Table 1: List of symbols.
Symbol Description
$\chi $ Polarization angle (N through E)
$\chi_0$ Polarization angle at $\lambda=0$
$\nu$ Frequency
$\delta\nu$ Channel width in frequency
$\nu_{\rm c}$ Central frequency of a channel
$\lambda$ Wavelength
$\lambda_0$ Wavelength to which all polarization vectors are derotated
$\lambda_{\rm c}^2$ Central wavelength squared of a channel
$\delta\lambda^2$ Channel width in wavelength squared
$\Delta\lambda^2$ Total bandwidth in wavelength squared. $\Delta\lambda^2 = \lambda^2_{\rm max} - \lambda^2_{\rm min}$
$\phi $ Faraday depth
$\delta\phi$ FWHM of the main peak of the RMTF
$\mbox{RM}$ Rotation measure
$W(\lambda^2)$ Weight function
wi Weight of the ith data point
K One over the integral of W or one over the sum of weights
$F(\phi)$ Faraday dispersion function without spectral dependence
$\tilde{F}(\phi)$ Reconstructed approximation to $F(\phi)$
$F(\phi, \lambda^2)$ General form of the Faraday dispersion function
$f(\phi)$ $F(\phi,\lambda^2)/s(\lambda^2)$
$s(\lambda^2)$ Spectral dependence in I, normalized to unity at $\lambda^2 = \lambda^2_0$
$\alpha$ Frequency spectral index
$P(\lambda ^2)$ Complex polarized surface brightness
$\tilde{P}(\lambda^2)$ Observed P: $W(\lambda^2)P(\lambda^2)$
$p(\lambda^2)$ Complex polarization fraction $P(\lambda^2)/I(\lambda^2)$
$R(\phi)$ Rotation Measure Transfer Function (RMTF)
$\vec{B}$ Magnetic induction
$\vec{r}$ Position vector
$n_{\rm e}$ Thermal electron density
$\gamma$ Spectral index of the relativistic electron energy distribution
$\Re z$ Real part of z
$\Im z$ Imaginary part of z
$\rho $ Merit function for traditional linear least squares fitting of rotation
measures. Defined in Eq. (49)
$\sigma$ rms noise in a single channel map
$\sigma_{\rm Q}$, $\sigma_{\rm U}$ rms noise in single Q or U channel maps
$\sigma_{\rm P}$, $\sigma_\chi$ Standard error of $\Vert P\Vert$ and $\chi $ in individual channel maps
$\sigma_\phi$, $\sigma_{\chi_0}$ Standard error in Faraday depth and position angle at $\lambda=0$
$\sigma_{\lambda^2}$ Standard deviation of the distribution of $\lambda ^2$ values that are sampled.
This is a measure of the effective width of the $\lambda ^2$ sampling
$\delta(x)$ Dirac delta function

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