Geometry-driven spectral encoding by maximizing distinguishability in encoding space

Making spectra easier to distinguish

Spectral analysis identifies materials by measuring how they absorb, reflect, or transmit light at different wavelengths. It is widely used in biomedical diagnostics, environmental monitoring, remote sensing, and industrial inspection. However, conventional spectrometers often rely on bulky prisms, gratings, or interferometers, limiting their use in compact and snapshot imaging systems.

Computational spectral imaging offers a more compact solution. A spectral encoder modulates incoming light into compressed measurements, and algorithms reconstruct the original spectrum. In this architecture, the encoder determines how much useful information reaches the detector.

A geometric design rule

Most existing encoder designs optimize randomness, correlation, or coherence of the encoding matrix. These metrics are useful, but they do not directly ensure that real spectra remain distinguishable after optical encoding, especially under noise or fabrication errors.

Researchers from Zhejiang Normal University, Zhejiang University, and Westlake University have introduced a geometry-driven design rule called the Euclidean Distance of Encoding space, or EDE. The work is published in PhotoniX.

EDE treats encoded spectra as points in a high-dimensional measurement space. By maximizing the minimum Euclidean distance between these points, the encoder makes different spectra “farther apart” after measurement, reducing ambiguity and improving reconstruction reliability.

From principle to thin-film device

To realize this concept, the team designed a 16-channel TiO₂/SiO₂ multilayer thin-film spectral encoder operating from 400 to 1700 nm. The multilayer structure provides rich spectral modulation through optical interference while remaining compatible with established fabrication methods.

The design was optimized using a stochastic–deterministic framework. A genetic algorithm first explored the complex design space, and an L-BFGS optimizer then refined the multilayer thicknesses. Automatic differentiation was embedded into the transfer-matrix method to provide accurate gradients of the optical response.

Improved reconstruction performance

The EDE-optimized encoder significantly improved spectral reconstruction. Compared with random, correlation-optimized, and coherence-optimized benchmarks, it increased peak signal-to-noise ratio by 3.60 dB, 2.82 dB, and 4.52 dB, respectively.

Across diverse targets, the system achieved a reconstruction spectral fidelity exceeding 98.63%. The improvement was observed not only for sparse reconstruction methods such as ADMM-LASSO, but also for neural-network reconstruction using a multilayer perceptron, showing that EDE improves the information content of the optical measurements themselves.

Experimental validation

The researchers fabricated the 16-channel multilayer thin-film encoder and measured its transmission spectra, which agreed well with transfer-matrix simulations. The system successfully reconstructed narrowband and dual-peak spectra, demonstrating its ability to resolve fine spectral features.

The team further demonstrated computational spectral imaging of real samples across the visible to short-wave infrared range. The reconstructed spectra closely matched reference measurements from commercial spectrometers.

In a material-identification test, the system distinguished polymer samples that appear similar in the visible range but have distinct short-wave infrared absorption features. This shows the potential of EDE-designed encoders for revealing spectral information beyond human vision.

Toward intelligent compact spectrometers

This work establishes EDE as an interpretable design criterion for computational spectral imaging. By optimizing the physical distinguishability of encoded spectra, it shifts encoder design from matrix statistics to measurement-space separability.

The approach can be extended to other photonic platforms, including metasurfaces, gratings, and low-dimensional material structures. It may also be combined with end-to-end learning, task-specific spectral libraries, and physics-informed priors to support future compact sensors for material identification, environmental monitoring, biomedical detection, industrial inspection, and intelligent machine vision.