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Related Concept Videos

Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
Scanning Electron Microscopy01:07

Scanning Electron Microscopy

A scanning electron microscope (SEM) is used to study the surface features of a sample by using an electron beam that scans the sample surface in a two-dimensional manner. Typically, areas between ~1 centimeter to 5 micrometers in width can be imaged. SEM can be used to image bacteria, viruses, tissues as well as larger samples like insects. Conventional SEM gives a magnification ranging from 20X to 30,000X and spatial resolution of 50 to 100 nanometers.
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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
The Uncertainty Principle04:08

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...
Overview of Microscopy Techniques01:22

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The early pioneers of microscopy opened a window into the invisible world of microorganisms. In 1830, Joseph Jackson Lister created an essentially modern light microscope. The 20th century saw the development of microscopes that leveraged nonvisible light, such as fluorescence microscopy that uses an ultraviolet light source and electron microscopy that uses short-wavelength electron beams. These advances significantly improved magnification, image resolution, and contrast. By comparison, the...
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

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Related Experiment Video

Updated: May 17, 2026

Picometer-Precision Atomic Position Tracking through Electron Microscopy
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Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

Uncertainty estimates for electron probe X-ray microanalysis measurements.

Nicholas W M Ritchie1, Dale E Newbury

  • 1Materials Measurement Science Division, National Institute of Standards and Technology, 100 Bureau Drive, MS 8372, Gaithersburg, Maryland 20899-8372, United States. nicholas.ritchie@nist.gov

Analytical Chemistry
|October 24, 2012
PubMed
Summary
This summary is machine-generated.

Electron probe microanalysis (EPMA) has historically underestimated uncertainty by focusing on precision, not accuracy. This study quantifies key accuracy-related uncertainties in EPMA matrix corrections for improved elemental analysis.

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Measurement of Total Calcium in Neurons by Electron Probe X-ray Microanalysis

Published on: November 20, 2013

Area of Science:

  • Materials Science
  • Analytical Chemistry
  • Physics

Background:

  • Electron probe X-ray microanalysis (EPMA) has been a cornerstone of elemental analysis for over 60 years.
  • Current EPMA uncertainty budgets often omit significant accuracy-related terms, relying primarily on measurement precision.
  • This omission can lead to an underestimation of the total uncertainty in quantitative EPMA measurements.

Purpose of the Study:

  • To address the historical underestimation of uncertainty in EPMA by quantifying key accuracy-related parameters.
  • To investigate the influence of mass absorption coefficients and backscatter coefficients on EPMA measurement accuracy.
  • To provide strategies for optimizing EPMA accuracy by minimizing the impact of poorly known model parameters.

Main Methods:

  • Analysis of uncertainty contributions from mass absorption coefficients [μ/ρ] within EPMA matrix correction models.
  • Evaluation of uncertainty contributions from backscatter coefficients (η) in quantitative EPMA analysis.
  • Focus on quantifying accuracy-related uncertainty terms, rather than solely measurement precision.

Main Results:

  • Identified mass absorption coefficients and backscatter coefficients as significant sources of uncertainty in EPMA.
  • Demonstrated that these accuracy-related terms can represent a substantial portion of the total uncertainty budget.
  • Provided insights into the utility and limitations of EPMA measurements based on quantified uncertainties.

Conclusions:

  • Accurate quantification in EPMA requires addressing uncertainties beyond measurement precision, specifically in matrix correction models.
  • Understanding and quantifying uncertainties in [μ/ρ] and η is crucial for reliable elemental analysis using EPMA.
  • Practitioners can improve EPMA accuracy by developing strategies to mitigate the influence of poorly constrained parameters.