1. Computed Tomography Principles
Ge Wang, Ph.D. Department of Radiology University of Iowa Iowa City, Iowa 52242, USA

2. Learning Objectives CT terms Data acquisition
Basic elements of CT scanner
Scanning modes
Image reconstruction
Spiral/helical CT
Image resolution and artifacts
Interaction among imaging parameters
Quality assurance
Radiation exposure

3. A Little Bit History
Nobel prizes Roentgen (1901): Discovery of X-rays Hounsfield & Cormack (1979): Computed tomography

4. Computed Tomography Principles
1. Projection measurement
2. Scanning modes
3. Scanner systems
4. Image reconstruction

5. X-ray Interactions - Photoelectric Effect
(From Aracor)
Photoelectric effect results in total absorption of
the X-ray photon and the emission of a bound electron

6. X-ray Interactions - Compton Scatter
(From Aracor)
Compton Scatter results in a free electron &
a scattered (less energetic) photon

7. Source and Detectors
Source - Rotating anode disk - Small focal spot down to 0.6 mm - Polychromatic beam Detectors - Xenon (50-60%) - Scintillation (>90%)
(From Siemens)

8. Exponential Attenuation of X-rayNi No m
Ni: input intensity of X-ray
No: output intensity of X-ray
m: linear X-ray attenuation x Ni No    x
Attenuated more
X-rays

9. Ray-Sum of X-ray AttenuationNi No k x
Ray-sum
Line integral

10. Projection & Sinogram  y P(t) t p  x f(x,y) t X-rays Sinogram
Projection: All ray-sums in a direction
Sinogram: All projections  y
P(t) t p  x
f(x,y) t
X-rays
Sinogram

11. Completeness Condition
There exists at least a source on any line
intersecting a cross-section

12. Computed Tomography Principles
1. Projection measurement
2. Scanning modes
3. Scanner systems
4. Image reconstruction

13. First Generation
One detector
Translation-rotation
Parallel-beam

14. Second Generation Multiple detectors Translation-rotation
Small fan-beam

15. Third Generation Multiple detectors Translation-rotation
Large fan-beam

16. Fourth Generation
Detector ring
Source-rotation
Large fan-beam

17. Third & Fourth Generations
(From Picker)
(From Siemens)

18. Spiral/Helical Scanning
Simultaneous
Source rotation
Table translation
Data acquisition

19. Cone-Beam Geometry

20. Scanning modes First generation One detector, translation-rotation
Parallel-beam
Second generation
Multiple detectors, translation-rotation
Small fan-beam
Third generation
Multiple detectors, rotation-rotation
Large fan-beam

21. Scanning modes Fourth generation Detector ring, source-rotation
Large fan-beam
Spiral/Helical scanning, cone-beam geometry

22. Computed Tomography Principles
1. Projection measurement
2. Scanning modes
3. Scanner systems
4. Image reconstruction

23. Spiral CT Scanner Network Gantry Source Computer Parallel processor
Display
Control
console
Table
Recording
Detectors
Data acquisition
system
Storage units:
Tapes, disks

24. Data Acquisition System (DAS)
Pre-Collimator
Post-Collimator
Scattering
Source
Detector
Filter
Patient

25. Data Acquisition System (DAS)
X-ray Tube
Source
Filter
Detectors
CT Gantry (From Siemens)
Detector

26. Spiral CT Scanner Gantry Data acquisition system Table Computer
Parallel processors
Control console
Storage units
Tapes, disks
Recording device
Network interface
X-ray generator
Heat exchanger
(From Elscint)

27. E-Beam CT Scanner Speed: 50, 100 ms Thickness: 1.5, 3, 6, 10 mm
ECG trigger cardiac images
(From Imatron)

28. Computed Tomography Principles
1. Projection measurement
2. Scanning modes
3. Scanner systems
4. Image reconstruction

29. Computed Tomography y
Computed tomography (CT): Image reconstruction from projections t
P(t)
P(t)
f(x,y)  x
f(x,y)
X-rays

30. Reconstruction Idea
=4
2=3
3=2
4=1

31. Algebraic Reconstruction Technique (ART)3 2 4 1 6 -2
Update a guess based on data differences
Guess 1
Guess 0
Guess 2
Error

32. Fourier Transformation
f(x,y)
F(u,v)
Fourier
Transform
Image
Space
Fourier
Space

33. Fourier Slice Theorem y P(t) v t F[P(t)]   u x F(u,v) f(x,y)
X-rays v
F[P(t)]  u
F(u,v)

34. From Projections to Imagey x v u
F-1[F(u,v)]
f(x,y)
P(t)
F(u,v)

35. Filtered Backprojection
f(x,y)
P(t)
P’(t)
1) Convolve projections with a filter
2) Backproject filtered projections

36. Example: Projection
Projection
Projection
Sinogram
Ideal Image

37. Example: Backprojection

38. Example: Backprojection
Sinogram
Backprojected Image

39. Example: Filtering
Sinogram
Filtered Sinogram

40. Example: Filtered Backprojection
Filtered Sinogram
Reconstructed Image

41. References
T. S. Curry III, J. E. Dowdey, R. C. Murry Jr. Christensen’s physics of diagnostic Radiology (4th edition), Lea & Febiger (for residents)
G. Wang, M. W. Vannier: Computerized tomography. Encyclopedia of Electrical and Electronics Engineering, edited by Webster JG, to be published by John Wiley & Sons (for engineers)
(on-line slides & handouts in the Teaching section)