Information-Theoretic Spectroscopy: Universal Sparsity of Extinction Manifold and Optimal Sensing across Scattering Regimes

TL;DR

This paper reveals a universal sparsity in the extinction manifold of dielectric materials, demonstrating that optimal sensing can be achieved with significantly fewer sensors by using the DCT basis, surpassing traditional methods across scattering regimes.

Contribution

It introduces a physics-based sparsity principle in optical extinction spectra and shows DCT-based compressed sensing outperforms FFT, enabling reduced hardware for high-fidelity material sensing.

Findings

DCT captures over 90% of spectral energy with fewer than 10 modes.

DCT achieves 12-fold compression advantage over FFT at 99% energy threshold.

Compressed sensing with DCT reduces sensor count by up to 94%, surpassing Nyquist limit.

Abstract

The inverse reconstruction of material properties from optical extinction efficiency (Qext) is constrained by the high-dimensional nature of Mie scattering. We demonstrate that the Qext manifold possesses an intrinsic, physics-governed sparsity universal across dielectric materials. By analyzing the spectral topology of a diverse polymer library, we identify a critical Information Bottleneck at the onset of the Mie transition (r approx 0.1 um), where a peak in spectral entropy signifies a fundamental limit on signal compressibility. While the Fast Fourier Transform (FFT) is conventionally used for spectral analysis, we show it is physically mismatched for this domain; its periodic boundary assumptions induce spectral leakage that forces a massive basis expansion to resolve Mie ripples. Conversely, the Discrete Cosine Transform (DCT) mirrors the non-periodic geometry of extinction profiles, uncovering inherent compressibility by capturing over 90% of signal energy using fewer than 10 harmonic modes. Even at the Mie bottleneck, the DCT maintains a 12-fold compression advantage over the FFT at a 99% energy threshold. Notably, while both bases converge to identical error floors for a fixed energy threshold, the DCT achieves this fidelity with significantly lower hardware overhead. Stress-testing under 10% additive Gaussian noise confirms the Information Bottleneck is spatially and structurally invariant, proving this complexity peak is a fundamental physical constant of the manifold. By mapping this sparsity onto a compressed sensing architecture, we resolve a 2.5-20 um spectral range using between 22 and 170 sensors: enabling a 51%-94% reduction in hardware complexity that breaks the traditional Nyquist sampling limit (350 sensors) for high-fidelity clinical and remote sensing applications.