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    This study presents a novel method for mapping spherical surfaces using interferometry. This technique is crucial for improving inertial sensors in future gravitational wave missions.

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    Area of Science:

    • * Optical metrology
    • * Precision measurement
    • * Gravitational wave detection instrumentation

    Background:

    • * Future space-based gravitational wave missions require highly sensitive inertial reference sensors with minimal acceleration noise.
    • * Spherical test masses offer advantages over cuboid shapes for inertial sensing due to suspension-free operation and reduced cross-coupling of attitude control noise.
    • * Interferometric readout of test mass position is susceptible to surface irregularities and attitude variations, necessitating accurate surface characterization.

    Purpose of the Study:

    • * To develop and demonstrate a method for creating a surface map of a spherical body using interferometric optical point sensors.
    • * To enable compensation for surface irregularities affecting the center of gravity readout in precision measurement applications.
    • * To support the development of improved inertial reference sensors for gravitational wave observatories.

    Main Methods:

    • * Employing heterodyne interferometry for high-precision (nanometer-level) measurements.
    • * Utilizing a rotating test subject (spherical body) to capture a complete surface map.
    • * Incorporating a cylindrical mirror adjacent to the sphere as a reference to suppress common-mode errors.

    Main Results:

    • * Successful demonstration of a method to measure a surface map of a spherical body.
    • * Achieved nanometer-level precision in surface mapping.
    • * Validated the effectiveness of the reference mirror in suppressing common-mode errors.

    Conclusions:

    • * The developed interferometric method provides an accurate surface map of spherical test masses.
    • * This characterization is essential for compensating optical path length changes caused by surface features in the measurement bandwidth.
    • * The technique is vital for enhancing the performance of inertial reference sensors in demanding applications like gravitational wave detection.