The manufacturing reasons
- Spherical elements are simpler and cheaper to produce than any other shape.
- Aligning several elements into a working lens is much easier when they share a common axis of symmetry.
- Focus and zoom are operated by rotation. A rectangular barrel cannot turn, so the mechanism itself calls for a circle.
The optical reason
One answer supplied a neat argument that supports the same conclusion from a different direction. How much light a lens gathers depends on its area, while the difficulty and expense of correcting its aberrations rise with its largest dimension. For any given area, a circle is the shape with the smallest maximum dimension — so it collects the most light for the least optical trouble. The same answer was careful to say manufacturing remains the overriding factor, and that the optics happen to agree.
Why the sensor is not round
The accepted answer turns the question round and points out the rectangle is the part that needs explaining. Rectangular is partly inherited from earlier image formats, and partly a consequence of how sensors are made: they are printed onto circular silicon wafers, and rectangles tile a surface without waste in a way circles do not. So the lens projects a circular image and the rectangle is cut out of the middle of it.
The visible consequence
- Out-of-focus points of light take the shape of the aperture, which is why they usually appear as discs.
- Where the aperture is formed by a small number of straight blades, those highlights appear as polygons instead.
- This is directly demonstrable: place a shaped cutout over the front of a lens and every out-of-focus highlight takes that shape.