[tortle]

A lens is a convolution. Imagine if a photograph was a 1D signal, then a lens would be a convolution of a signal with a square wave (Lens sliced along one plane). Now, typically when a square wave is convolved with a signal, if you look at the magnitude of the fourier transform, you'll notice that you are multiplying the frequencies of the signal with a sinc function. Sinc functions hit zero amplitudes at various points, thereby destroying information when multiplied. Therefore, if you could create a lens (known as a mask), which didn't destroy signal, but instead was more like a band-pass filter, then you could effectively recover the signal and adjust for amplitude changes digitally. Now take this model to the 3D and you've just created a lightfield.

[Ono-Sendai]

Calling a lens a convolution is an idealisation. It only convolves the signal on the focal plane/sensor, for perfectly focused light.