= Solution
Take the ArF wavelength as $\lambda=193\,\mathrm{nm}$ and assume an \b[on-axis coherent illuminator]. A grating of period $P$ has diffraction orders with transverse spatial frequencies $m/P$. To reproduce amplitude modulation, the pupil must pass the zero order and at least the first spatial-frequency components. For symmetric on-axis illumination this requires $1/P<\mathrm{NA}/\lambda$.
For equal lines and spaces, the printed feature width is the half-pitch $w=P/2$. The ideal limiting values are therefore
$$
\boxed{w_{\min}=\frac{\lambda}{2\mathrm{NA}}=\frac{193}{1.2}=161\,\mathrm{nm}},\qquad
\boxed{P_{\min}=322\,\mathrm{nm}}.
$$
These are limiting values approached from within the pupil, with adequate mask contrast and a suitable resist; a weakly modulated mask need not supply sufficient image contrast. They are not the Rayleigh separation of two incoherent point objects. Off-axis coherent illumination can shift the admitted orders and changes this particular geometry.
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