3. $T_{2}^{*}$-decay
The $T_{2}^{*}$-decay is the signal decay produced by microscopic distribution of off-resonance.
The exact distribution of off-resonance is
$$p_{\Delta w}(w) = \frac{T_2^{'}}{\pi(1+T_2^{'2} w^2)},\quad\text{with }\frac{1}{T_2^{*}} = \frac{1}{T_2} + \frac{1}{T_2^{'}}.$$
In this excercise we will simplify this distribution, but we will obtain a similar effect.
(3.1) Create a new phantom named obj_t2star with spins at the same positions as the original phantom obj, each having a linear distribution of off-resonance. To achieve this, follow these steps:
(3.1.1) Create an empty phantom called obj_t2star.
(3.1.2) Create a linear off-resonance distribution such that the range $2\pi [-10, 10]\,\mathrm{rad/s}$ is covered uniformly with $N_{\mathrm{isochromats}} = 20$ (use the function range(start, stop, length)).
(3.1.3) Iterate over the elements off of the linear distribution (for loop) and create copies of the original phantom (obj_aux = copy(obj)) and set the off-resonance of that copy to off with obj_aux.Δw .= off.
(3.1.4) Update obj_t2star by appending the modified copies obj_aux (obj_t2star += obj_aux).
(3.1.5) Finally, outside the loop, divide the proton density obj_t2star.ρ by $N_{\mathrm{isochromats}} = 20$ and rename the phantom obj_t2star.name = "T2 star phantom".
(3.2) Plot obj_t2star with plot_phantom_map(obj_t2star, :Δw) and verify it is correct