Volumetric Optical Scattering Neural Networks
Optical neural networks rely on planar photonic circuits or spatially separated diffractive planes, limiting volumetric integration and requiring precise alignment. Here we propose a volumetric optical scattering neural network (OSNN) comprising densely packed refractive-index neurons with weak contrast $Δn = 0.006$. Direction-dependent first-order Born scattering provides local coupling, while ordered propagation accumulates these weak updates into global task-specific transformations. Fabrication-aware training and two-photon nanolithography produced a sub-$4 \times 10^{-4}$ mm$^3$ device containing 376,320 neurons at $1.0 \times 10^9$/mm$^3$ in a continuously written, intrinsically registered volume. Experimentally, a classifier performed class-selective energy routing with 95.8% blind-test accuracy on MNIST. The calculated passive optical transit time is below 1 ps. A separately optimized imager provided fourfold full-field spatial-sampling compression, resolved 1-$μ$m features and enabled cross-domain transfer. An OSNN co-designed for multiple tasks encoded single-cell fluorescence-derived images into measured output maps, which were pooled into a 16-dimensional representation supporting organelle classification, morphology reconstruction, doublet detection and morphology regression, with all reported metrics exceeding 0.92. Volumetric weak scattering thus establishes an ultracompact, intrinsically registered optical computing architecture, opening a new route to scalable machine vision and biomedical analysis.