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    Area of Science:

    • Optical engineering
    • Telescope design and alignment

    Background:

    • Nodal aberration theory (NAT) is crucial for reflective telescope alignment.
    • Traditional sigma vector calculation using paraxial ray tracing is complex and limited for multi-mirror systems.

    Purpose of the Study:

    • To develop an improved method for calculating the sigma vector in NAT.
    • To extend NAT's applicability to multi-mirror reflective telescopes.
    • To propose an aberration field simulation and alignment algorithm.

    Main Methods:

    • Combining NAT with real-ray-tracing data.
    • Implementing a numerical iteration algorithm for aberration field simulation.
    • Applying the algorithm to a co-axis four-mirror reflective telescope.

    Main Results:

    • Successfully addressed misalignment in a multi-mirror telescope.
    • Significantly reduced computational complexity compared to traditional methods.
    • Validated the feasibility and flexibility of the proposed approach.

    Conclusions:

    • The proposed method effectively calculates the sigma vector using real-ray tracing data.
    • This approach overcomes limitations of traditional NAT, enabling alignment of complex multi-mirror telescopes.
    • The method offers flexibility for integration with various ray-tracing tools.