Problem

A square object with side-width of 40 cm is imaged by a first generation CT scanner....

A square object with side-width of 40 cm is imaged by a first generation CT scanner.

(a) What type of collimators should be used for the source and the detector?

(b) What is the smallest circular FOV to cover the entire object?

(c) Suppose the smallest angular increment of the scanner is 0.25° and we strictly obey the CT ‘‘rule of thumb.’’ How many line integrals should we measure for each angle? If the reconstructed image is just large enough to cover the FOV, what is the size of the pixels?

(d) We found that the reconstructed image was noisy. Is it possible to double the SNR given that we cannot change the 0.25-degree angular increment and will not violate the rule of thumb? Explain.

(e) Suppose the object has a constant linear attenuation coefficient of 0.1 cm⁻¹, sketch and carefully label the axes.

(f) Sketch b₄₅° (x, y). Find the value b₄₅° (10, 10).