Calculation of Mie derivatives.

Area of Science:

• * Atmospheric Optics and Particle Characterization
• * Computational Electromagnetics and Light Scattering

Background:

• * Mie scattering theory is fundamental for understanding light interaction with particles.
• * Calculating derivatives of Mie scattering parameters is crucial for model inversion and sensitivity analysis.
• * Numerical methods for derivative calculation can be computationally intensive.

Purpose of the Study:

• * To derive analytical expressions for the derivatives of key Mie scattering parameters.
• * To extend these analytical derivatives to particle populations with log-normal size distributions.
• * To assess the computational speed advantage of analytical versus numerical derivative calculations.

Main Methods:

• * Derivation of analytical expressions for Mie scattering amplitudes a(n) and b(n) derivatives.
• * Application of these derivatives to absorption efficiency, scattering efficiency, and angular intensity functions.
• * Formulation of analytical derivatives for volume coefficients and intensity functions for log-normal distributions.

Main Results:

• * Established analytical expressions for Mie scattering parameter derivatives with respect to size and refractive index.
• * Derived analytical derivatives for particle populations, considering number density, size distribution parameters, and refractive index.
• * Demonstrated that analytical methods are 2.5 to 6.5 times faster than numerical computations.

Conclusions:

• * Analytical derivatives offer a significant computational speed-up for Mie scattering calculations.
• * The derived expressions provide a more efficient tool for particle optics research and applications.
• * This work facilitates faster and more accurate analysis of light-particle interactions.