Weighted Average Calculation for Sample Analysis Accuracy
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Solution Overview
Problem
Existing sample analyzers using multiple X-ray spectrometers face challenges in achieving accurate quantitative analysis due to the disproportionate contribution of low and high X-ray intensity measurements, leading to impaired quantitative accuracy when averaging concentration values.
Innovation Solution
A method and apparatus that calculate weighted averages based on the intensities of characteristic X-rays detected by multiple spectrometers, using weights such as peak intensities or ratios of peak to background intensities, to enhance quantitative accuracy in sample analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If concentration values from multiple X-ray spectrometers are simply averaged, then the calculation is straightforward, but the quantitative accuracy is impaired because low X-ray intensity measurements contribute equally to high intensity measurements
Solution Approach 1:
The patent changes the parameter of averaging from simple arithmetic mean to weighted mean, where weights are determined by X-ray intensity values. This transforms the calculation from equal contribution to proportional contribution based on measurement quality, resolving the contradiction between simplicity and accuracy.
Solution Approach 2:
The patent applies different weights to different spectrometer measurements based on their local characteristics (X-ray intensity). Each measurement is treated differently according to its quality, with higher intensity measurements receiving greater weight, thus improving overall quantitative accuracy while maintaining a systematic approach.
2Measurement precision
If multiple X-ray spectrometers are used to detect characteristic X-rays, then detection sensitivity and coverage are improved, but the complexity of data processing increases when calculating resultant concentrations
Solution Approach 1:
The patent introduces intensity-based weighting as a parameter to simplify the data processing of multiple spectrometers. Instead of complex statistical methods, it uses a straightforward weighted average formula where weights are directly proportional to X-ray intensities, reducing processing complexity while maintaining high detection sensitivity.
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 allows for higher quantitative accuracy by weighting the contributions of different X-ray measurements according to their intensities, improving the precision of concentration calculations compared to straightforward averaging methods.
Implementation Method 1
directing an electron beam at the sample and detecting characteristic X-rays emanating from the sample in response to the incident electron beam
Implementation Method 2
detecting characteristic X-rays emanating from the sample by means of an X-ray spectrometer
Data Source
AI summary
A method of sample analysis is offered which provides improved quantitative accuracy. This method starts with irradiating a sample with an electron beam. Characteristic X-rays emanating from the sample are detected. Plural data sets about intensities of characteristic X-rays corresponding to a specific element contained in the sample are obtained. The element is quantitatively analyzed based on the plural data sets. This method includes a step (S20) for calculating quantitative values for the element for the plural data sets, respectively, about the characteristic X-ray intensities, a step (S30) for calculating weights for the quantitative values, respectively, based on the plural data sets about the characteristic X-ray intensities, and a step (S40) for calculating a weighted average of the quantitative values based on the weights.