Inverse Design for Robust Inference in Integrated Computational Spectrometry

We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse design of the scattering media does not need a training set of spectra, a distribution of detector noise, or an inference algorithm. Our approach allows the selection of the inference algorithm to be decoupled from that of the scatterer. For smooth spectra, we additionally devise a regularized reconstruction algorithm based on Chebyshev interpolation, which yields higher accuracy compared with conventional methods in which the spectra are sampled at equally spaced frequencies or wavelengths with equal weights. Our approaches are numerically demonstrated via inverse design of integrated computational spectrometers and reconstruction of example spectra. The inverse-designed spectrometers exhibit significantly better performance in the presence of noise than their counterparts with random scatterers. Our method provides a useful complement to end-to-end co-design methods.