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A real positive photoresist pattern usually has finite edge slope and rounding rather than mathematically sharp vertical steps. The optical aerial image and finite resist contrast give a graded exposure boundary. Absorption through the film, focus, reflections from silicon and development kinetics can make the opening narrower or wider at different heights.

Incomplete development can leave residual material at the floor; standing-wave exposure can cause sidewall ripples, and substrate-related chemistry can produce footing. Bake history and developer transport can modify corners and line width. An undercut can be engineered with a suitable resist stack, but it is not an automatic consequence of ordinary positive-tone processing. The final profile must therefore be measured rather than inferred solely from the mask artwork.

On a graph of normalized remaining thickness against ${\log }_{10}D$, both positive photoresist curves remain near unity below $D_0$ and fall to zero by $D_c$. Their transition widths are ${\log }_{10}(D_c/D_0)=1/\gamma$: $0.752$ decades for the lower-contrast material and $0.177$ decades for the higher-contrast material. The latter therefore has a much steeper transition. The curves can be aligned at a common illustrative clearing dose; their absolute horizontal placement cannot be inferred from photoresist contrast alone.

The higher-contrast material distinguishes bright and dark regions even when diffraction has reduced their intensity modulation. The lower-contrast material requires a much stronger aerial-image modulation and loses small features earlier. Finite resist thickness, standing waves, acid diffusion, development conditions and photon statistics can limit actual performance beyond this threshold model.

For a positive photoresist, let $D_0$ be the largest exposure preserving the initial film thickness and $D_c$ the clearing dose. The photoresist contrast is $\gamma =1/{\log }_{10}(D_c/D_0)$. An aerial image $I=\bar{I}[1+M\cos (2\pi \nu x)]$ can clear its maxima while retaining its minima only ifThus $M_c=0.6991$ and $0.2006$ for the lower- and higher-contrast materials. Reading those levels on the supplied modulation transfer function gives maximum normalized spatial frequencies approximately $\nu /{\nu }_0=0.40$ and $0.60$, respectively. The stated partial coherence is already represented by that curve; do not multiply the read frequencies by another coherence factor.

The unambiguous pattern dimensions are full pitch $P=1/(x{\nu }_0)$ and equal line/space width $w=P/2$, where $x$ is the read normalized frequency. To convert the paper's Rayleigh-frequency label into lengths, explicitly use the circular-pupil Rayleigh criterion $d_R=0.61\lambda /NA$ and ${\nu }_0=1/d_R$. With the ArF vacuum wavelength $193\mathrm{nm}$ and the stated numerical aperture, $d_R=235.5\mathrm{nm}$, givingThe higher-contrast material resolves a line/space feature about two-thirds as wide. The pitch and half-pitch distinction matters: the point-separation Rayleigh criterion is not itself an equal-line/space width. If a course defines ${\nu }_0$ as an optical cutoff rather than $1/d_R$, use that specified frequency in $w=1/(2x{\nu }_0)$; the normalized graph readings and their ratio are unchanged. No absolute clearing dose is provided.