http://graphics.stanford.edu/papers/lfwigner/

This is not a task-oriented paper so you can barely expect any “novel techniques”. The real product is just equivalence between light field and Wigner distribution : no magic knowing geometric optics an extreme case of Fourier optics. I personally see this as an enhancement of light field to work in the microcopy domain, to account for oscillation, or at least as claimed by the author, to see what has already been done by the optics people and avoiding doing it again with light field.

Despite the tough mathematics in the paper, the path of equivalence is straightforward. As in Fourier Slice Photography it uses shift and slope to specify a wave, but with a bit different interpretations for both of them. The shift is no longer a pinhone on the exit pupil but a small aperture to avoid argument that single point light sources emit un-directed waves; and the slope corresponds to a specific angular spectrum, or a planar wave component of that specific direction defined by the virtual “light ray”. If one understands that the image formation process in wave optics is quadratic (integrating over squared norm of the scalar field), the derivation of the equivalence now becomes straight-forward. And one might not be surprised that conherence of light plays a central role in this formulation.

The applications in this paper can all be found in previous works. Interestingly, just like Levin et.al. downgraded Fourier optics to geometric optics to analyze wavefront coding with light field, this paper shows how uncertainty principle, which due to the quantum nature of light, can be intepretated in wave optics. And the authors have already done that in the context of geometric optics! It’s still a question to me how this is going to be useful somehow, besides keeping CP and optics people closer and closer.

After all I would still say it’s a well-grounded paper and requires struggling for sometime to really get anything from the paper. And it’s worth the price if you want to understand light and camera in depth.