Nowadays underwater vision systems are being widely applied in ocean research. However, the largest portion of the ocean - the deep sea - still remains mostly unexplored. Only relatively few image sets have been taken from the deep sea due to the physical limitations caused by technical challenges and enormous costs. Deep sea images are very different from the images taken in shallow waters and this area did not get much attention from the community. The shortage of deep sea images and the corresponding ground truth data for evaluation and training is becoming a bottleneck for the development of underwater computer vision methods. Thus, this paper presents a physical model-based image simulation solution, which uses an in-air texture and depth information as inputs, to generate underwater image sequences taken by robots in deep ocean scenarios. Different from shallow water conditions, artificial illumination plays a vital role in deep sea image formation as it strongly affects the scene appearance. Our radiometric image formation model considers both attenuation and scattering effects with co-moving spotlights in the dark. By detailed analysis and evaluation of the underwater image formation model, we propose a 3D lookup table structure in combination with a novel rendering strategy to improve simulation performance. This enables us to integrate an interactive deep sea robotic vision simulation in the Unmanned Underwater Vehicles simulator. To inspire further deep sea vision research by the community, we release the source code of our deep sea image converter to the public at GitHub: https://github.com/omv-ysong/DeepSeaRenderer.