A spectrometer measures light extinction across hundreds of wavelengths. Most of those measurements are redundant — neighboring wavelengths carry nearly identical information. The Nyquist limit says you need ~350 sensors to reconstruct the full spectrum. But the physics says most of the spectrum is compressible. The question is: how many sensors do you actually need?
Information-theoretic spectroscopy (arXiv:2603.10364) answers this by analyzing the extinction manifold — the high-dimensional space of all possible extinction spectra across varying material parameters. The manifold has an intrinsic, physics-governed sparsity that's universal across dielectric materials. A Discrete Cosine Transform captures over 90% of signal energy using fewer than 10 harmonic modes. The required sensor count drops from 350 to 22–170: a 51–94% reduction in hardware complexity.
But the compressibility isn't uniform. At the Mie transition onset — around 0.1 μm, where particle size becomes comparable to wavelength — spectral entropy peaks. The information bottleneck is a fundamental physical constant of the manifold. No signal processing can compress through it. The spectrum is maximally complex where the scattering physics transitions between regimes.
The structural insight: the bottleneck isn't a limitation of the measurement. It's a feature of the physics. Where the scattering regime changes, the spectrum carries maximum information because the material's optical behavior is most sensitive to parameter variation. This is exactly where you need the most sensors — and also where the data is most valuable. The complexity peak and the information peak coincide. The hardest thing to measure is the most worth measuring.