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    Area of Science:

    • Optics and Photonics
    • Materials Science

    Background:

    • Freeform reflector design is crucial for light manipulation.
    • Surface roughness, modeled as microfacets, affects light scattering.
    • Solving inverse problems is key in optical system design.

    Purpose of the Study:

    • To develop a computational method for designing reflectors with scattering surfaces.
    • To integrate microfacet scattering models into freeform reflector design.
    • To analyze the impact of surface scattering on reflector geometry.

    Main Methods:

    • Combined two-dimensional freeform reflector design with microfacet surface scattering models.
    • Formulated scattered light intensity using a convolution integral.
    • Employed deconvolution to transform the problem into a standard inverse specular design problem.

    Main Results:

    • The scattering surface model resulted in a convolution integral for light intensity.
    • Deconvolution enabled solving an inverse specular problem.
    • Surface scattering introduced a few percentage difference in reflector radius, varying with scattering amount.

    Conclusions:

    • A novel method allows computation of reflector shapes with scattering surfaces.
    • The approach simplifies the design of optical components with controlled roughness.
    • Understanding scattering effects is important for precise reflector design.