**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	$8 \times 10^{-3}$

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