Glossary

$\mathbb{L}$, $N$ One-dimensional grid, number of elements in  $\mathbb{L}$
$\mathbb{G}=\mathbb{L}\times\mathbb{L}$ Two-dimensional grid
$\mathbf{p}=(p,q)$ Two-dimensional integer vector
$\mathbf{x}=(x,y)$ Two-dimensional angular position variable
$\mathbf{u} = (u,v)$ Two-dimensional angular spatial frequency
$\Delta x$ Extension of the synthesized field
$\delta x$ Resolution scale of the synthesized field
$\Delta u$ Extension of the Fourier domain
$\delta u$ Basic Fourier sampling interval
$\mathbb{G} \delta x$, $\mathbb{G} \delta u$ Object grid, Fourier grid
$\mathcal{L}$ Global frequency list
$\mathcal{L}_e$, $\mathcal{L}_r$ Experimental frequency list, regularization frequency list
$\mathcal{H}$ Fourier domain  $[-\Delta u/2, \Delta u/2]$
$\mathcal{H}_s$ Frequency coverage to be synthesized
$\mathcal{D}_s$ Support of the neat beam $\Theta _s$
$\chi^2$ Energy confinement parameter
$\Theta _s$ Apodized point-spread function (neat beam)
$\Theta_d$ Instrumental point-spread function (dirty beam)
$H_o$, $e_{\mathbf{p}}(\mathbf{x})$ Object space, basis functions of $H_o$
$E$, $F$ Object representation space, image of $E$ by $A$
$K_e$, $K_d$ Experimental data space, data space
$W(\mathbf{u})$ Weighting function
$\rho(\mathbf{u})$, $\sigma_e(\mathbf{u})$ Redundancy of  $\mathbf{u}$, standard deviation of  $\Psi_{\! e}(\mathbf{u})$
$A$ Regularized Fourier sampling operator
$A_e$, $A_r$ Fourier sampling operator on  $\mathcal{L}_e$, on  $\mathcal{L}_r$
$P_E$, $A_E$ Projection operator onto $E$, restriction of $A$ to $E$
$\Phi_{\! o}$, $\Phi_{\! s}$ Original object function, image to be reconstructed
$\Phi _E$, $\delta\Phi_E$ Reconstructed image, reconstruction error on $\Phi _E$
$\Psi_{\! e}$, $\Psi_{\! s}$ Experimental data, damped experimental data
$\Psi_{\! d}$ Regularized data vector
$\Psi _F$, $\delta\Psi_F$ Projection of  $\Psi_{\! d}$ onto $F$, effective error on $\Psi _F$
$\lambda_k, \Phi_k$ Eigenvalue of  $A^*_E A^{\vphantom{*}}_E$ and related eigenmode
$\theta_k$ Separation angle between $\Phi _E$ and $\Phi_k$
$\lambda,\lambda'$ Smallest and largest eigenvalues of  $A^*_E A^{\vphantom{*}}_E$
$\kappa _E$ Condition number of $A_E$
$q(\phi)$ Regularized criterion
$q_e(\phi)$, $q_r(\phi)$ Experimental criterion, regularization criterion