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Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
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Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

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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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Instrument Calibration01:12

Instrument Calibration

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Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...
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Random and Systematic Errors01:20

Random and Systematic Errors

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Systematic Error: Methodological and Sampling Errors01:15

Systematic Error: Methodological and Sampling Errors

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In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
Sampling errors originate from improper sampling methods or the wrong sample population. These errors can be minimized by refining the sampling strategy. Defective instruments or faulty calibrations are the sources of instrumental...
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Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Related Experiment Video

Updated: Jan 4, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM
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Two-dimensional stitching interferometry for self-calibration of high-order additive systematic errors.

Lei Huang, Tianyi Wang, Josep Nicolas

    Optics Express
    |November 2, 2019
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces two novel 2D self-calibration stitching algorithms to precisely map surfaces by estimating and correcting systematic errors in stitching interferometry, crucial for applications like X-ray mirror measurement.

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    Calibration Procedures for Orthogonal Superposition Rheology
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    Area of Science:

    • Optical Metrology
    • Surface Metrology
    • Interferometry

    Background:

    • Stitching interferometry reconstructs surface topography from sub-aperture data.
    • Systematic error propagation is a major challenge in accurate surface mapping.
    • Existing methods struggle with high-order additive errors in X-ray mirror metrology.

    Purpose of the Study:

    • To develop 2D self-calibration stitching algorithms for in situ estimation of repeatable high-order additive systematic errors.
    • To improve the accuracy of surface topography reconstruction in stitching interferometry.
    • To address error sources in X-ray mirror metrology.

    Main Methods:

    • Proposed two algorithms: 'Calibrate, and then Stitch' (CS) and 'Stitch, and then Calibrate' (SC).
    • Utilized redundant overlapped subset data for error estimation.
    • Implemented 2D scans with step randomization and regularization for low-order terms.

    Main Results:

    • Successfully retrieved 2D high-order repeatable additive systematic errors from redundant overlapped data.
    • Demonstrated algorithm effectiveness through numerical simulations and experimental verification.
    • Reduced stitching errors, particularly periodic ones, using step randomization.

    Conclusions:

    • The proposed 2D self-calibration algorithms effectively mitigate high-order systematic errors in stitching interferometry.
    • The methods enhance the accuracy of surface topography reconstruction for demanding applications.
    • Redundant data and randomization are key to robust error correction in interferometric measurements.