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    Area of Science:

    • Optical Metrology
    • Surface Science
    • Imaging Techniques

    Background:

    • Interference microscopy is a 3D imaging technique for quantitative surface topography analysis.
    • Existing instrument modalities share a common theoretical basis for interferogram formation.

    Purpose of the Study:

    • To present a unified theoretical framework for 3D image formation in interference microscopy.
    • To elucidate the relationship between surface topography and scattered amplitude under different approximations.
    • To explore the implications of this framework for measurement accuracy and error correction.

    Main Methods:

    • Formulation of a 3D linear filtering process relating illuminating and scattered waves to object characteristics using Ewald and McCutchen spheres.
    • Analysis of Born and Kirchhoff approximations for scattered amplitude.
    • Reduction of the 3D filtering process to 2D for near-planar surfaces under the small height approximation.

    Main Results:

    • Demonstrated linear relationship between scattered amplitude and surface topography.
    • Defined the 3D filtering process based on spatial frequencies.
    • Showcased the framework's ability to explain interferometric defocus and optical aberrations.
    • Incorporated nonlinear effects like multiple scattering and estimation nonlinearities.

    Conclusions:

    • The unified 3D framework provides a comprehensive understanding of interference microscopy.
    • It offers insights into mitigating measurement errors and improving accuracy for 3D surface topography.
    • The framework accommodates both linear and nonlinear scattering phenomena.