We study the formation of caustic surfaces produced by a concave conic mirror considering a point source placed at arbitrary position along the optical axis. Using the caustic formula and a paraxial approximation, we derive analytic expressions to evaluate the spherical aberration at the third order. A formula to reduce this aberration at any order is provided, which gives the condition for stigmatic points. Furthermore, we apply the formulas to evaluate the circle of least confusion for a concave conic mirror as a function of all parameters involved in the process of reflection.
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