Problem

A first-generation CT scanner is used to image a unit-square shaped object (i.e, len...

A first-generation CT scanner is used to image a unit-square shaped object (i.e, length of each side = 1). The object is surrounded by air and has a constant linear attenuation coefficient of μ₀ .The coordinate system is set up such that the origin is at the object center, and the x- and y-axes are parallel to the sides of the object.

(a) Write a mathematical expression for the linear attenuation function μ(x, y). (Hint: Use the rect function.)

(b) What is the Fourier transform of μ(x, y)?

(c) Write a mathematical relationship between the projection (computed using the observed x-ray intensities) and μ(x, y).

(d) Using the projection-slice theorem, find

(e) Take the inverse Fourier transform of to find an expression for

(f) Sketch (include axis labels) and sketch its backprojection image b_30° (x, y).