Least-mean-squares algorithm to determine submicrometer particle diameter, volume fraction, and size distribution...

Area of Science:

• Particulate science
• Optical characterization
• Computational methods

Background:

• Diffraction-based methods struggle with submicrometer particles.
• Accurate determination of particulate properties (volume median diameter, volume fraction, size distribution width) is essential.
• Existing ratio-style calculations lack robust uncertainty quantification.

Purpose of the Study:

• To present a computationally fast method for determining particulate system parameters and their uncertainties.
• To address limitations of diffraction-based methods for submicrometer particles.
• To provide a more accurate and reliable alternative to current calculation methods.

Main Methods:

• Least-mean-squares fitting over a prespecified size range and distribution width.
• Application of the method to synthetic data with varying noise levels and distributions (monodisperse, log-normal).
• Evaluation of the algorithm's performance and accuracy using quantitative metrics.

Main Results:

• The method accurately determines volume median diameter, volume fraction, and size distribution width with uncertainty.
• Prespecifying the size range significantly reduces computational load for large datasets.
• Analyzing log-normal distributions with monodisperse models introduces systematic errors, highlighting the need for appropriate model selection.

Conclusions:

• The developed least-mean-squares method provides a fast and accurate way to characterize particulate systems, including submicrometer particles.
• The method offers superior uncertainty quantification compared to traditional ratio-style calculations.
• Accurate analysis requires using models that account for the actual particulate size distribution, especially for systems with significant width.