Multivariate Optical Element Nonlinear Calibration
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Solution Overview
Problem
Existing multivariate optical computing systems face challenges in accurately deriving information from light due to non-linear relationships between sample qualities and analyte concentrations, leading to inaccuracies in calibration methods that assume linear relationships.
Innovation Solution
The introduction of nonlinear calibration procedures for multivariate optical computing design algorithms, which include calibrating to the antilogarithm of concentration, combining calibration data sets to account for nonlinear spectral artifacts, and modifying the design function to optimize standard error using nonlinear fitting functions, addresses the limitations of linear calibration methods.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If linear calibration methods are used in multivariate optical computing systems, then the calibration process is simple and straightforward, but the accuracy of analyte concentration predictions deteriorates when non-linear relationships exist between sample qualities and analyte concentrations
Solution Approach 1:
The patent transforms the calibration problem by changing the parameter space through logarithmic transformation. By calibrating to the antilogarithm of concentration rather than linear concentration, the method captures non-linear relationships between optical spectra and analyte concentrations. This parameter transformation allows the system to handle non-linear spectral artifacts and complex sample matrices while maintaining computational tractability.
Solution Approach 2:
The patent introduces a new dimensional approach by combining multiple calibration data sets and using non-linear fitting functions. This adds complexity to the calibration dimension, allowing the system to account for non-linear spectral artifacts and interferences that single-dimension linear methods cannot capture. The multi-dimensional calibration space enables more accurate modeling of complex optical-sample interactions.
2Reliability
If conventional linear calibration procedures are used, then the calibration process is fast and efficient, but the system cannot adequately handle non-linear spectral artifacts and interferences from complex sample matrices
Solution Approach 1:
The patent performs preliminary transformations on the calibration data by working with logarithms of concentrations during the calibration phase. This preliminary action prepares the data in a transformed space where non-linear relationships can be captured more effectively. The antilogarithmic transformation is applied in advance to the calibration model, enabling the system to inherently handle non-linear spectral artifacts before actual measurements are made.
Solution Approach 2:
The patent uses logarithmic transformation as an intermediary step between the raw optical spectra and the final concentration predictions. This intermediary transformation allows the calibration model to bridge the gap between linear optical measurements and non-linear concentration relationships. By introducing this mathematical intermediary, the system can process complex non-linear relationships through a structured transformation process rather than requiring direct non-linear modeling.
3Measurement precision
If the calibration model assumes linear relationships between light intensity and analyte concentration, then the mathematical processing is simple, but the precision of concentration estimates deteriorates in the presence of non-linear spectral variations
Solution Approach 1:
The patent fundamentally changes the parameter representation by using logarithmic transformation of concentration values. Instead of modeling concentration directly, the calibration model operates in log-concentration space, which linearizes certain non-linear relationships. This parameter change enables the use of simpler linear regression techniques while capturing non-linear spectral behavior, thereby improving precision without requiring complex non-linear fitting functions.
Solution Approach 2:
The patent introduces curvature into the calibration model through logarithmic transformation. The log-transformation creates a curved relationship between optical intensity and concentration that better matches the physical reality of non-linear spectral artifacts. This curved modeling approach, represented mathematically through logarithmic functions, allows the calibration to follow the natural curvature of spectral responses rather than forcing linear relationships.
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
These nonlinear calibration approaches improve the accuracy and robustness of multivariate optical computing systems by effectively handling non-linear interferences and spectral complexities, enhancing the precision of analyte concentration predictions.
Implementation Method 1
When light interacts with matter, for example, it carries away information about the physical and chemical properties of the matter. A property of the light, for example, its intensity, may be measured and interpreted to provide information about the matter with which it interacted.
Implementation Method 2
Light from each of several samples may be directed to a series of bandpass filters that separate predetermined wavelength bands from the light.
Implementation Method 3
Light detectors following the bandpass filters measure the intensity of each light band.
Data Source
AI summary
The present subject matter is direct to methodologies for calibrating data obtained from an optical analysis system. An initial calibration matrix of sampled analyte concentrations is modified using mean-centering techniques and selection of low and high analyte concentration spectra to produce a two-point calibration. A modified calibration matrix is produced by generating a non-linear calibration matrix by multiplying the initial calibration matrix by the two-point calibration. In an alternate embodiment, an initial multivariate optical element design is modified by iteratively adjusting the design based on standard error of calibration determination based on non-linerly fitted functions.