At present, photorealistic augmentation is not yet possible since the computational power of mobile devices is insufficient. Even streaming solutions from stationary PCs cause a latency that affects user interactions considerably. Therefore, we introduce a differential rendering method that allows for a consistent illumination of the inserted virtual objects on mobile devices, avoiding delays. The computation effort is shared between a stationary PC and the mobile devices to make use of the capacities available on both sides. The method is designed such that only a minimum amount of data has to be transferred asynchronously between the participants. This allows for an interactive illumination of virtual objects with a consistent appearance under both temporally and spatially varying real illumination conditions. To describe the complex near-field illumination in an indoor scenario, HDR video cameras are used to capture the illumination from multiple directions. In this way, sources of illumination can be considered that are not directly visible to the mobile device because of occlusions and the limited field of view. While our method focuses on Lambertian materials, we also provide some initial approaches to approximate non-diffuse virtual objects and thereby allow for a wider field of application at nearly the same cost.