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    Compressive sensing (CS) reconstructs sparse signals using fewer measurements. This study demonstrates CS in optical hardware without extra components, successfully reconstructing modal structures using random sub-Nyquist sampling.

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    Area of Science:

    • Optics and Photonics
    • Signal Processing

    Background:

    • Compressive sensing (CS) integrates data acquisition and compression to minimize measurements for sparse signal reconstruction.
    • Traditional optical CS involves projecting fields onto random spatial patterns, often requiring additional optical components.

    Purpose of the Study:

    • To demonstrate the feasibility of exploiting compressive sensing in native optical hardware without added components.
    • To reconstruct the modal structure of a field using random sub-Nyquist sampling of an interferogram within system constraints.

    Main Methods:

    • Utilized a generalized Mach-Zehnder interferometer, replacing temporal delay with a fractional transform.
    • Implemented random sub-Nyquist sampling by varying the order of the fractional transform.
    • Leveraged the incoherent and isotropic properties of structurally constrained sensing matrices for successful CS.

    Main Results:

    • Successfully reconstructed the modal content of an input beam in Hermite-Gaussian and Laguerre-Gaussian bases.
    • Demonstrated that random sub-Nyquist sampling of an interferogram is sufficient for field reconstruction.
    • Validated CS in native optical hardware, confirming its efficiency and reduced measurement requirements.

    Conclusions:

    • Compressive sensing can be effectively implemented in existing optical systems without requiring additional hardware.
    • Random sub-Nyquist sampling within a fractional transform framework enables efficient modal reconstruction.
    • The study highlights the potential of CS for simplifying optical measurement systems and reducing data acquisition needs.