Sinusoidal Single-Pixel Imaging Based on Fourier Positive-Negative Intensity Correlation

Single-pixel imaging techniques extend the time dimension to reconstruct a target scene in the spatial domain based on single-pixel detectors. Structured light illumination modulates the target scene by utilizing multi-pattern projection, and the reflected or transmitted light is measured by a single-pixel detector as total intensity. To reduce the imaging time and capture high-quality images with a single-pixel imaging technique, orthogonal patterns have been used instead of random patterns in recent years. The most representative among them are Hadamard patterns and Fourier sinusoidal patterns. Here, we present an alternative Fourier single-pixel imaging technique that can reconstruct high-quality images with an intensity correlation algorithm using acquired Fourier positive-negative images. We use the Fourier matrix to generate sinusoidal and phase-shifting sinusoid-modulated structural illumination patterns, which correspond to Fourier negative imaging and positive imaging, respectively. The proposed technique can obtain two centrosymmetric images in the intermediate imaging course. A high-quality image is reconstructed by applying intensity correlation to the negative and positive images for phase compensation. We performed simulations and experiments, which obtained high-quality images, demonstrating the feasibility of the methods. The proposed technique has the potential to image under sub-sampling conditions.