The ability to overcome the negative effects, induced by obstacles and turbulent atmosphere, is a core challenge of long-distance information transmission, and it is of great significance in free-space optical communication. The spatial-coherence structure, that characterizes partially coherent fields, provides a new degree of freedom for carrying information. However, due to the influence of the complex transmission environment, the spatial-coherence structure is severely damaged during the propagation path, which undoubtedly limits its ability to transmit information. Here, we realize the robust far-field orbital angular momentum (OAM) transmission and detection by modulating the spatial-coherence structure of a partially coherent vortex beam with the help of the cross-phase. The cross-phase enables the OAM information, quantified by the topological charge, hidden in the spatial-coherence structure can be stably transmitted to the far field and can resist the influence of obstructions and turbulence within the communication link. This is due to the self-reconstruction property of the spatial-coherence structure embedded with the cross-phase. We demonstrate experimentally that the topological charge information can be recognized well by measuring the spatial-coherence structure in the far field, exhibiting a set of distinct and separated dark rings even under amplitude and phase perturbations. Our findings open a door for robust optical signal transmission through the complex environment and may find application in optical communication through a turbulent atmosphere.

Realizing high-fidelity optical information transmission through a scattering medium is of vital importance in both science and applications, such as short-range fiber communication and optical encryption. Theoretically, an input wavefront can be reconstructed by inverting the transmission matrix of the scattering medium. However, this deterministic method for retrieving light field information encoded in the wavefront has not yet been experimentally demonstrated. Herein, we demonstrate light field information transmission through different scattering media with near-unity fidelity. Multi-dimensional optical information can be delivered through either a multimode fiber or a ground glass without relying on any averaging or approximation, where their Pearson correlation coefficients can be up to 99%.