 Solution

The projection lens maps the mask's angular spectrum into its back focal plane: within scalar Fourier optics this is the Fraunhofer diffraction or spatial-Fourier plane. A periodic mask produces discrete diffraction orders, separated by $1/P$ in object-side spatial frequency after accounting for projection magnification. The finite numerical aperture bounds the transverse wave vectors admitted by the lens, so the pupil is a spatial-frequency filter.

For an ideal on-axis coherent system,A second Fourier transformation forms the image, and the recorded intensity is $|U_{\mathrm{image}}{|}^2$. If only the zero order passes, the field is uniform and the line pattern disappears. Passing zero and first orders restores a periodic modulation; passing more orders sharpens the edges. Thus the loss of fine structure is explained by rejected diffraction orders, not by a geometrical inability to draw narrow lines. The field-transfer cutoff differs from the twice-as-large incoherent intensity-transfer cutoff.^[ref]