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Updated: Jul 7, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
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Published on: August 30, 2013

Polygon approximation of the fringes of diffractive elements.

I Kallioniemi, J Saarinen, K Blomstedt

    Applied Optics
    |February 12, 2008
    PubMed
    Summary

    Polygon approximation in diffractive optics introduces errors. A new roughness parameter (beta) quantifies these errors, showing that even small phase errors can distort diffraction patterns, impacting signal fidelity in lenses and axicons.

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    Published on: October 11, 2016

    Area of Science:

    • Optics and Photonics
    • Computational Physics
    • Diffractive Optics

    Background:

    • Electron-beam fabrication of diffractive optical elements often uses polygon approximation of continuous fringes to reduce data volume.
    • This approximation introduces local wave-front errors, leading to light scattering and background noise.
    • Quantifying these errors is crucial for understanding their impact on optical performance.

    Purpose of the Study:

    • To introduce a roughness parameter (beta) for quantifying local phase errors in polygon-encoded diffractive structures.
    • To develop an efficient numerical method for computing Fresnel diffraction patterns of polygon apertures.
    • To investigate the effect of polygon approximation errors on the signal fidelity of diffractive axicons and lenses.

    Main Methods:

    • Introduction of a roughness parameter, beta, to characterize local phase errors.
    • Development of an efficient numerical method for calculating Fresnel diffraction patterns from polygon apertures.
    • Simulation and analysis of polygon-approximated diffractive axicons and lenses.

    Main Results:

    • A roughness parameter beta is defined to quantify local phase errors in polygon-encoded diffractive structures.
    • An efficient numerical method for computing Fresnel diffraction patterns of polygon apertures is presented.
    • It is found that a maximum local phase error of pi/6 rad is required before the Strehl ratio (S) of a paraxial diffractive lens drops below 0.9.
    • Significantly smaller phase errors can still noticeably degrade the circular symmetry of the diffraction pattern.

    Conclusions:

    • The roughness parameter beta effectively quantifies local phase errors in polygon-approximated diffractive elements.
    • The developed numerical method allows for efficient analysis of diffraction patterns from polygon apertures.
    • Signal fidelity in diffractive lenses and axicons is sensitive to local phase errors; even minor errors can break symmetry, impacting performance.