Optical Sensor Peak Center Tracking via Linear Sinusoidal Fit
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Solution Overview
Problem
Existing optical sensor systems face challenges in accurately measuring the center wavelength/frequency at high frequency and high sensitivity, particularly with high sensor counts, due to computational intensity and noise instability in current fitting methods like Gaussian and polynomial fits.
Innovation Solution
A method and system that utilize a sinusoidal fit with a fixed spectral peak width, reducing computational complexity by solving a set of linear equations, and incorporating weighted fits to enhance noise tolerance and stability, suitable for high-frequency and high-sensitivity operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Gaussian fit is used to accurately determine peak center, then measurement precision is improved, but device complexity and computational resources increase significantly
Solution Approach 1:
The patent transforms the non-linear Gaussian fitting problem into a linear system by changing the parameter representation. Instead of directly fitting Gaussian parameters (amplitude, center, width), the method uses a basis function expansion where the peak center is determined by solving a linear system of equations derived from the sampled data points. This parameter transformation eliminates the need for iterative non-linear optimization while maintaining accuracy.
Solution Approach 2:
The patent replaces the iterative mechanical optimization process (non-linear least squares minimization) with a direct algebraic solution. By formulating the peak fitting as a linear system Ax=b where A contains basis function evaluations and b contains weighted data sums, the solution is obtained through direct linear algebra operations rather than iterative numerical optimization, significantly reducing computational complexity.
2Measurement precision
If polynomial fit of higher order is used to improve accuracy, then measurement precision is improved, but stability deteriorates due to increased degrees of freedom and noise
Solution Approach 1:
The patent changes the functional basis from high-order polynomials to a localized basis set centered at the estimated peak position. By using basis functions that are concentrated around the peak rather than global high-order polynomials, the method achieves high accuracy with fewer degrees of freedom, preventing overfitting and maintaining stability even with noisy data.
3Measurement precision
If non-linear minimization algorithms are used to fit Gaussian function, then measurement precision is improved, but productivity decreases due to iterative nature and non-deterministic runtimes
Solution Approach 1:
The patent substitutes the iterative non-linear minimization algorithm with a direct linear system solver. By reformulating the Gaussian fitting problem as a linear least squares problem through basis function expansion, the method eliminates iteration entirely. The peak center is obtained by solving a linear system in a fixed number of computational steps, providing deterministic and predictable runtime suitable for real-time processing.
4Productivity
If polynomial fit is used for computational efficiency, then productivity is improved, but measurement precision deteriorates compared to Gaussian and Lorentzian fits
Solution Approach 1:
The patent changes the approach by using a linear basis function expansion that explicitly models the peak shape characteristics. Rather than using generic polynomials that require high order for accuracy, the method uses a basis set tailored to represent peaked functions, achieving both linear computational complexity and high measurement precision simultaneously.
Data Source
AI summary
A system and method of determining the center of a peak of data points of an optical sensor are disclosed. The method can comprise the steps of performing an initial setup measurement of the sample points and extracting a peak; fitting the peak with a function that uses at least one of the peak's width, amplitude and center offset as fitting parameters; producing a set of linear equations which when solved calculate the optimum fit of a function to the peak assuming the previously calculated peak's width; and performing subsequent measurements of the data points to find peaks and solving the set of linear equations to determine the center of the peaks.