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Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
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    Random fluctuations in Ronchi grating fill factors smooth near-field images and cancel far-field diffraction orders. This study develops a theoretical model and confirms it with numerical simulations for grating analysis.

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    Area of Science:

    • Optics and Photonics
    • Diffraction Theory
    • Nanofabrication

    Background:

    • Ronchi gratings are optical elements used in various applications.
    • Fabrication imperfections, such as random fill factor fluctuations, can affect grating performance.
    • Understanding these effects is crucial for precise optical system design.

    Purpose of the Study:

    • To analyze the diffraction patterns produced by Ronchi gratings with random fill factor variations.
    • To develop a theoretical framework describing near-field and far-field diffraction.
    • To investigate the impact of different nominal fill factors on diffraction behavior.

    Main Methods:

    • Development of a theoretical formalism for diffraction analysis.
    • Application of the Rayleigh-Sommerfeld diffraction integral for numerical simulations.
    • Direct integration method to corroborate theoretical predictions.

    Main Results:

    • Theoretical analysis reveals smoothing of self-images in the near field due to fill factor randomness.
    • Cancellation of higher diffraction orders is observed in the far field.
    • Different nominal fill factors exhibit distinct diffraction behaviors when randomness is present.

    Conclusions:

    • The developed theoretical model accurately describes the diffraction phenomena.
    • Numerical results strongly agree with theoretical predictions, validating the formalism.
    • Fill factor randomness in Ronchi gratings significantly alters diffraction characteristics, impacting optical performance.