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….

## Find the FWHM of the cascade system

In practice the spatial resolution in a clinical nuclear medicine image is determined by three factors: the intrinsic resolution of the camera (I), the collimator resolution (C), and patient effects (P). Suppose the impulse response could be modeled as arising from the cascade of three linear shift-invariant systems, one for each factor.

(a) Suppose each system has an impulse response given by a rect function, and suppose their widths are r_{I}, r_{c}, and r_{p}, respectively. Find the FWHM of the cascade system.

(b) Suppose each system has an impulse response given by a Gaussian, and suppose their standard deviations are σ_{I}, σ_{c}, and σ_{p}, respectively. Find the FWHM of the cascade system