End-to-end metasurface design for temperature imaging via broadband Planck-radiation regression

We present a theoretical framework for temperature imaging from long-wavelength infrared thermal radiation (e.g. 8-12 $\mu$m) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. We introduce a new nonlinear reconstruction algorithm, ``Planck regression," that reconstructs the temperature map from a grayscale sensor image, even in the presence of severe chromatic aberration, by exploiting blackbody and optical physics particular to thermal imaging. We combine this algorithm with an end-to-end approach that optimizes a manufacturable, single-layer metasurface to yield the most accurate reconstruction. Our designs demonstrate high-quality, noise-robust reconstructions of arbitrary temperature maps (including completely random images) in simulations of an ultra-compact thermal-imaging device. We also show that Planck regression is much more generalizable to arbitrary images than a straightforward neural-network reconstruction, which requires a large training set of domain-specific images.