= Solution
For a positive <photoresist>, let $D_r$ be the largest dose retaining the nominal film and $D_c$ the clearing dose. With the conventional <photoresist contrast> definition,
$$
\gamma=\left[\log_{10}(D_c/D_r)\right]^{-1},\qquad r=\frac{D_c}{D_r}=10^{1/\gamma}.
$$
For a sinusoidal aerial image, the bright-to-dark dose ratio is $(1+C)/(1-C)$, where $C$ is the <Michelson contrast>. A dose window that clears bright regions while retaining dark regions requires
$$
\frac{1+C}{1-C}\geq r,\qquad
\boxed{C_{\min}=\frac{10^{1/\gamma}-1}{10^{1/\gamma}+1}}.
$$
This assumes a fully modulated input pattern and that the plotted <modulation transfer function> gives the aerial-image contrast. It is a dose-window criterion, not a statement that the resist creates optical information absent from the image.<Contrast and Important Properties by Heinrich Kirchauer>[§2.6.1, equation 2.6: logarithmic resist-dose contrast]{ref}
The two thresholds are approximately
$$
\gamma=1.05:\ C_{\min}=0.799,\qquad
\gamma=3.72:\ C_{\min}=0.300.
$$
Reading their intersections with the supplied curve gives, to graphical accuracy,
$$
\boxed{\nu_{\max}\simeq0.40\nu_0\quad\text{and}\quad0.60\nu_0}
$$
for the lower- and higher-contrast resists respectively. These are the results independent of the dimensional frequency convention. Their minimum full periods are $P=1/\nu$, and equal line/space widths are half those periods:
$$
\boxed{P_{\min}\simeq\frac{2.50}{\nu_0},\ \frac{1.67}{\nu_0};\qquad
w_{\min}\simeq\frac{1.25}{\nu_0},\ \frac{0.833}{\nu_0}}.
$$
An ArF <excimer laser> uses $\lambda\simeq193\,\mathrm{nm}$. A numerical length requires specifying what the caption's “Rayleigh limit” means. Taking it literally as the reciprocal of the <Rayleigh criterion> point separation gives
$$
R_R=\frac{0.61\lambda}{\mathrm{NA}}=294.3\,\mathrm{nm},\qquad \nu_0=1/R_R,
$$
$$
\boxed{P_{\min}\simeq736,\ 491\,\mathrm{nm};\qquad
w_{\min}\simeq368,\ 245\,\mathrm{nm}}.
$$
If instead the graph uses the common \b[incoherent-cutoff normalization] $\nu_0=2\mathrm{NA}/\lambda$, the widths are \b[$302\,\mathrm{nm}$ and $201\,\mathrm{nm}$], with periods twice those values. The caption does not explicitly provide an equation for $\nu_0$ or define whether “feature size” means period or half-pitch, so these conventions must not be silently mixed. The higher-contrast resist resolves the higher normalized frequency in either convention.
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