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A circle in the coordinate plane is defined as the set of all points that lie at a constant distance, known as the radius, from a fixed point called the center. This relationship is captured using the distance formula. For a point (x, y) on the circle and a center (h, k), the distance between them equals the radius r. By squaring both sides of the distance formula, the equation of the circle is written in standard form:Constructing the Equation from Geometric InformationIf the center and the...
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Flexible calibration method for an inner surface detector based on circle structured light.

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    A novel calibration method for inner surface detectors using structured light offers improved flexibility and accuracy. This practical technique simplifies calibration by accounting for alignment errors, achieving high precision in measurements.

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    Area of Science:

    • Optical Metrology
    • Precision Engineering
    • Sensor Technology

    Background:

    • Inner surface detection requires accurate calibration of measurement systems.
    • Existing calibration methods for inner surface detectors can be inflexible and sensitive to assembly errors.
    • Structured light techniques offer potential for non-contact 3D measurement.

    Purpose of the Study:

    • To propose a new, flexible, and practical calibration method for inner surface detectors.
    • To develop a mathematical model that accounts for alignment errors, unlike previous methods.
    • To validate the accuracy and ease of application of the proposed calibration technique.

    Main Methods:

    • Utilizing a circle structured light approach with an additional precalibrated camera.
    • Employing a blank planar board observed from multiple unknown orientations.
    • Implementing a binocular intersection algorithm for calibration point coordinate calculation.

    Main Results:

    • The new method demonstrates high flexibility and practicality, requiring only a planar board and an additional camera.
    • The mathematical model effectively incorporates alignment errors, reducing the need for precise assembly.
    • Field tests showed excellent performance with a maximum relative error below 0.18%.

    Conclusions:

    • The proposed calibration method is highly accurate and suitable for inner surface detection applications.
    • This technique offers a significant improvement over existing methods in terms of ease of use and robustness.
    • The method's ability to handle alignment errors makes it practical for real-world industrial scenarios.