  In this paper, we present a new Light Field representation for efficient
Light Field processing and rendering called Fourier Disparity Layers (FDL). The
proposed FDL representation samples the Light Field in the depth (or
equivalently the disparity) dimension by decomposing the scene as a discrete
sum of layers. The layers can be constructed from various types of Light Field
inputs including a set of sub-aperture images, a focal stack, or even a
combination of both. From our derivations in the Fourier domain, the layers are
simply obtained by a regularized least square regression performed
independently at each spatial frequency, which is efficiently parallelized in a
GPU implementation. Our model is also used to derive a gradient descent based
calibration step that estimates the input view positions and an optimal set of
disparity values required for the layer construction. Once the layers are
known, they can be simply shifted and filtered to produce different viewpoints
of the scene while controlling the focus and simulating a camera aperture of
arbitrary shape and size. Our implementation in the Fourier domain allows real
time Light Field rendering. Finally, direct applications such as view
interpolation or extrapolation and denoising are presented and evaluated.
