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    This study introduces a novel single-lens system for precise light-field control, simplifying optical design. The innovative approach achieves unified angular-spatial modulation using double freeform surfaces, offering a compact and effective solution.

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    Area of Science:

    • Optics and Photonics
    • Optical Design
    • Freeform Optics

    Background:

    • Simultaneous control of angular and spatial light-field distributions is difficult with traditional multi-element lenses.
    • Existing methods often require complex and bulky optical configurations.

    Purpose of the Study:

    • To develop a compact, single-lens solution for unified angular-spatial light-field modulation.
    • To overcome the limitations of conventional multi-lens systems in optical design.

    Main Methods:

    • Co-optimization of double freeform surfaces within a single lens.
    • Formulation as an extended caustic design with dual-plane irradiance constraints.
    • Numerical simulations to verify performance and control accuracy.

    Main Results:

    • Achieved precise and stable control of both angular and spatial light-field properties.
    • Demonstrated performance comparable to conventional multi-lens systems.
    • Eliminated the need for auxiliary optical components.

    Conclusions:

    • The proposed double freeform surface lens offers a practical foundation for compact, high-performance optical systems.
    • This approach provides a promising route for integrated angular-spatial light-field engineering.
    • Advances in optical design through simplified, efficient solutions.