Multi-angle Dynamic Light Scattering Scaling Factor Iteration
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Solution Overview
Problem
Current multi-angle dynamic light scattering (MADLS) techniques face challenges in accurately determining particle size distributions due to errors in scaling factor calculation and noise contamination, leading to inconsistent results across different scattering angles.
Innovation Solution
A nested approach using a non-linear solver to iterate scaling factor estimates and a linear solver to determine particle size distribution, along with incorporating noise terms specific to each angle and size-dependent regularization coefficients to improve accuracy and robustness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multi-angle dynamic light scattering measurements are performed to improve particle size distribution accuracy, then measurement precision is improved, but device complexity and data processing complexity increase
Solution Approach 1:
The patent segments the complex multi-angle DLS data processing into distinct components: individual angle analyses are performed first to obtain separate particle size distributions, then these are combined using weighting coefficients. This segmentation allows each angle to be processed independently using standard DLS algorithms, reducing the overall complexity compared to treating all angles simultaneously.
Solution Approach 2:
The patent introduces weighting coefficients as an intermediary element that mediates between measurements from different scattering angles. These coefficients quantify the relative quality and reliability of data from each angle, allowing the system to objectively combine results while accounting for variations in signal quality, detector performance, and scattering intensity across different angles.
2Measurement precision
If iterative methods are used to determine weighting coefficients for combining multi-angle data, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The patent performs preliminary actions by first obtaining individual particle size distributions from each scattering angle before combining them. This preliminary separation allows the use of established, optimized single-angle DLS algorithms, and the subsequent combination step using weighting coefficients is computationally efficient compared to fully iterative multi-parameter optimization approaches.
Solution Approach 2:
The patent changes the approach from directly optimizing complex multi-parameter models to instead optimizing simpler weighting coefficients that combine pre-obtained distributions. This parameter transformation reduces the computational search space and allows for faster convergence to accurate results.
3Reliability
If noise contamination is present in multi-angle measurements, then reliability of results decreases, but performing measurements at multiple angles increases robustness against noise
Solution Approach 1:
The patent merges results from multiple scattering angles, each affected by different noise characteristics. By combining these independent measurements using weighting coefficients, the system achieves robustness against noise because contaminants affecting one angle do not necessarily affect others, and the combination process emphasizes the most reliable data.
Solution Approach 2:
The weighting coefficients provide a feedback mechanism that automatically adjusts the contribution of each angle's data based on its quality. Angles with higher noise contamination receive lower weighting, while cleaner angles receive higher weighting, creating a self-correcting system that maintains reliability despite the presence of harmful factors.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This method provides more robust and faster solutions for MADLS, enabling a larger size range and higher resolution in particle size distribution measurements while effectively accounting for noise and contaminants, resulting in consistent results across multiple scattering angles.
Implementation Method 1
Dynamic light scattering is a widely used method for analysing particles in which a time series of measurements of scattered light is used to determine a size or size distribution of particles
Implementation Method 2
Typically, an autocorrelation is performed on the time series of scattered light intensity, and a fit (e.g. Cumulants, CONTIN, NNLS/non-negative least squares) is performed to the autocorrelation function to determine particle characteristics
Implementation Method 3
Alternatively, a fourier transform may be used to determine a power spectrum of the scattered light, and an analogous fit to the power spectrum performed to determine particle characteristics
Implementation Method 4
Multi-angle dynamic light scattering (MADLS) measurements may also be performed, in which light scattered at more than one angle is used in a dynamic light scattering measurement
Data Source
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AI summary
A method of determining particle size distribution from multi-angle dynamic light scattering data, comprising: obtaining a series of measured correlation functions g(θi) at scattering angles θi; and solving an equation comprising gθ1…gθn=α1Kθ1…αnKθnx, wherein: K(θi) is the instrument scattering matrix computed for angle i, x is the particle size distribution, and αi is the scaling coefficient for angle i. The method comprises using the steps: a) providing initial estimates for scaling factors α2 to αn, and defining α1 = 1; b) iterating scaling factors α2 to αn using a non-linear solver; c) solving for x using a linear solver; d) calculate residual; e) repeat steps a) to d) while the residual is greater than a predefined exit tolerance.