Speckle Pattern Calculation and Scattering Imaging for General Surface Scattering Problem

Establishing accurate models for light scattering has attracted widespread attention in optical research. Existing works include the linear system model and the Lambertian model, which achieve imaging small objects through a scattering medium or identifying scenes hidden from the direct line of sight. However, predicting speckle patterns accurately at a specific location after scattering with minimal computational resources remains a challenge. In this work, we introduce a scattering model that considers a scattering surface as a wavefront modulation matrix, which is validated by using the finite-difference time-domain simulation method. The modulating parameters of the scattering surface are retrieved, and the speckle patterns can be accurately calculated by utilizing the retrieved modulating parameters quickly. The results of simulations and experiments demonstrated that the calculated speckles are highly correlated to their corresponding ground truths captured by a charge-coupled device (CCD) sensor. Further experiments show that images of objects hidden from the line of sight can be reconstructed via these calculated speckle patterns. This work provides a general solution to the surface scattering problem and can enhance the utilization of conventional coded imaging techniques in scattering imaging problems.