If I were asked to make such a device, I would build a flexible mirror whose curve could be adjusted by an array of attached screws. I'd fix said mirror to a car, and adjust the screws until the desired curve was reached. I'd then measure the curve and duplicate it in a rigid finished product.

It's actually amazing that it took a physicist/mathematician to think of this thing. I doubt I would have come up with the idea. It goes to show how domain knowledge shapes your perception of the world.