Joe is designing a new CT scanner. It will be a fan-beam design, with one source and...

Joe is designing a new CT scanner. It will be a fan-beam design, with one source and D detectors. He will use M angles, reconstruct images with N by N pixels, and strictly enforce the design rule of thumb D = M = N. The width of each detector d will be selected to be as large as possible in order to completely fill a 1 meter detector array with D detectors. The reconstruction ramp filter will be designed using a rectangular window with bandwidth

(a) Joe requires that a lesion with contrast C = 0.005 embedded in water will have a SNR of at least 20 dB. Suppose D = M = N = 300. What is the minimum number of photons per projection at

the detectors that is required in order to meet this SNR constraint.

(b) Assume the patient has 0.125 m² cross-sectional area (lying completely in each fan beam). Assume that the patient is exposed to 1 roentgen when 2.5 × 10¹⁰ photons pass through 1 cm² of tissue, and assume that the dose to the patient in rads is equal to the exposure in roentgens. What is the largest D(= M = N) that can be selected which will satisfy the SNR requirement of part (a) and will keep the total dose for the entire cross-sectional scan less than or equal to 2 rads. (Neglect attenuation due to the patient and assume the detectors have 100% efficiency.)