Acquiring and representing the 4D space of rays in the world (the light field) is important for many computer vision and graphics applications. Yet, light field acquisition is costly due to their high dimensionality. Existing approaches either capture the 4D space explicitly, or involve an errorsensitive depth estimation process. This paper argues that the fundamental difference between different acquisition and rendering techniques is a difference between prior assumptions on the light field. We use the previously reported dimensionality gap in the 4D light field spectrum to propose a new light field prior. The new prior is a Gaussian assigning a non-zero variance mostly to a 3D subset of entries. Since there is only a lowdimensional subset of entries with non-zero variance, we can reduce the complexity of the acquisition process and render the 4D light field from 3D measurement sets. Moreover, the Gaussian nature of the prior leads to linear and depth invariant reconstruction ...