Random matrix theory yields a closed-form noise-error bound for reconstructive spectrometers and predicts a 17.9 µm optimal cavity in on-chip FDTD
Using Fisher information and random matrix theory, the authors derive a closed-form expression for the noise-induced error of chaotic/diffusive reconstructive spectrometers, linking the variance bound σ²_ε Tr[(AᵀA)⁺] to the spectral correlation length Γ_corr, mean transmittance T₀, and the numbers of frequency channels N and measurement channels M, establish conditions for super-resolution, and validate the theory with a random matrix model and full-wave FDTD simulations, where the predicted optimal on-chip cavity size is about 17.9 µm.