What a lens does is fully reversible if you have phases as well as amplitudes at infinitely high resolution. Unfortunately, you don't. You have a sensor that c

What a lens does is fully reversible if you have phases as well as amplitudes at infinitely high resolution. Unfortunately, you don't. You have a sensor that captures only amplitudes, on a spatially quantized grid, with some noise. It loses a lot of information. If your lens has very low aberration and not too much distortion, most of that information is information you don't care about. If your lens has a lot of aberration and distortion, a lot of the information you care about is encoded in exactly the stuff that the sensor is losing.