Design starting points for freeform aspheric telescopes

David ShaferDavid Shafer Optical Design

1) One approach to a good reflective telescope design with freeform aspherics is to base it on a good design with conventional aspherics

2) Just as is the case with camera lenses, a combination of wide angle and fast speed is best served by the retrofocus configuration, with a negative power first element

3) We will look at a simple three mirror design

The Baker-Paul design combines the great aberration correction of two confocal parabolic mirrors with the Schmidt principle and a spherical third mirror to get an image with good correction. The parabolic secondary mirror becomes a sphere when the Schmidt aspheric has its deformation superimposed on it.

This design is only good for small field sizes and the image is not accessible.

Parabola

Hyperbola Sphere

Image

There is an inverse, or retrofocus version of the design, where the first mirror is a convex parabola and the second mirror is a concave parabola. It is at the center of curvature of the third mirror, which is a sphere. The Schmidt aspheric to correct for the sphere now adds its deformation to the second mirror and turns the parabola into a hyperbola.

This inverse or retrofocus configuration is much better suited to large field sizes than the classical Baker-Paul design from the previous slide.

There is an alternate solution which, at first, looks very unpromising. We start out with the first two confocal parabolas but now we add the Schmidt aspheric to the first mirror, the convex one. That turns this parabola into an oblate spheroid. There is then a virtual image formed of this mirror by the second mirror and it lies quite a bit to the left of the second mirror. We then make the third mirror, the sphere, concentric about this virtual Schmidt aspheric location.

This has terrible obscuration but the image is now in a better location and the system length is much shorter.

Sphere

Parabola

Oblate Spheroid

This design can then be used far off-axis to avoid most of the obscuration and it makes a good starting point for a freeform aspheric design.

Three freeform aspheric mirrors, f/2.0 and a 10 degree diameter flat field. Spot size is 10 arc seconds over field

Freeform aspherics allow this to become an unobscured design with a good image location

f/2.0, 10 degree diameter flat field, spot size = 20 arc seconds over the field.

These designs are only partially optimized and better performance is probably possible

This shows how a design with conventional aspherics can make for a good starting point for a freeform aspheric design