1. In Figure 1.40, calculate the X-ray intensity, as a function of the incident intensity l0. that reaches the film for each of the three X-ray beams. The dark-shaded area represents hone and the light-shaded area represents tissue. The linear attenuation coefficients at the effective X-ray energy of 68 keV are 10 and 1 cm-1 for bone and tissue, respectively.
2. Explain why μbone >> μtissue at low X-ray energies. but the two values of μ become closer as the X-ray energy increases.
3. The linear attenuation coefficient of a gadolinium-based phosphor used for detection of X-rays is 560 cm at an X-ray energy of 150 keV. What percentage of X-rays are detected by phosphor layers of 100, 250 and 500 μm thickness?
What are the tradeoffs in terms of spatial resolution?
4. In Figure 1.41, calculate the relative intensities of the signals S1, S2 and S3 produced by each crystal. The value of μtissue is 0.5 cm-1, and is 0.5 cm-1, μbone is 1 cm-1 and μcrystal is 2 cm-1.
5. Intensifying screens can be placed on both sides of the X-ray film (double-sided) or on one side only (single-sided). Explain why double-sided screens give a higher image SNR, but single-sided screens have a better spatial resolution.
6. An X-ray with energy 60 keV strike: a gadolinium based intensifying screen, producing photons at a wavelength of 415 run. The energy conversion coefficient for this process is 20%, How many photons are produced for each incident X-ray?
7. In mammographic examinations, the breast is compressed between two plates, as shown in Figure 1.42. Answer the following with a brief explanation:
(a) Is the geometric unsharpacss increased or decreased by compression?
(b) Why is the image contrast improved by this procedure?
(c) Is the required X-ray dose for a given image SNR higher or lower with compression?
8. For the two X-ray film characteristic curves shown in Figure 1.43
(a) Which one corresponds to the film with the higher speed?
9. Considering the effects of beam hardening, draw the actual CT projection that would be obtained from the sample in Exercise 1.14.
10. Sketch the final image that would be formed filtered backprojection of all of the projections acquired in a full scan of the sample in Exercise 1.14.
11. For the set of projections shown in Figure 1.45, perform one series of a ray-by-ray itcration on the horizontal. the. diagonal, and the vertical projections. Calculate the minimum squared error alter each iteration.
12. For the object shown in figure B1 (Appendix B), draw the projections that would he acquired at angles Φ = 0.45, 90, 135, and 180.
13. For the object shown in Figure 1.46, sketch the sinogram for values of Φ from 0 to 360o.