Reconstructive spectrometers: hardware miniaturization and computational reconstruction

Abstract Spectrometers serve as indispensable analytical tools across chemistry, materials science, environmental monitoring, medical diagnostics, and beyond. The emergence of reconstructive spectrometers represents a transformative leap in spectral analysis, combining miniaturized encoding hardware with advanced computational algorithms to revolutionize conventional approaches. These devices encode unknown spectral data into measurable signals, for which sophisticated algorithms then decode to reconstruct the original spectrum with high fidelity—all achieved within an ultra-compact footprint. In this review, we first establish the mathematical foundations governing spectral encoding and decoding. We then provide a detailed analysis of encoding strategy and state-of-the-art decoding techniques, followed by recent breakthroughs in hardware design for optimized spectral reconstruction systems. Finally, we address key challenges and future opportunities, offering insights into how reconstructive spectrometers may redefine spectroscopy beyond traditional laboratory settings.