Contents

• A brief introduction to ultrasound
  • Resolution, beamforming and the point spread function
  • Sound wave propagation as a linear process
  • The scattering and reflection of sound
    • Scatterer sizes less than and equal to the wavelength
    • Reflecting structures larger than the wavelength
    • Coherent and incoherent scattering
  
  
• Ultrasound and Fourier optics
  • Propagation as a linear operation
  • The significance of the Fraunhofer approximation
  • The development of the Fraunhofer approximation
    • The Fresnel approximation
    • The Fraunhofer approximation
  • The two-dimensional Fourier transform
    • The analytic form of the 2-D Fourier transform
    • Important properties of the 2-D Fourier transform
    • Transforms and properties in the context of a typical aperture
  • Propagation as a spatial transfer function
  
  
• Ultrasound and k-space
  • K-space transforms of elementary geometries
  • Spatial resolution and spatial frequencies
  • K-space transforms of large apertures and arrays
  • K-space is a two-dimensional frequency space
  • Imaging trade-offs
  • The target function and scattering:
  • Frequency dependent effects:
  • Tissue anisotropy
  
  
• A beginner's guide to speckle
  • The statistics of fully-developed speckle
  • Coherent components and Rician statistics
  
  
• First order speckle statistics
  • Magnitude (using Trahey's notation)
  • Intensity (using Goodman's notation)
  • A review of random variables
  
  
• Second Order Speckle Statistics
  • Speckle and the phase spectrum
  • The autocorrelation of speckle
  • Important speckle references:
  
  
• Spatial and temporal coherence
  • The correlation coefficient in k-space
  
  
• Speckle reduction techniques
  • Spatial compounding
  • Frequency compounding
  
  
• Additional topics
  • Phase aberration
  • The Van Cittert-Zernicke theorem
  • Deconvolution and super resolution methods
  • Detection:
  • Elastography imaging
  • Limitations of k-space
  
  
• Bibliography