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

w_i 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

**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
w_i	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

Source LaTeX | All tables | In the text

	1 Introduction
	2 Derivation
	3 Spectral dependence
	4 n ${\pi }$ ambiguities and the RMTF
	5 RM-synthesis with only Q or U
	6 General experiment layout
	7 Conclusions
	References
	Online Material
	Appendix A: Standard errors in RM estimations
	Appendix B: Example simulations