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    Area of Science:

    • Optics and Photonics
    • Image Processing
    • Metrology

    Background:

    • Optical Phase Retrieval (OPR) is crucial for determining beam transverse phase profiles.
    • Interference methods, particularly off-axis holography, are standard for converting phase to intensity patterns.
    • Several algorithms exist for phase retrieval from single off-axis interference patterns, necessitating careful selection based on application requirements.

    Purpose of the Study:

    • To provide a detailed explanation and quantitative comparison of three noniterative, transform-based OPR algorithms: Fourier Transform (FT), Continuous Wavelet Transform (CWT), and Hilbert Transform (HT).
    • To evaluate the performance of these algorithms using root-mean-square (rms) error and structural similarity measure (SSIM).
    • To discuss the constraints, advantages, and practical limitations of each method in the context of quantitative phase imaging.

    Main Methods:

    • Detailed explanation of the FT, CWT, and HT algorithms for OPR.
    • Quantitative comparison using a combination of rms error and standard structural similarity measure.
    • Validation of a standard unwrapping algorithm's advantages using the same metrics.

    Main Results:

    • The HT method demonstrates superior performance for object beams with high spatial frequency content, though it is more susceptible to noise.
    • The FT and CWT methods exhibit better noise immunity but are limited by the spatial frequency range of the object beam.
    • Experimental results using monodispersed polymethyl methacrylate beads illustrate the practical trade-offs of each method.

    Conclusions:

    • The choice of OPR algorithm significantly impacts performance based on object beam characteristics and noise levels.
    • FT and CWT methods are robust against noise but limited in spatial frequency handling.
    • HT is effective for high spatial frequencies but requires careful noise management, highlighting the need for method selection tailored to specific experimental conditions.