Lurie Houghton
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The Houghton telescope is a catadioptric telescope. Instead of the fairly hard to make Schimdt and Maksutov corrector lenses, the corrector for the Houghton (or the Lurie) is relatively easy to make. It consists of two lenses, a positive and a negative, at the front of the telescope which sets the size of the aperture. All lens and primary mirror surfaces are spheroidal which eases construction. These lenses are relatively thin, though not as thin as the Schmidt corrector. With a good antireflection coating, light loss and reflections are minimal.
[edit] The corrector
The lenses for the corrector create degrees of freedom to correct aberrations. There are enough degrees of freedom to correct for spherical aberration, coma and field curvature. The total power of the corrector lens is per definition zero and it's used where the light rays are parallel, so the residual chromatic aberration is essentially zero. The Lurie or Houghton correctors can be made of the same type of glass e.g. BK7 only. Also the tolerances are very modest contrary to eg. Maksutov telescopes.
There are two types of correctors, the symmetric and the asymmetric one. The symmetric version has the benefit of R1=-R3, R2=-R4 which allows for interferometry testing of the surfaces against each other. However, the correction is slightly worse than the asymmetric one with four different radii.
[edit] The mirrors
One thing which differentiate the Houghton and the Lurie is the fact that the Lurie implement an aspheric primary, this will permit a better correction and less work on the corrector, the shape being less curved.
The Houghton primary mirror is a spherical mirror with a radius of curvature of slightly less than the total system. However, apart from the shape there is a difference compared to Newtonian primary mirror: that one has to make it bigger than the true aperture to avoid vignetting. The secondary mirror is comparable to an ordinary Newtonian secondary.