Mie forward scattering: improved semiempirical approximation with application to particle size distribution inversion

Area of Science:

• Atmospheric optics
• Light scattering theory
• Particle characterization

Background:

• Mie theory accurately describes light scattering by particles but is computationally intensive.
• Approximations like Penndorf and Shifrin-Punina simplify Mie theory for forward scattering.
• Accurate approximations are crucial for analyzing particle size distributions.

Purpose of the Study:

• To extend the accuracy of forward scattering approximations to smaller size parameters.
• To evaluate a new approximation (Eq. 7) against Mie solutions for various refractive indices.
• To discuss the implications for reconstructing particle size distributions.

Main Methods:

• Extending Penndorf and Shifrin-Punina approximations to smaller size parameters.
• Comparing the new approximation (Eq. 7) with Mie scattering solutions.
• Analyzing the accuracy for different size parameters (x) and refractive indices (m).

Main Results:

• The new approximation (Eq. 7) accurately represents Mie solutions down to size parameters of x ~ 0.5-1.0 for m = 1.33.
• Accuracy extends to x ~ 2.0 for larger refractive index values.
• The approximation's validity range is significantly improved for forward scattering.

Conclusions:

• The developed approximation enhances the applicability of Mie scattering theory for small particles.
• This advancement is vital for accurate particle size distribution reconstruction using forward scattering data.
• Improved analytical inversion methods can be developed based on these findings.