polarized intensity $P(\lambda^2)$ as a function of wavelength $\lambda$ is expressed as, $$\begin{aligned}
\label{eq:PI}
P(\lambda^2)
&=& p(\lambda^2)I(\lambda^2) \nonumber \\
&=& Q(\lambda^2)+iU(\lambda^2) \nonumber \\
&=& \int_{-\infty}^{+\infty}F(\phi)e^{2i\phi\lambda^2} d\phi,\end{aligned}$$ where $p$ is the complex fractional polarization, and $I$, $Q$, and $U$ are the Stokes parameters. $F(\phi)$ is the Faraday dispersion function (FDF), which is a complex polarized intensity as a function of Faraday depth $\phi$. The Faraday depth (or the RM when the FDF consists of a single delta function) is defined as $$\label{eq:FD}
\phi(x)
= 810 \int_x^0 \left( \frac{n_{\rm e} (x')}{1~{\rm cm}^{-3}} \right)
               \left( \frac{B_\parallel(x')}{1~\mu {\rm G}} \right)
               \left( \frac{dx'}{1~{\rm kpc}} \right) ~ {\rm rad/m^2},$$ where $n_{\rm e}$ is the electron density, $B_\parallel$ the LOS component of magnetic fields, $x'$ the physical distance, and $x$ is the distance to a source from an observer at $x'=0$.

The FDF can be reconstructed by the inverted equation of Eq. (\[eq:PI\]): $$\label{eq:FDF}
F(\phi)
=\int_{-\infty}^{+\infty}P(\lambda^2)e^{-2i\phi\lambda^2}d\lambda^2.$$ This transform is called Faraday RM synthesis, which gives the FDF from observed $P(\lambda^2)$.

It should be noted that there is, in general, no one-to-one correspondence between $\phi$ and $x$. The FDF thus does not straightforwardly give the distribution of polarized intensity in physical space. Nevertheless, the distribution of magnetic fields 