Houghton's original design uses a two-lens corrector at the front of the telescope and a spherical mirror at the back; it was patented in 1944.
Light loss and "ghost" reflections, troublesome in the past, are minimal with modern anti-reflective coatings.
It is placed in the path of the incoming light rays, which are parallel, so the residual chromatic aberration is very nearly zero.
A spheroidal mirror is much easier to make because the entire surface appears to uniformly "black out" when checked with a Foucault test.
This eliminates star image diffraction spikes, caused by the vanes of the spider mount.