Optical Lithography Resolution

How small a feature a projection scanner can print. A reticle (mask) pattern is imaged through a lens of numerical aperture $\mathrm{NA}$ at wavelength $\lambda$. The lens pupil passes only spatial frequencies $|f|\le \mathrm{NA}/\lambda$, so the aerial image is $I(x)=\big|\,\mathcal F^{-1}[\,\mathrm{pupil}(f)\,\mathcal F\{t\}(f)\,]\big|^2$ and the resolvable half-pitch is the Rayleigh limit $R=k_1\lambda/\mathrm{NA}$. The reticle here is a line/space test pattern whose half-pitch shrinks left to right; in the aerial image the coarse zones print crisply and the zones finer than $R$ blur to flat grey. The bottom bars are the per-zone contrast (red once a zone is below the Rayleigh limit). Switch the wavelength from i-line (365 nm) through DUV/ArF (193 nm) to EUV (13.5 nm) and watch the resolvable pitch collapse: smaller $\lambda$ is sharper. Everything is closed form (gate-tested).