1. An experiment in computed tomography
Elliot Mylott
Ryan Klepetka
Justin Dunlap
Ralf Widenhorn
Previous undergraduate labs involving computed tomography have been designed around a laser rather than X-rays. These experiments, however, were composed of equipment not always easily found in an undergraduate lab. They have also required that the teacher or student have a certain level of computer programming experience. And finally, the amount of time spent on data collection and image processing was prohibitive for a typical lab session.
Buzug, Thorsten M. Computed Tomography: From Photon Statistics to Modern Cone-Beam CT
Physics Department
Portland State University, Portland, OR

2. Objectives To design a lab that Introduces students to CT
Utilizes light instead of X-rays
Requires little setup
Fast data collection and analysis
Reinforces concepts of light/matter interaction
Can highlight CT specific issues
It was our main goal, therefore, to design an experiment that served as an introduction to computed tomography that also required little time for preparation and data collection and analysis. With the reduction in scan time, students are now able to perform multiple scans of objects of differing sizes and locations. We were also able to highlight more computed tomography related topics than was previously possible.

3. An Example of X-rays and Projections for Students
X-ray film
Projections
X-ray tube
One of the limitations to X-rays is that they are 2D representations of a 3D object. Some spatial information is inherently lost. For example, let’s say we have a box, in which we know there are a sphere and a cone. The exact locations of the objects are unknown, so we can take an x-ray to determine them. Notice that the X-ray film is white. It is only after it has become exposed to the X-rays that it darkens.
So our X-ray image may look something like this. The X-ray image reflects the attenuation of the X-ray as it passed through the box. White areas signify complete attenuation and black complete transmission. These data are called projection. The image tells us some things about the contents, but other information is completely lost. Is the cone in front of the sphere or the sphere in front of the cone?
To find that out we can rotate the X-ray source and take another scan. The new image tells us even more about the contents. This illustrates the key idea behind CT: projection data from multiple X-rays taken at different locations can be put together to form an image of an obscured area.

4. CT and Back Projection
Projection Data
Projection Data
X-ray source rotates around an object accumulating projection data
Projection data reflect the attenuation of the X- ray by the object
Projection data is spread back onto a reconstructed image
Multiple scans from different angles result in an image of the original object
Projection Data 1
X-ray Source
Back projection is one of the simplest methods to create an image using CT and is the basis of our reconstruction algorithm. (click) In this process, the light or X-rays from the source is attenuated by objects in the scanned area, which is recorded as projection data. That data is spread onto a reconstruction along the original line. (click) When done for multiple angles an image of the original object forms. 1
Back projection image

5. An Example of Back Projection for Students
Three light sources on a cylinder
Shadows (projections) converge at the cylinder

6. Scanner Generations 1st Generation 2nd Generation 4th Generation
Translation & Rotation
Pencil Beam
Single Detector
Small Fan Beam
Small Detector Array
Rotation Only
Large Fan Beam
Stationary Detector Array
3rd Generation
Rotation Only
Large Fan Beam
Large Detector Array
Rotation Only
Pencil Beam (Simulated Fan Beam)
Single Detector (Simulated Large Detector Array)
One of the reasons for the long scan time in the previous experiments was that they were 1st generation scanners, which required both translation and rotation. (click) For our experiment we created what is effectively a 3rd generation scanner. Though our scanner has only a single pencil beam and detector, by rotating the photogate both the fan beam and detector array are simulated.

7. Hidden Objects
To further highlight the ability of CT scans to image areas, into which one would not normally be able to see. We built a small enclosure using a light filter mostly opaque in the visible spectrum, but nearly transparent to the near IR light of the photogate.

8. Apparatus
In addition to some standard equipment often found in undergraduate labs like stands, clamps and a rotating platform, we incorporated a Vernier photogate and rotary motion sensor, which we were able to program through LabVIEW using a LabPro board.

9. Comparison to X-ray CT Scanners
Rotate X-ray Source
In a X-ray based scanner, the X-ray source rotates about the scanned area. We built our scanner so that the enclosure rotates. This simplifies the apparatus design.
Rotate Scanned Area

10. Comparison to X-ray CT Scanners
Attenuation 1
X-ray tube
Photogate
Scan
Digital Projection Data
Analog Projection Data
X-ray based scanners produce analog projection data. Notice that for the uniform object in the grid, the attenuation is larger through the thickest section of the object. Since our scanner is based on a photogate, the projection data is digital. Zero when the photogate is unblocked and 1 when it is blocked.

11. Scanner Geometry Variables
FCD – distance between the center of the grid and the rotary motion sensor
θ - The angle between the rotary motion sensor and the x-axis
φ – The angle between the focal length line and the scanning line
Output
Equation for the scanning line (y=mx+b)
Rotational Axis y
IR Source
Scanning line
IR Detector
Focus-Center Distance (FCD)
In order to translate the data onto the reconstruction, we needed to find the equation of the scanning line. With the help of some simple geometry and trigonometry, we were able to do this using only the focal length and the angles theta and phi as inputs. x

12. LabVIEW Displays data in real time No programming experience needed
Can be adjusted for different computer speeds
Will be available as an .exe file

13. Creating an Image
For this scan we placed two objects inside the enclosure as shown in the picture on the left. (click) The two thick lines are the back projections of the two objects inside the filter. (click) The thin lines are caused by the enclosure. (click) After multiple scans the lines caused by the enclosure form a ring on the final image in the same position as the enclosure itself.

14. Creating an Image
Original Positions
Final Reconstruction
θ=360
θ=180

15. CT Concepts - Artifacts
Back projection results in additional, unwanted data.

16. CT Concepts -Windowing
Change in Gray Scale Value

17. Conclusion
In conclusion, we have developed a lab which introduces students to multiple topics relevant to computed tomography, but which is simple to reconstruct. Thank you!