  Recent works use the Neural radiance field (NeRF) to perform multi-view 3D
reconstruction, providing a significant leap in rendering photorealistic
scenes. However, despite its efficacy, NeRF exhibits limited capability of
learning view-dependent effects compared to light field rendering or
image-based view synthesis. To that end, we introduce a modification to the
NeRF rendering equation which is as simple as a few lines of code change for
any NeRF variations, while greatly improving the rendering quality of
view-dependent effects. By swapping the integration operator and the direction
decoder network, we only integrate the positional features along the ray and
move the directional terms out of the integration, resulting in a
disentanglement of the view-dependent and independent components. The modified
equation is equivalent to the classical volumetric rendering in ideal cases on
object surfaces with Dirac densities. Furthermore, we prove that with the
errors caused by network approximation and numerical integration, our rendering
equation exhibits better convergence properties with lower error accumulations
compared to the classical NeRF. We also show that the modified equation can be
interpreted as light field rendering with learned ray embeddings. Experiments
on different NeRF variations show consistent improvements in the quality of
view-dependent effects with our simple modification.
