Ghost diffractive deep neural networks: Optical classifications using light’s second-order coherence

Since Hanbury Brown and Twiss proposed intensity interferometry in 1956, light's fluctuating nature, high-order coherence, and spatial correlations have become not only the cornerstones of quantum optics but also resources for many classical optical applications. Correlation-based optical metrologies, including ghost imaging and ghost diffraction, have distinct advantages ranging from local to nonlocal geometry, spatially coherent to incoherent light, and array to single-pixel sampling. In this paper we propose ghost diffractive deep neural networks (${\mathrm{GD}}^{2}\mathrm{NNs}$), a nonlocal optical information-processing system that combines traditional ghost diffraction with cascaded diffraction layers ``learned'' with use of diffractive deep neural networks. ${\mathrm{GD}}^{2}\mathrm{NNs}$ use light's second-order coherence to enable image-free and interferometer-free coherent beam-demanded phase-object sorting with thermal light. Furthermore, ${\mathrm{GD}}^{2}\mathrm{NNs}$ convert the general encoder-decoder-detector cascaded framework into a parallel one, resulting in no optical interaction between the encoder and the decoder. As a proof-of-principle demonstration, we numerically and experimentally classify different phase objects using three-layer and two-layer ${\mathrm{GD}}^{2}\mathrm{NNs}$, respectively. This paper effectively provides a paradigm shift, particularly for diffraction-related coherent linear optical information processing systems, from spatially coherent to incoherent light and from cascaded to parallel processing.