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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Subaperture stitching computation time optimization using a system of linear equations.

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    A new, fast subaperture stitching method using linear equations accurately measures large optical surfaces. This technique optimizes interferometry, reducing manufacturing time for complex optical components.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Surface Metrology

    Background:

    • Interferometric measurement of large or aspheric optical surfaces is challenging due to numerical aperture limitations and slope deviations.
    • These limitations can cause vignetting and spatial aliasing, hindering accurate full-aperture analysis.
    • Subaperture stitching is a viable solution but often computationally intensive.

    Purpose of the Study:

    • To introduce a novel and computationally efficient subaperture stitching method for optical metrology.
    • To mathematically describe a new stitching algorithm based on a system of linear equations.
    • To validate the performance and speed of the proposed method against existing algorithms.

    Main Methods:

    • Developed a novel stitching algorithm based on solving a system of linear equations.
    • Performed theoretical analysis of computation complexity for the new method.
    • Tested the algorithm using real measurement data from spherical surfaces with a QED ASI and an experimental interferometer.

    Main Results:

    • The proposed linear equation-based stitching method demonstrates high accuracy and efficiency.
    • Theoretical computation complexity was found to be favorable compared to other algorithms.
    • Practical testing confirmed the method's effectiveness in stitching subaperture data from spherical surfaces.

    Conclusions:

    • The novel stitching method offers a fast and accurate solution for measuring large and aspheric optical surfaces.
    • This approach can significantly reduce computation time, leading to faster overall manufacturing processes.
    • The method provides a valuable tool for advancing optical metrology and surface characterization.