Scalar Diffraction from a Circular Aperture

Scalar Diffraction from a Circular Aperture by Charles J. Daly, Navalgund A.H.K. Rao.

Scalar diffraction from a circular aperture is a ubiquitous problem that arises in a variety of disciplines, such as optics (lenses), acoustics (speakers), electromagnetics (dish antennas), and ultrasonics (piston transducers). The problem endures despite centuries of research because each new gener...

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Bibliographic Details
Main Authors: Daly, Charles J. (Author), Rao, Navalgund A.H.K (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer US : Imprint: Springer, 2000.
Edition:1st ed. 2000.
Series:The Springer International Series in Engineering and Computer Science, 549
Springer eBook Collection.
Subjects:
Optical data processing.
Lasers.
Photonics.
Biomedical engineering.
Signal processing.
Image processing.
Speech processing systems.
Materials science.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Introduction
  • 1. Ultrasonic Reflection Imaging
  • 2. Diffraction from a Circular Aperture
  • 3. The Arccos & Lommel Diffraction Formulations
  • 4. One-way and Two-way Diffraction
  • 5. Spatial Averaging
  • 6. The Need for Diffraction Correction
  • 7. Mathematical Definitions
  • 8. Scope and Assumptions
  • 9. Preview
  • 10. Criticism and Counter
  • 2. Literature Review
  • 1. Ultrasonic Reflection Imaging
  • 2. Diffraction from a Circular Aperture
  • 3. Spatially Averaged Diffraction Corrections
  • 4. Short-Time Fourier Techniques
  • 5. Short-Time Fourier Techniques in Ultrasound
  • 6. Chapter Summary
  • 3. Two Diffraction Formulations
  • 1. The Lommel Diffraction Formulation
  • 2. Discussion of the Lommel Diffraction Formulation
  • 3. The Arccos Diffraction Formulation
  • 4. Discussion of the Arccos Diffraction Formulation
  • 5. Similarities and Differences
  • 6. An Approximate Fourier Transform Pair
  • 7. Verification
  • 8. Computational Considerations
  • 9. The Focused Case
  • 10. Chapter Summary
  • 4. Spatially Averaged one-way Diffraction
  • 1. Spatially Averaged Arccos Diffraction Formulation
  • 2. Analysis of Time-Domain Results
  • 3. Spatially Averaged Lommel Diffraction Formulation
  • 4. Analysis of Frequency-Domain Results
  • 5. Extending Fourier Equivalence
  • 6. Verification
  • 7. Computational Considerations
  • 8. Chapter Summary
  • 5. Spatially Averaged two-way Diffraction
  • 1. Spatially Averaged Arccos Diffraction Formulation
  • 2. Spatially Averaged Lommel Diffraction Formulation
  • 3. Analysis of Frequency-Domain Results
  • 4. Extending Fourier Equivalence
  • 5. Verification
  • 6. Computational Considerations
  • 7. Chapter Summary
  • 6. Experimental Investigation
  • 1. A Computational Consideration
  • 2. Equipment and Processing
  • 3. Experiments, Images, and Centroids
  • 4. Discussion of Results
  • 5. Chapter Summary
  • 7. Analytical Investigation
  • 1. Diffraction and Linear Models
  • 2. Harmonic Imaging and Non-Linear Ultrasound
  • 3. Focused One-Way Results
  • 4. Coherent vs. Incoherent Averaging
  • 5. Mirror-Image vs. Autoconvolution Diffraction
  • 6. Chapter Summary
  • 8. Recommendations for Further Research
  • 1. General
  • 2. Fourier Equivalence
  • 3. Spatially Averaged One-Way Diffraction
  • 4. Spatially Averaged Autoconvolution Diffraction
  • 5. More Experiments and Analysis.

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