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Influence of Earth's Curvature and Atmospheric Refraction on Leveling01:26

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During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance.
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Phase measuring deflectometry for convex aspheric surface measurement.

Ziliang Yan, Dahai Li, Xinwei Zhang

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    |March 4, 2024
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    Summary
    This summary is machine-generated.

    This study presents a novel method for precisely measuring convex aspherical surfaces using structured light and iterative data processing. The technique achieves high accuracy, comparable to advanced profilers, for complex surface shapes.

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    Area of Science:

    • Optical metrology
    • Surface characterization
    • Aspherical optics

    Background:

    • Accurate measurement of convex aspherical surfaces with large slope gradients is challenging.
    • Existing methods may struggle with high slope gradients and require complex setups.

    Purpose of the Study:

    • To introduce a novel, accurate method for measuring convex aspherical surfaces with large slope gradients.
    • To enhance structured light visibility using a pre-distortion system.
    • To achieve high-precision surface shape data through iterative processing.

    Main Methods:

    • Utilizing a pre-distortion system to improve structured light pattern visibility for camera capture.
    • Employing iterative data processing methods for surface shape determination.
    • Establishing a reference plane for experimental calibration and initiating an iterative surface height calculation.

    Main Results:

    • The method successfully measures a steep convex aspherical surface (5.2 mm diameter, 7.7 mm radius of curvature).
    • Achieved root mean square accuracy can reach half a wavelength compared to high-precision profilers.
    • Demonstrates the effectiveness of iterative slope integration for precise height derivation.

    Conclusions:

    • The proposed novel approach offers a highly accurate solution for measuring complex convex aspherical surfaces.
    • The pre-distortion system and iterative processing are key to achieving sub-wavelength accuracy.
    • This method advances the capabilities of optical metrology for challenging surface measurements.