Glossary

$\text{\boldmath$L$\unboldmath }$, N One-dimensional grid, number of elements in  $\text{\boldmath$L$\unboldmath }$
$\text{\boldmath$G$\unboldmath }=\text{\boldmath$L$\unboldmath }\times\text{\boldmath$L$\unboldmath }$ Two-dimensional grid
p=(p,q) Two-dimensional integer vector
x=(x,y) Two-dimensional angular position variable
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
$\text{\boldmath $G$\unboldmath}\,\delta x$, $\text{\boldmath $G$\unboldmath}\,\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_p(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(u) Weighting function
$\rho(\mathbf{u})$, $\sigma_e(\mathbf{u})$ Redundancy of  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