Derive an expression for the depth resolution in the far field as a function of z0.

An L × L ultrasound transducer is centered at the origin and pointing in the +z direction. The narrowband signal generated by the transducer has an envelope

 

Two point scatterers with reflectivity of R are located at (0, 0, z0) and (0, 0, z0 + z). Ignore attenuation and multiple reflections.

(a) Assume the scatterers are within the region where the geometric assumption holds and find the estimated reflectivity Rˆ (x, y, z).

(b) How far should the scatterers be separated in order for the imaging system to distinguish them?

(c) If the scatterers are in the far field where the Fraunhofer approximation holds, what would be the estimated reflectivity Rˆ (x, y, z)?

(d) Derive an expression for the depth resolution in the far field as a function of z0.

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….