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Vectorial aberrations of biconic surfaces.

Yi Zhong, Herbert Gross

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |August 16, 2018
    PubMed
    Summary

    Biconic surfaces offer distinct focal powers for anamorphic systems, correcting aberrations where spherical surfaces fail. This study analyzes their aberrations and conversion to freeform surfaces, aiding optical design.

    Area of Science:

    • Optical Engineering
    • System Design
    • Aberration Theory

    Background:

    • Spherical surfaces are insufficient for correcting aberrations in non-rotationally symmetric optical systems.
    • Anamorphic systems utilize biconic surfaces for differential focal power in tangential and sagittal planes.
    • Biconic surfaces serve as a foundational shape for freeform surface representation in optical design.

    Purpose of the Study:

    • To analyze the aberrations of biconic surfaces using an expansion up to the fourth order.
    • To investigate the decoupling of astigmatism and coma generated by biconic surfaces.
    • To explore the conversion of biconic surfaces into Zernike fringe freeform surfaces for optical system design.

    Main Methods:

    • Expansion of biconic surface sag up to the fourth order, decomposing it into spherical, aspherical, and freeform components.

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  • Derivation of vectorial aberrations using the extended nodal aberration theory.
  • Analysis of aberration characteristics and conversion methods for biconic surfaces.

    • Main Results:

    • Biconic surfaces generate field-constant astigmatism, decoupled from coma, which is beneficial for optical system initial setup.
    • The expansion and decomposition provide insights into the aberration contributions of different surface components.
    • Demonstrated the conversion of biconic surfaces into Zernike fringe freeform surfaces.

    Conclusions:

    • Biconic surfaces are advantageous for initial optical system design, particularly for off-axis and reflective camera systems, due to decoupled aberrations.
    • The analysis facilitates a deeper understanding of biconic surface aberrations and their management.
    • The conversion to Zernike fringe freeform surfaces offers a pathway for advanced optical element fabrication and optimization.