PARABOLA
MIRRORS, DISHES AND THE FOCUS
A parabola is the only curve that turns a beam of parallel light into a single point.
BEGIN — CHAPTER 01 →Every ray travels the same distance to the focus
A parabola is the set of points equally far from the focus and the directrix.
Equal path length is the whole secret.
The drawing is to scale for a 1 m mirror.
The difference is smaller than a wavelength — and it decides everything
A sphere is easy to make; a parabola has to be figured.
For a small, slow mirror a sphere is fine.
Hubble, 1990: a perfect mirror of the wrong shape
Hubble's primary was polished to the wrong conic constant.
You can recover the size of the mistake from two numbers.
Curve computed from the two published conic constants.
Even a perfect parabola turns a star into a small disc
The Airy pattern sets the limit.
Move the two stars together and watch them merge.
Area grows with the square of the diameter. So does every difficulty
A mirror is a light bucket.
A single piece of glass stops around 8 metres.
Discs drawn to scale.
Webb's mirror only works if 18 pieces agree to within nanometres
Webb's primary is 18 hexagonal beryllium segments.
Alignment took months and went in stages.
Computed with a 256 × 256 FFT.
A radio dish only has to be as smooth as its wavelength demands
Ruze's rule.
ALMA, Green Bank, FAST.
FAST: pulling a sphere into a parabola
Geometry from Nan et al. [9].
The parabola is one member of a family, and big telescopes use its relatives
The conic constant K.
Cassegrain, Ritchey–Chrétien, three-mirror anastigmat.
Cassegrain layout traced on this page.
The mirror only delivers light. The focus is where it becomes data
Instruments must be colder than the light they measure.
A radio telescope puts a feed horn at the focus.
Seventy-five years of ever larger parabolas
Every one of these instruments is the same idea.