I believe the lytro camera was a plenoptic, or light field, camera. Light field cameras capture information about the intensity together with the direction of light emanating from a scene. Conventional cameras record only light intensity at various wavelengths.

While conventional cameras capture a single high-resolution focal plane and light field cameras sacrifice resolution to "re-focus" via software after the fact, the CMU Split-Lohmann camera provides a middle ground, using an adaptive computational lens to physically focus every part of the image independently. This allows it to capture a "deep-focus" image where objects at multiple distances are sharp simultaneously, maintaining the high resolution of a conventional camera while achieving the depth flexibility of a light field camera without the blur or data loss.

Something I find interesting is that while holograms and the CMU camera both manipulate the "phase" of light, they do so for opposite reasons: a hologram records phase to recreate a 3D volume, whereas the CMU camera modulates phase to fix a 2D image.

I remember Lytro. There was a lot of fanfare behind that company and then they fizzled. They had a lauded CEO/founder and their website demonstrated clearly how the post-focus worked. It felt like they were going to be the next camera revolution. Their rise and demise story would make a good Isaacson-style documentary.

Light field cameras are mentioned under "related work":

https://imaging.cs.cmu.edu/svaf/static/pdfs/Spatially_Varyin...

The article mentions a spatial light modulator, which I believe the Lytro camera did not have.