Yes. In fact, some of the most advanced radio and optical systems deliberately use surfaces that are not simple parabolas.
Some examples:
1. Spherical reflectors
A sphere is easier to construct than a true paraboloid.
- The now-collapsed Arecibo Observatory used a spherical primary reflector.
- The FAST telescope also has a spherical dish about 500 m across.
A sphere suffers from spherical aberration, because rays do not all come to the same focus. This is corrected by additional optics.
At FAST, thousands of actuators actively deform a portion of the spherical surface into a paraboloid aimed at the desired source.
2. Gregorian and Cassegrain systems
Many large radio telescopes use a shaped pair of mirrors.
Examples include the Green Bank Telescope and the Effelsberg Radio Telescope.
The primary may start as a paraboloid, but the secondary is often a carefully calculated aspheric surface. Both mirrors can be “shaped” to:
- increase aperture efficiency,
- reduce spillover,
- improve illumination,
- lower sidelobes.
The resulting surfaces are much more complicated than simple conic sections.
3. Shaped reflector antennas
Satellite communications frequently use “shaped reflectors.”
Instead of focusing all energy to a point, the reflector redistributes it to create a desired beam pattern.
For example:
- Earth-coverage satellite antennas,
- spot-beam telecommunications satellites,
- radar antennas.
Their surfaces may have no simple mathematical description and are generated by optimisation software.
4. Schwarzschild optics
In optical astronomy, the German physicist Karl Schwarzschild designed two-mirror systems in which both mirrors have complex aspheric shapes to eliminate aberrations.
Modern telescopes descended from these ideas include:
- Ritchey-Chretien designs,
- Schwarzschild-Couder telescopes used in gamma-ray astronomy.
5. Freeform optics
The most advanced systems now use freeform surfaces.
These have no rotational symmetry at all. Their shape is defined numerically by thousands of coefficients.
Applications include:
- adaptive optics,
- space telescopes,
- military imaging systems,
- specialised radio antennas.
Could this be useful for amateur hydrogen-line work?
Possibly.
For example, if you built a folding 3 m dish from flat panels, you could deliberately shape the panels to:
- improve edge illumination,
- compensate for feed blockage,
- reduce sidelobes,
- optimise performance for your specific feed horn.
However, the gain over a well-made paraboloid at 1420 MHz is usually modest unless you are trying to achieve extremely low sidelobes or unusual beam shapes.
So the paraboloid is not the only solution—it’s simply the simplest shape that converts plane waves to a point focus. Once engineers want additional properties, reflector surfaces often become surprisingly complicated.