We solve time-harmonic wave scattering problems on unbounded domains without domain truncation by mapping the unbounded domain to a bounded domain and scaling the oscillatory decay towards infinity. The technique, first developed in numerical relativity for time-domain wave equations, solves for the far-field pattern using compactification at infinity, avoiding the outer boundary problem. We design a layer that restricts the transformations to an annular domain. The resulting null infinity layer solves both the outer boundary and radiation extraction problems. We demonstrate its practical implementation using finite difference, Chebyshev collocation, spectral Galerkin, and finite element methods in one and two dimensions.