by about a factor 2.

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  1. H. C. van de Hulst, Light Scattering by Small Particles (J. Wiley & Sons, Inc., New York, 1957), p. 143.
  2. If K(3)K(e), the notation K only will be used because it is unequivocal.
  3. R. Penndorf, "Scattering coefficients for absorbing and nonabsorbing spheres," AFCRL-TN60-667 Technical Report RAD-TR-60-27, Avco Co., Wilmington, Massachusetts, October 1960, 92 p.
  4. G. Mie, Ann. Physik 4, 25, 377 (1908)
  5. The subscript R indicates Rayleigh approximation. Higher approximations are indicated by the use of RR and RRR as subscripts.
  6. H. Blumer, Z. Physik 32, 119 (1925); 38, 304 (1926).
  7. J. C. Johnson and J. R. Terrell, J. Opt. Soc. Am. 45, 451 (1955).
  8. F. C. Chromey, J. Opt. Soc. Am. 50, 730 (1960).
  9. Chromey lists in his table the equivalent value of K(s) and not K(e)-K(s) as he has stated in the text and in the heading of his Table I.

Blumer, H.

H. Blumer, Z. Physik 32, 119 (1925); 38, 304 (1926).

Chromey, F. C.

F. C. Chromey, J. Opt. Soc. Am. 50, 730 (1960).

Johnson, J. C.

J. C. Johnson and J. R. Terrell, J. Opt. Soc. Am. 45, 451 (1955).

Mie, G.

G. Mie, Ann. Physik 4, 25, 377 (1908)

Penndorf, R.

R. Penndorf, "Scattering coefficients for absorbing and nonabsorbing spheres," AFCRL-TN60-667 Technical Report RAD-TR-60-27, Avco Co., Wilmington, Massachusetts, October 1960, 92 p.

Terrell, J. R.

J. C. Johnson and J. R. Terrell, J. Opt. Soc. Am. 45, 451 (1955).

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (J. Wiley & Sons, Inc., New York, 1957), p. 143.

Other

H. C. van de Hulst, Light Scattering by Small Particles (J. Wiley & Sons, Inc., New York, 1957), p. 143.

If K(3)K(e), the notation K only will be used because it is unequivocal.

R. Penndorf, "Scattering coefficients for absorbing and nonabsorbing spheres," AFCRL-TN60-667 Technical Report RAD-TR-60-27, Avco Co., Wilmington, Massachusetts, October 1960, 92 p.

G. Mie, Ann. Physik 4, 25, 377 (1908)

The subscript R indicates Rayleigh approximation. Higher approximations are indicated by the use of RR and RRR as subscripts.

H. Blumer, Z. Physik 32, 119 (1925); 38, 304 (1926).

J. C. Johnson and J. R. Terrell, J. Opt. Soc. Am. 45, 451 (1955).

F. C. Chromey, J. Opt. Soc. Am. 50, 730 (1960).

Chromey lists in his table the equivalent value of K(s) and not K(e)-K(s) as he has stated in the text and in the heading of his Table I.

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