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Generalized projection-slice theorem for fan beam diffraction tomography.

A J Devaney

    Ultrasonic Imaging
    |July 1, 1985
    PubMed
    Summary
    This summary is machine-generated.

    A generalized projection-slice theorem for fan beam tomography is derived. This method, using the paraxial approximation, maps object data to an ellipsoidal surface in Fourier space.

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    Area of Science:

    • Physics
    • Applied Mathematics
    • Imaging Science

    Background:

    • Tomography reconstructs object properties from measurements.
    • Existing methods like plane beam tomography have limitations.
    • Diffraction tomography accounts for wave scattering effects.

    Purpose of the Study:

    • To generalize the projection-slice theorem for transmission fan beam diffraction tomography.
    • To develop a theoretical framework applicable under the Born or Rytov approximations.
    • To explore the implications of the paraxial approximation in this context.

    Main Methods:

    • Derivation of a generalized projection-slice theorem.
    • Application of the paraxial approximation for fan beam geometry.
    • Analysis of the transmitted field in relation to the object's Fourier transform.

    Main Results:

    • The transmitted field determines the 3D spatial Fourier transform of the object profile.
    • The transform is mapped onto an ellipsoid of revolution in Fourier space.
    • Under far-field conditions, this reduces to the spherical surface of the plane beam theorem.

    Conclusions:

    • The derived theorem extends projection-slice principles to fan beam diffraction tomography.
    • The paraxial approximation provides a tractable framework for analysis.
    • This work offers a foundation for advanced tomographic imaging techniques.