In order to solve some practical problems in scientific research and engineering, all five expressions of Seidel monochromatic aberration coefficients were deduced for single aspherical mirror system. The most important one is that a unified spherical aberration formula of single aspherical mirror imaging was set, which the object is at arbitrary positions on the principal optic axis. Based on the spherical aberration formula, researched the relationship between the best fit spherical surface and longitudinal spherical aberration of the aspherical mirror, which made the best fit sphere calculation more indicative and easier.
In order to make the plan of aspheric surface testing more convenient and efficient, the dynamic range of aspheric surface by the non-null interferometry was studied. The rule of maximum dynamic range of aspheric surface by the non-null interferometry is: the fringes of the densest zone is not only at the margins of the pattern, but also in some middle one general zone, and can be distinguished all at the same time. Based on the aberration theory, an expression about dynamic range was deduced, which was an intuitive and accurate judging criterion. An example was made to verify the theory of dynamic range; and it is also proved that the retrace error can increase the dynamic range slightly by simulation.
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