Extended Operational Ghost Correlation Model: Ghost Arithmetic Operations for Multi-Channel Information Synthesis

Ghost imaging, ghost interference, and ghost diffraction retrieve an object’s spatial distribution and interference–diffraction patterns via intensity correlation. Flexibly synthesizing multi-channel optical information within a single correlation architecture is a key challenge in the evolution of optical correlation from fundamental research to information processing platforms. This study proposes the Extended Operational Ghost Correlation Model (EO-GCM), which introduces the four arithmetic operations (addition, subtraction, multiplication, and division) into optical correlation data processing. Within circular complex Gaussian pseudothermal light fields, the study systematically derives the analytical expressions for the second-order intensity fluctuation correlations with these operations. The theory shows that addition and subtraction obey superposition, whereas for multiplication and division, the average intensity of one object path becomes a weighting factor for the information of the other path. When weakly correlated, multiplication yields a weighted sum, whereas division yields a weighted difference, with the two weights having opposite signs. Experiments on ghost interference or diffraction and ghost imaging verify theoretical predictions and confirm the proportionality between the absolute value of the negative weight in division and the average intensity of the numerator path. The proposed model enables basic operations on multipath object signals, endowing optical correlation systems with reconfigurable, weighted correlation fusion-based information modulation capabilities.