Pairs of Spherical Mirrors as Prime Focus Correctors for the Anglo-Australian Telescope

Last year I described pairs of spherical mirrors that remove the coma and astigmatism in the image formed by a paraboloid mirror and leave the spherical aberration corrected. The investigation can be extended to deal with other shapes of primary mirror, for example the hyperboloid primary of the Anglo-Australian Telescope. The algebraic analysis becomes more complicated than for a paraboloid; but it still has the feature that at an early stage a cubic equation has to be solved, each real root of which gives rise to a second cubic. Thus in principle the mathematics could lead to nine solutions. However, it again turns out that not all the roots are real; and even for the real roots not all the solutions are physically useful, because in some cases the final image is virtual, and in others the tertiary mirror lies behind the secondary where light can not reach it. When the primary is a paraboloid, there are three useable solutions all with the property that the field corrector (consisting of the pair of spherical mirrors) can simply be scaled up or down at the user’s pleasure according to the diameter of the field he wishes to photograph. When the primary is of any other shape this is no longer possible.