Show that the time delay for a point (x0, y0, 0) on the flat face is approximately as below

A transducer can be focused by curving the crystal to conform to the shape of a sphere, as shown in Figure P10.1. To analyze the field pattern, however, it is convenient to assume that the transducer is flat but that we can independently control the time delay of each element on its face. Assume that the point (xm, ym, 0) is the point farthest out on the flat face.

(a) Show that the time delay for a point (x0, y0, 0) on the flat face is approximately

where  m and d is the desired focal depth.

(b) Use the steady-state approximation and show that at z = d the Fresnel field pattern is

where S(u, v) is the 2-D Fourier transform of s(x, y)

(c) Discuss the merits of focusing.

Figure P10.1 Geometry of curved transducer for Problem 10.16.


find the cost of your paper

Explain why attenuation is not a big problem in PET.

Consider a 2-D object consisting of two triangle compartments, as shown in Figure P9.4. Suppose a solution containing a 511 KeV gamma ray emitting radionuclide with concentration f = 0.5….

Give the mean and the variance of the reconstructed image, mean[ˆ f(x, y)] and var[ˆ f(x, y)].

Ignoring the inverse square law and attenuation, an approximate reconstruction for SPECT imaging is given by where c˜() =  {||W()} and W() is a rectangular windowing filter that cuts off at = 0…..

Find the numerical responses in each to an event in crystal C(4, 6).

Suppose a PET detector comprises four square PMTs (arranged as a 2 by 2 matrix) and a single BGO crystal with slits made in such a way that it is….