Subwavelength diffractive optics known as meta-optics have demonstrated the potential to significantly miniaturize imaging systems. However, despite impressive demonstrations, most meta-optical imaging systems suffer from strong chromatic aberrations, limiting their utilities. Here, we employ inverse-design to create broadband meta-optics operating in the long-wave infrared (LWIR) regime (8-12 μm). Via a deep-learning assisted multi-scale differentiable framework that links meta-atoms to the phase, we maximize the wavelength-averaged volume under the modulation transfer function (MTF) surface of the meta-optics. Our design framework merges local phase-engineering via meta-atoms and global engineering of the scatterer within a single pipeline. We corroborate our design by fabricating and experimentally characterizing all-silicon LWIR meta-optics. Our engineered meta-optic is complemented by a simple computational backend that dramatically improves the quality of the captured image. We experimentally demonstrate a six-fold improvement of the wavelength-averaged Strehl ratio over the traditional hyperboloid metalens for broadband imaging.

The emerging consensus in monetary policy and business cycle analysis is that money aggregates are not useful as an intermediate target for monetary policy or as an information variable. The uselessness of money as an intermediate target is driven, at least in part, by empirical research that suggests that money demand is unstable. In addition, the informational quality of money has been called into question by empirical research that fails to identify a relationship between money growth and inflation, nominal income growth, and the output gap. Nevertheless, this research is potentially flawed by the use of simple sum money aggregates, which are not consistent with economic, aggregation, or index number theory. This paper therefore reexamines previous empirical evidence on money demand and the role of money as an information variable, using Divisia monetary aggregates. These aggregates have the advantage of being derived from microtheoretic foundations, as well as being consistent with aggregation and index number theory. The results of the reevaluation suggest that previous empirical work might be driven by mismeasurement.