The design principles of three familiar compensators are introduced. They are null lens compensator, offner compensator
and reflective mirror compensator. Base on the three different theories, three different kinds of compensators for the
testing of F/3 hyperbolic mirror are designed. The initial parameters of every compensator are analyzed in detail. The
residual wavefront error, RMS radius of the spot diagrams and the tolerance of the three compensators are presented
respectively. Due to the residual wavefront error consisted in these compensators themselves, higher order aspheric terms
will be introduced into the hyperbolic mirror when using these compensators to test the mirror during the process of the
fabrication. These higher order aspheric terms will influence the image quality of R-C system which primary mirror is
this hyperbolic mirror. The simulation of this influence is analyzed in this paper. The residual wavefront error of the three
final designs are all less than λ/30. The RMS radii of the spot diagrams are all less than 0.48μm.
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