In this work, we analyze the interference patterns measured in lab-based dual-phase grating interferometry and for the first time explain the spatial dependencies of the measured interference patterns and the large visibility deviations between the theoretical prediction and the experimental results. To achieve this, a simulator based on wave propagation is developed. This work proves that the experimental results can be simulated with high accuracy by including the effective grating thickness profile induced by the cone-beam geometry, the measured detector response function and a non-ideal grating shape. With the comprehensive understanding of dual-phase grating interferometry, this provides the foundations for a more efficient and accurate algorithm to retrieve sample's structure information, and the realistic simulator is a useful tool for optimizing the set-up.