Resolution and Robustness Bounds for Reconstructive Spectrometers

Reconstructive spectrometers are an emerging class of devices that combine complex light scattering with inference. Thus far, the physical determinants of their performance remain underexplored. Within the regime of chaotic or diffusive scattering, the noise-induced error for spectral reconstruction is governed by Fisher information. We use random matrix theory to derive a closed-form relation linking the variance bound to physical parameters: the spectral correlation length, mean transmittance, and the number of frequency and measurement channels. This analysis reveals fundamental trade-offs between the physical parameters and establishes the conditions for "super-resolution" below the limit set by the spectral correlation length. Our theory is validated numerically using a random matrix model as well as full-wave simulations. These results establish a physically grounded framework for designing compact, performant, and robust reconstructive spectrometers.