Hybrid Inverse Algorithm for Dynamic Light Scattering Data Deconvolution
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Solution Overview
Problem
Current methods for inverting the Laplace transform of experimental data from Dynamic Light Scattering and other techniques face challenges in accurately extracting particle size distributions, especially for broad or multimodal distributions due to susceptibility to noise and limitations in existing numerical inversion methods.
Innovation Solution
A hybrid inverse method using unsupervised machine learning and Non-negative Matrix Factorization (NMF) combined with a custom clustering algorithm, which integrates the physics of diffusion processes to deconvolute the data and determine the number of modes and parameters in particle size distributions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If numerical inversion of Laplace transform is used to extract particle size distribution, then the diffusion coefficient distribution function A(D) can be obtained, but the results are unreliable due to high susceptibility to noise
Solution Approach 1:
The patent applies preliminary action by using a hybrid method that combines regularization with non-negative matrix factorization before final inversion. This preliminary processing step prepares the data by reducing noise sensitivity and constraining the solution space, ensuring that the subsequent inversion produces reliable results even in the presence of experimental noise
Solution Approach 2:
The patent introduces an intermediary approach by using a two-stage inversion process. The first stage uses regularization to obtain a preliminary solution, and the second stage refines this using non-negative matrix factorization. This intermediary step acts as a bridge between raw data and final results, filtering out noise while preserving meaningful signal
2Measurement precision
If Provencher's constrained regularization method is used for inverting integral equations, then multimodal distributions with well-separated peaks can be resolved, but broad or overlapping distributions cannot be accurately determined
Solution Approach 1:
The patent applies dynamics by making the inversion method adaptive to different distribution types. The hybrid algorithm dynamically adjusts its parameters and constraints based on the characteristics of the input data, allowing it to effectively resolve both well-separated peaks and broad or overlapping distributions that would challenge traditional fixed-approach methods
Solution Approach 2:
The patent utilizes parameter changes by modifying the regularization parameters and constraints during the inversion process. By dynamically adjusting these parameters based on the observed data characteristics, the method can adapt to resolve various distribution shapes including broad and overlapping peaks that static parameter methods cannot handle
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 approach effectively inverts integral equations, providing reliable and accurate particle size distribution analysis even in complex cases, improving upon existing methods by stabilizing clustering and reducing noise-related errors, and can be applied to various spectroscopic and analytical techniques.
Implementation Method 1
the experimentally obtained autocorrelation function g1(t) is the Laplace transform of the size distribution function A(D). Hence, to extract the useful information in A(D), the Laplace transform is numerically inverted
Implementation Method 2
The diffusion coefficient and each solute species is related to its hydrodynamic radius using the Stokes-Einstein relationship where kBT is the thermal energy of the system, η is the shear viscosity of the solvent and R is the particle radius
Implementation Method 3
The DLS method is based on measuring the intensity of the photon auto-correlation function when the light is scattered by a suspension of particles, droplets, polymers, etc
Data Source
AI summary
A system that expands a hybrid inverse method (hNMF) to integral equations and applications comprising: a laser source, a first lens that focusses light from said laser source on a sample with unscattered light creating a reference light line and with scattered light focused by a plurality lenses to a plurality of detectors at several scattering angles θi, measured with respect to said reference light line, and for each said angle, θi, a processor records the autocorrelation function g1(t, θi) over a period of time, T.