Optical EngineeringSome properties of Mertz-type aspheric surfaces
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The aspheric reflecting surface types studied by L. Mertz for correcting certain aberrations of a spherical primary telescope mirror are examined and some properties of these surfaces are presented. For the one-surface aspheric that corrects spherical aberration of all orders, a sixth-order equation for the surface shape is derived. For the set of two aspheric surfaces correcting spherical aberration and coma of all orders, a set of differential equations has been developed to describe the surface shapes. The off-axis imaging performance is derived from the on-axis imaging properties and compared with ray-trace results.