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    Area of Science:

    • Optics and Photonics
    • Image Processing

    Background:

    • Optical systems often face challenges with limited depth of field, affecting image clarity.
    • Modulation Transfer Function (MTF) is a key metric for evaluating optical system performance.

    Purpose of the Study:

    • To investigate the use of Hadamard-coded annular masks for optically narrowing the field depth.
    • To enhance the influence of focus error on MTF without compromising light throughput.

    Main Methods:

    • Utilizing annular masks coded with Hadamard matrix elements.
    • Performing numerical evaluations of irradiance point spread functions (PSFs) and MTFs.
    • Assessing Fisher information of Walsh-Hadamard masks.

    Main Results:

    • Demonstrated that Hadamard-coded annular masks can narrow field depth.
    • Showed enhanced influence of focus error on MTF with no loss in light throughput.
    • Presented numerical evaluations and digitally generated images validating the approach.

    Conclusions:

    • Hadamard-coded annular masks offer an effective method for optical depth-of-field control.
    • The technique allows for translating out-of-focus information into background noise, enabling 3-D scene slicing.
    • This approach provides a novel way to improve optical imaging and depth perception.