  We introduce end-to-end metaoptics inverse design for multi-channel imaging:
reconstruction of depth, spectral and polarization channels from a single-shot
monochrome image. The proposed technique integrates a single-layer metasurface
frontend with an efficient Tikhonov reconstruction backend, without any
additional optics except a grayscale sensor. Our method yields multi-channel
imaging by spontaneous demultiplexing: the metaoptics front-end separates
different channels into distinct spatial domains whose locations on the sensor
are optimally discovered by the inverse-design algorithm. We present large-area
metasurface designs, compatible with standard lithography, for multi-spectral
imaging, depth-spectral imaging, and ``all-in-one'' spectro-polarimetric-depth
imaging with robust reconstruction performance ($\lesssim 10\%$ error with 1\%
detector noise). In contrast to neural networks, our framework is physically
interpretable and does not require large training sets. It can be used to
reconstruct arbitrary three-dimensional scenes with full multi-wavelength
spectra and polarization textures.
