Inversion of light-scattering measurements for particle size and optical constants: theoretical study

Area of Science:

• Optical physics
• Scattering theory
• Particle characterization

Background:

• Accurate determination of particle size distribution and refractive index is crucial for understanding light scattering phenomena.
• Existing methods for inverting scattering data can be limited in accuracy and scope.

Purpose of the Study:

• To develop and validate a novel inversion technique for retrieving particle size distribution functions and refractive indices from Fredholm integral equations of light scattering.
• To enhance the accuracy and robustness of particle characterization using optical scattering data.

Main Methods:

• Inversion of the Fredholm equation governing light scattering from spherical particles.
• Expansion of the particle size distribution function using a combination of Schmidt-Hilbert eigenfunctions and orthogonalized supplemental basis functions.
• Minimization of residual errors using orthogonality properties and a trial function constraint.

Main Results:

• Successful retrieval of particle size distribution functions and refractive indices from simulated scattering data.
• Demonstration of the method's effectiveness in handling both single particles and distributions.
• Validation of the mathematical framework through the analysis of simulated datasets.

Conclusions:

• The proposed inversion method provides a robust and accurate approach for determining particle properties from scattered light.
• The use of orthonormal basis functions and specific orthogonalization procedures is key to the method's success.
• This technique offers a valuable tool for advanced particle characterization in various scientific and industrial applications.