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    We developed an optimization algorithm for 3D particle localization using extended-axial-depth point spread functions (PSFs). This method enhances localization precision and temporal resolution without complex post-processing.

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    Area of Science:

    • Optics and Photonics
    • Biophysics
    • Microscopy

    Background:

    • Accurate 3D particle localization is crucial for understanding biological processes.
    • Extended-axial-depth point spread functions (PSFs) enable precise depth determination.
    • Existing PSFs often require complex post-processing, limiting temporal resolution.

    Purpose of the Study:

    • To develop an optimization algorithm for extended-axial-depth PSFs.
    • To improve the transfer function efficiency of PSFs for 3D particle localization.
    • To enhance localization precision and temporal resolution in 3D imaging.

    Main Methods:

    • Utilized Fresnel approximation (FA) imaging for PSF optimization.
    • Employed iterative constraints in object, spatial, and Fourier domains.
    • Incorporated effective photon number or Cramer-Rao lower bound as iteration termination criteria.
    • Allowed flexible adjustment of peak intensity ratios and modulation function weights.

    Main Results:

    • Optimized twin-Airy (TA) PSF demonstrated improved transfer function efficiency.
    • The optimized TA-PSF eliminated the need for complex post-processing.
    • Achieved enhanced localization precision and temporal resolution for 3D particle localization.

    Conclusions:

    • The FA-based optimization algorithm significantly improves extended-axial-depth PSFs.
    • This advancement is vital for high-precision, high-speed 3D particle localization.
    • The method offers a more efficient and streamlined approach to 3D imaging challenges.