Table 3: Theoretical formulae for the physical resolution ${\cal R}_Z$ in the vertical direction as functions of the number M of source points,s-parameter and disc semi-thickness h. The last column corresponds to a 3-point, finite-difference method.
        Finite-diff.
    This method methods
Aspect     $z \rightarrow \pm h$  
ratio Z $z \rightarrow Z$ $(z ~ \ne Z)$  
  $\ne 0$ $\frac{1\pm\frac{Z}{h}}{2s(M-1)^{1/s}}$ $\frac{1\pm\frac{Z}{h}}{2s(M-1)}$  
$\frac{h}{R} \ge 1$       $\frac{1}{M-1}$
  0 $\frac{1}{s}\left(\frac{2^{1-s}}{M-1}\right)^{1/s}$ $\frac{1}{s(M-1)}$  
$\left(\frac{h}{R}\right)^2 \ll 1$ any $\frac{1}{s}\left(\frac{2^{1-s}}{M-1}\right)^{1/s}$ $\frac{1}{s(M-1)}$ $\frac{1}{M-1}$
examples        
(M,s)        
$(8,\frac{1}{2})$   0.08 0.28 0.14
$(32,\frac{1}{2})$   $4 \times 10^{-3}$ 0.06 0.03
$(128,\frac{1}{2})$   $2 \times 10^{-4}$ 0.02 $8 \times 10^{-3}$
$(128,\frac{1}{4})$   10-7 0.03 $8 \times 10^{-3}$

Source LaTeX | All tables | In the text