You more or less described it. If you put a microlens over, say, each 3x3 pixel sub-array, then each of those 3x3 squares now captures a locally incident light

You more or less described it. If you put a microlens over, say, each 3x3 pixel sub-array, then each of those 3x3 squares now captures a locally incident light ray and its direction (with low resolution). You can now treat that as a single image pixel, but now containing angular information describing how that pixel changes with rotation in the field of view. Effectively you end up with an array of tiny cameras. Applying the same principle in reverse, you can also create a 3D display by adding a microlens array on top of an image. If you use the same microlens array to capture the image as to display it (swapping out the sensor with a display, or a camera film with its developed photograph) then optical physics does all the necessary image processing for you. The idea goes back at least as far as Gabriel Lippmann in the 1900s: https://en.wikipedia.org/wiki/Lenticular_printing#Gabriel_Lippmann's_integral_photography https://en.wikipedia.org/wiki/Lenticular_printing#Gabriel_Li...