Conic mirror
Reflects from an exact conic surface — sphere, parabola, ellipse or hyperbola — with an optional real central opening.
Open in the canvas →In the real world
A spherical mirror is easy to make and wrong in a specific way: rays striking it far from the axis cross ahead of the ones near the axis, so a distant star never quite comes to a point. That is spherical aberration, and it is not a manufacturing defect — it is what a sphere does. The conic sections fix it, each one exactly, for one particular pair of conjugate points.
The surface is described by a vertex radius and a conic constant k, which selects the section: k = 0 is a sphere, k = −1 a parabola, −1 < k < 0 a prolate ellipse, k < −1 a hyperbola, and k > 0 an oblate ellipse.
Each conic images one pair of points perfectly. A parabola takes a source at infinity to its focus, which is why it is the shape of a telescope primary and of the off-axis parabolic mirror. An ellipse images one of its two foci onto the other, both at finite distance. A hyperbola does the same for one real and one virtual focus.
Combining two of them is how reflecting telescopes and objectives are built: a Cassegrain pairs a parabolic primary with a hyperbolic secondary, a Gregorian with an elliptical one, and a Ritchey–Chrétien uses two hyperbolas to clear coma as well. The same two-mirror idea, turned into a microscope objective, is the standard tool of infrared microscopy and FTIR: mirrors have no dispersion at all, so the focus does not move with wavelength, and no glass is asked to transmit light it would simply absorb.
What every on-axis two-mirror system pays is the central obstruction. The secondary sits in the beam, so the aperture is an annulus: some light is lost outright, and in a real instrument the rest is redistributed, with a diffraction pattern whose rings are stronger than an unobstructed aperture's.
In OpticalSetup
The mirror is a real conic surface, intersected analytically. Each ray's hit point and surface normal are solved on the conic itself rather than on a paraxial stand-in, so aberration is a result here: give a mirror k = 0 and the marginal rays really do cross ahead of the paraxial ones, by an amount you can measure with a detector.
The signed vertex radius sets curvature and which way the surface bends — a radius of zero is a plane — and the coated side chooses which face reflects; the other is opaque, and reflectivity below 100% is absorbed rather than transmitted, as a solid mirror substrate would.
The central opening is a real hole, not a drawing. Rays inside it pass through the mirror entirely, and — because the search does not stop at the opening — a ray that enters through the hole at an angle can still strike the annulus further along, which is exactly the path the light takes in a Cassegrain. Because a requested radius can be too short for the requested aperture to exist, the Geometry used readout always reports the radius and opening actually realized, so a silently adjusted prescription cannot pass unnoticed.
This is a two-dimensional meridional section. There is no sagittal plane, so nothing here reproduces astigmatism or field curvature as a real conic would show them off-axis, and a rotational surface's behaviour is only being sampled along one cut.
Nothing is diffractive: there is no Airy pattern, none of the ring redistribution a central obstruction causes, and no spider vanes, so the geometric point focus a well-matched conic pair produces is sharper than any real instrument's. Reflectivity is a single flat percentage with no angle, polarization or wavelength dependence, so a coating's spectrum and an infrared detector's responsivity are both outside the model. The conic constant is bounded to ±20 and the radius to ±5000 mm.