1) Suppose that we are imaging a body with a line source x-ray imaging system to diagnose a diseased tissue as shown below. The thicknesses of tissue 1 is " = 1.5 cm and tissue 2 is ( = 4 . The estimated diseased tissue length , = 1 . The linear attenuation coefficients of these three tissues are " = 0.15 /", ( = 0.45 /" and , = 0.75 /".
a) Find the detected intensity when rays pass through the diseased tissue. This is the “target” intensity, 2. Find the detected intensity when rays pass through tissue 1 and 2 (but not through the diseased tissue). This is the “background” intensity, 3. Then, calculate the local contrast of the diseased tissue. Assume narrow beam geometry with monoenergetic x-ray photons.
b) Consider that there are sensitive tissues in the body that we would like to protect from x-ray exposure. We find two shields in the lab with thicknesses of Δ 6 = 5 and Δ 3 = 1.5 , with corresponding linear attenuation coefficients of 6 = 6.5 /", 3 = 17 /". We want the shield to provide at most 5% transmission (i.e., at least 95% attenuation of x-ray photons). Explain whether any of these shields meet this requirement.
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2) A uniform hexagon with side length = 20 and vertex to vertex length = 40 is being imaged with a point source x-ray imaging system, = 2 away from the detector. The object with linear attenuation coefficient ; = 0.03 /" is placed between the source and the detector as shown below. Assuming ; is the intensity of the incident beam, formulate the intensity on the detector along the x-axis, 2( ) for " = 0.5 and " = 1.5 , separately. Do not ignore obliquities.
3) MATLAB Question: Include your MATLAB codes in your solution.
For Question 2, assume that the detector has a size of 128 with 512 elements on it (i.e., it generates an x-ray image of 512 pixels). We place the object at the two locations indicated in Question 2 (i.e., " = 0.5 and " = 1.5 ) and take x-ray images separately for those two cases.
a) Plot the 1-D normalized intensity profiles (i.e., AB C) for these two cases.
