  By co-designing a meta-optical front end in conjunction with an
image-processing back end, we demonstrate noise sensitivity and compactness
substantially superior to either an optics-only or a computation-only approach,
illustrated by two examples: subwavelength imaging and reconstruction of the
full polarization coherence matrices of multiple light sources. Our end-to-end
inverse designs couple the solution of the full Maxwell equations---exploiting
all aspects of wave physics arising in subwavelength scatterers---with
inverse-scattering algorithms in a single large-scale optimization involving
$\gtrsim 10^4$ degrees of freedom. The resulting structures scatter light in a
way that is radically different from either a conventional lens or a random
microstructure, and suppress the noise sensitivity of the inverse-scattering
computation by several orders of magnitude. Incorporating the full wave physics
is especially crucial for detecting spectral and polarization information that
is discarded by geometric optics and scalar diffraction theory.
