Geometry-driven spectral encoding by maximizing distinguishability in encoding space

Abstract Computational spectral imaging overcomes the trade-off between spectral resolution and light throughput, but its performance still remains fundamentally limited by the geometric separability of spectral signatures in the encoding space. Current encoder designs predominantly focus on minimizing correlation or coherence, often overlooking the direct maximization of distinguishability among diverse spectra. Here we show that maximizing the minimum Euclidean distance in the encoding space (EDE) serves as a physically direct criterion for designing high-fidelity spectral encoders. To navigate the complex, high-dimensional design space under fabrication constraints, we developed a stochastic-deterministic optimization framework that couples global exploration via genetic algorithms with efficient local refinement using automatic differentiation on the transfer-matrix method. We demonstrate that EDE-optimized encoders significantly extend the minimum distance between distinct spectra in encoding space, yielding improvements in peak signal-to-noise ratio of 3.60 dB, 2.82 dB, and 4.52 dB compared with random, correlation-optimized, and coherence-optimized benchmarks, respectively, and achieving a reconstruction spectral fidelity exceeding 98.63% across diverse targets. Our approach enables high-precision spectral reconstruction, establishing a new geometric paradigm for the design of intelligent computational optical systems.