Information encryption with optical technologies has become increasingly important due to remarkable multidimensional capabilities of light fields. However, the optical encryption protocols proposed to date have been primarily based on the first-order field characteristics, which are strongly affected by interference effects and make the systems become quite unstable during light–matter interaction. Here, we introduce an alternative optical encryption protocol whereby the information is encoded into the second-order spatial coherence distribution of a structured random light beam via a generalized van Cittert–Zernike theorem. We show that the proposed approach has two key advantages over its conventional counterparts. First, the complexity of measuring the spatial coherence distribution of light enhances the encryption protocol security. Second, the relative insensitivity of the second-order statistical characteristics of light to environmental noise makes the protocol robust against the environmental fluctuations, e.g, the atmospheric turbulence. We carry out experiments to demonstrate the feasibility of the coherence-based encryption method with the aid of a fractional Fourier transform. Our results open up a promising avenue for further research into optical encryption in complex environments.

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We examine the effect of spatial coherence on the image quality of a classic 4f imaging system when its Fourier plane is partially blocked by an opaque obstacle. We find that although reducing the degree of spatial coherence of the source results in the improved image quality, the concurrent distortions in the image plane are inevitable. Employing a suitable decomposition of a partially coherent light source into a set of coherent pseudo-modes with a multitude of linear phase shifts, we demonstrate that the distortions are primarily induced by the modes whose maxima are located at the obstacle edges. We show that by tailoring spatial coherence of the source we can enable all the coherent modes to circumnavigate the obstacle, ensuring the same image quality as if the obstacle were absent from the Fourier plane. We expect our findings to be instrumental in high-contrast optical microscopy with coherence structured light.

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