Ritchey–Chrétien telescope
Two hyperboloids that are measurably worse on the optical axis than a classical Cassegrain, and better everywhere else — the trade behind Hubble, the VLT and Keck.
Open in the canvas →Background
A classical Cassegrain is exact on its axis. A parabolic primary brings starlight to a point, and a hyperbolic secondary sharing that focus relays it to another point, each surface doing the one thing its shape does perfectly. Measured on the axis, it cannot be beaten.
Point it slightly off axis and the image falls apart. Rays through opposite sides of the aperture no longer land together; a star grows a one-sided flare, brighter at one end, like a small comet. This is coma, and it grows linearly with field angle, which is why a classical Cassegrain is a superb instrument for looking at one object and a poor one for surveying a field.
George Ritchey and Henri Chrétien's answer, around 1910, was to stop insisting on the axis. Make both mirrors hyperbolic and two free parameters become available instead of one — enough to cancel spherical aberration and coma together rather than spherical aberration alone. The design is aplanatic: no longer perfect anywhere, and nearly as good everywhere.
That trade is why it is the standard for research telescopes. Hubble, the VLT and the Keck telescopes are all Ritchey–Chrétiens, because a telescope earns its cost on the field it can image at once, not on the single point at the centre of it.
What this setup demonstrates
The geometry is fixed and only the two conic constants change, so any difference between the designs is surface shape alone.
The classical Cassegrain's secondary follows from the shared-focus construction, k = −((m+1)/(m−1))² = −2.609467 at a secondary magnification of m = 4.25. The Ritchey–Chrétien's pair cannot be built that way — neither mirror images the conjugates on its own — so it was solved against this app's own tracer by bisection: the secondary conic chosen to null the signed spherical aberration at the focal plane, then the primary conic chosen to null the signed coma of a 0.1° bundle. That gives k₁ = −1.040245 and k₂ = −2.971093.
Spot size at the focal plane, measured:
| Design | on axis | 0.1° | 0.3° |
|---|---|---|---|
| Classical Cassegrain | 4.5×10⁻⁷ mm | 5.0×10⁻³ mm | 2.2×10⁻² mm |
| Ritchey–Chrétien | 5.4×10⁻⁴ mm | 1.9×10⁻³ mm | 1.4×10⁻² mm |
The Cassegrain is a thousand times better on the axis and two and a half times worse a tenth of a degree off it. Set the primary to k = −1 and the secondary to k = −2.609467 in the inspector and you can watch the axis sharpen and the field degrade together.
By 0.3° the two designs are close again, and that is worth understanding rather than hiding: what remains at that field is largely astigmatism, which the Ritchey–Chrétien does not claim to correct. Removing it needs a third element — a corrector plate — which is exactly what wide-field survey telescopes add.
A 2D meridional section cannot show astigmatism or field curvature the way a real instrument does: a rotationally symmetric system is being sampled along a single cut, so the off-axis numbers above describe that cut and not a full spot diagram. The aplanatic pair was solved against this tracer's exact ray geometry rather than from third-order theory, so the conic constants are close to but not identical with the textbook closed-form values.
Nothing is diffractive — no Airy disc, no obstruction-driven ring redistribution, no spider vanes — and the aperture is a teaching scale, not a catalogue instrument. Reflectivity carries no angle, polarization or wavelength dependence.