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The modulation transfer function is the magnitude of the normalized optical transfer function in a linear, shift-invariant incoherent imaging model. It describes how strongly the system transfers sinusoidal image contrast at each spatial frequency, while discarding the transfer function's phase.

For an input $I(x)=I_0[1+m\cos (2\pi \nu x)]$ and a unit-integral point spread function, the output modulation magnitude is $mM(\nu )$. Fine alternating bars contain higher spatial frequencies, so their diminishing visibility illustrates loss of transferred modulation. Measuring image contrast across a calibrated pattern tests this response, but detector sampling, noise and nonlinear image processing can alter the result. A transfer magnitude alone does not locate image features or specify their phase shifts.

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.

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,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 requiresThis 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.^[ref]

The two thresholds are approximatelyReading their intersections with the supplied curve gives, to graphical accuracy,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:An ArF excimer laser uses $\lambda \simeq 193\mathrm{nm}$. A numerical length requires specifying what the caption's “Rayleigh limit” means. Taking it literally as the reciprocal of the Rayleigh criterion point separation givesIf instead the graph uses the common incoherent-cutoff normalization ${\nu }_0=2\mathrm{NA}/\lambda$, the widths are $302\mathrm{nm}$ 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.