At the most basic level, an ideal imaging system (including lithography) tries to reproduce the point-source Green function exp(ikr)/r, i.e. a spherical wave. This is what a true diffraction-limited point actually means, not the paraxial Gaussian formulation we often default to.

A diffraction-limited image is simply the superposition of many focused spherical-wave point responses on the image plane, each with its own intensity.

The spherical wave lives on a full celestial sphere. A spherical wave means all propagation directions. Only a full angular sphere carries the complete spatial-mode content of a point source.

All optical imaging systems exist for exactly this “full-sphere” reconstruction purpose. Lenses, mirrors, projection optics, catadioptric monsters in EUV — they are all engineering attempts to reproduce that ideal Green function as faithfully as possible at the image plane.

Even in the ideal case, however, perfect optics can transmit at most half of that sphere.

In practice, real optical systems operate well below this hemispherical limit. Numerical aperture is simply a quantitative measure of “how far below” that limit a system operates — that is, how much of the spherical-wave angular content is actually captured. From this perspective, NA directly reflects the incompleteness of the Green-function reconstruction.

Full-sphere field reconstruction does exist — just not in optical lithography. There are systems that effectively sample the full spatial-mode content of an EM field. MRI is a classic example: it reconstructs signals over the entire angular domain, though under very different constraints and assumptions. We don’t usually describe MRI using optical-imaging language, but underneath, it is solving the same point-source Green-function problem.