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Related Concept Videos

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.
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Calibration Curves: Linear Least Squares01:20

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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.
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Calibration Curves: Correlation Coefficient01:10

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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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Glassware Calibration01:11

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Accurate calibration of glassware, such as volumetric flasks, pipettes, and burettes, is essential to ensure accurate measurements in the analytical laboratory. Calibration helps maintain consistency across measurements and prevents errors arising from inaccurate volumes.
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Linearization and Approximation01:26

Linearization and Approximation

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Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
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Non-inertial Frames of Reference01:27

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A reference frame accelerating or decelerating relative to an inertial frame is a non-inertial frame. To help understand this, consider what taking off in an airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone all have in common. All these systems are accelerating, decelerating, or rotating relative to the Earth; hence, they all are non-inertial frames. All these systems exhibit inertial forces, which merely seem to arise from motion,...
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Updated: Mar 16, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy iPALM
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Three-frame self-calibration phase shift algorithm using the Gram-Schmidt orthonormalization approach.

Hubing Du, Honghong Gao

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    |August 25, 2016
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    Summary
    This summary is machine-generated.

    This study introduces a robust Gram-Schmidt orthonormalization method for phase-shifting shadow moiré, overcoming limitations of traditional techniques. The new approach offers improved accuracy and flexibility in optical metrology applications.

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    Area of Science:

    • Optical Metrology
    • Interferometry
    • Computational Imaging

    Background:

    • Phase-shifting shadow moiré is limited by height-dependent effects and approximate phase steps.
    • Conventional methods struggle with complex fringe intensity distributions, leading to unstable phase shift extraction.
    • Fixed phase steps (around π/2 rad) reduce flexibility in grating translation-based techniques.

    Purpose of the Study:

    • To develop a more robust and flexible phase-shifting shadow moiré technique.
    • To address the instability issues in phase shift extraction algorithms.
    • To introduce a self-calibrating algorithm for accurate phase measurement.

    Main Methods:

    • Developed a Gram-Schmidt orthonormalization approach.
    • Implemented a three-frame self-calibration phase-shifting algorithm with equal, unknown phase steps.
    • Utilized an arctangent function for phase shift calculation.

    Main Results:

    • The proposed method demonstrates robustness and speed.
    • Optical experiments confirmed the method's correctness by comparison with conventional five-step algorithms.
    • The arctangent-based calculation overcomes the instability of arccosine/arcsine methods.

    Conclusions:

    • The Gram-Schmidt orthonormalization approach provides a stable and accurate solution for phase-shifting shadow moiré.
    • The self-calibrating, three-frame algorithm enhances flexibility and reliability in optical measurements.
    • This method is suitable for a wide range of applications requiring precise phase retrieval.