# The MRI signal: why do we consider the phase in the MRI signal

I am trying to understand the imaging principles behind MRI and I was looking at some lecture slides found here

Specifically, I am looking at slide 41 where we look at some of the equations regarding the MRI signal.

I understand that when a proton is subjected to an external magnetic field, it precesses with an angular frequency which is proportional to the field strength. This is given by the Larmor equation.

$$\omega = \gamma B_0$$

Ignoring the other gradient components (to altar the main magnetic field at some spatial points), we see that the instantaneous phase would just be the integral of this frequency:

$$\phi(t) = \int \gamma B_0 dt$$

Now the signal given by one of the spin particles (elemental signal in the lecture) is given by:

$$s(t) = \rho \exp (i \phi(t))$$

where $\rho$ is the magnetization from the particle. I do not understand why this exponential term is there. Basically, why does the MRI signal contribution from a particle have this form? It is not intuitive to me at all. I think it might have something to do with the quadrature detection but I am not convinced at all at the moment.

MRI signal is always complex and it is related with signal demodulation. The detected signal is multiplied by a sinusoid or cosinusoid with frequency equals to $\omega_0 +\delta \omega$, respectively leading to the real and imaginary channels. You can find the complete algebra at $Haacke,\ Magnetic\ resonance\ imaging$ chapter 7.3.3