Question

6.13 Consider the object in Figure P6.1 that is an equilateral triangle centered at the origin, each side of which is of length a and one side of which is parallel to the x axis. Suppose the object has constant linear attenuation coefficient u and is being imaged in a 16 CT scanner. Assume u = 1 and a = 6. a A (0,0) (a) Find a formula for the projection g(1,60%) and sketch it. (b) What is the value of b60(0,a/4) for g(l, 60°)? (c) Find Flo cos 60°, e sin 60°).

Answer 1

6:13) Griven le=1 and a=6 height of Equilateral triangle a a = 3 2 110,0) 7 ♡ fig P6.1 a) As we know Formula for Projection g14,60)= {Br(2+1), -aclso 134(1-1) o clear otherwise -3<lso old< 3 (3 (3 te V3 (3-2) otherwise 0 69(1,60) Sketch of projection of fig.p6.1 Bra l alr al g (1,60°) 383 3 -3

- 8 Ba b) we have 1600(0,9%) = g(0 cos 60 ta a sin60, 60) Ba, 600) = Bula V3 40 (4-13) 8 EBX6 (4-13) 8 bor(0,0%) 2.9461 ท otherwise Otherwise 2 g c). Let function fit be defined by scaling a red functie f(t)={K - 9545 Convolution f(t) *f(t) = Sk?(n+t) -nstson K2(n-t) osts ne comparing with g (1,60), we find that it is a consolution of function fil) with itself where K²= Br, and (4,60) = voureet (29)* Veurec (347 By the projection of slice theorem Flecoso, & sine) = G (0,0) = + (314,03} g 11, 60) is a con volution of rect with itsells f(0, 61, 60°)3=[+{13751 rect ( 34)} J-Papa'sinlage }{3,4,603) = [}{3134 sect (13)}) - vg de sine ( 'Flocosso, ai singo)= vBu a " since they We get 1 therefore, 915.58 sind? (38)

- 8 Ba b) we have 1600(0,9%) = g(0 cos 60 ta a sin60, 60) Ba, 600) = Bula V3 40 (4-13) 8 EBX6 (4-13) 8 bor(0,0%) 2.9461 ท otherwise Otherwise 2 g c). Let function fit be defined by scaling a red functie f(t)={K - 9545 Convolution f(t) *f(t) = Sk?(n+t) -nstson K2(n-t) osts ne comparing with g (1,60), we find that it is a consolution of function fil) with itself where K²= Br, and (4,60) = voureet (29)* Veurec (347 By the projection of slice theorem Flecoso, & sine) = G (0,0) = + (314,03} g 11, 60) is a con volution of rect with itsells f(0, 61, 60°)3=[+{13751 rect ( 34)} J-Papa'sinlage }{3,4,603) = [}{3134 sect (13)}) - vg de sine ( 'Flocosso, ai singo)= vBu a " since they We get 1 therefore, 915.58 sind? (38)