Tomography (UMAP)

This module will give students: 1) an aquaintance with a significant applied math problem utilizing Fourier Transforms; 2) a generalization of the Fourier Transforms to two dimensions; 3) practice with Fourier Transforms; and 4) an introduction to the Hankel Transform.

Table of Contents:

1. THE PROBLEM

2. NOTATION

3. BACK PROJECTION: AN APPROXIMATION

4. FOURIER TRANSFORM NOTATION

5. THE EXACT SOLUTION

6. THE BASIC THEOREM

7. CIRCULAR SYMMETRY

8. THE CIRCULARLY ASYMMETRIC CASE

9. HISTORICAL AND BIBLIOGRAPHICAL NOTE

10. ANSWERS AND SUGGESTIONS TO EXERCISES