asphere

An asphere, in optics, is a surface whose curvature deviates from that of a sphere. Most commonly, aspheres are rotationally symmetric about the optical axis and are used to correct aberrations that arise from spherical surfaces, such as spherical aberration and coma. Aspheric surfaces can be used in lenses, mirrors, and other optical elements to achieve flatter fields and better focusing with fewer elements.

The shape of an aspheric surface is typically described by a sag function z = z(r) with radial coordinate r measured from the axis. For a conic section, z(r) = (c r^2) / (1 + sqrt(1 − (1 + k) c^2 r^2)), where c is the curvature (the reciprocal of the radius) and k is the conic constant. Real-world aspheres often add higher-order terms, z(r) = z_conic(r) + sum a_n r^{2n}, to tailor the profile precisely.

Manufacture and design: Aspheres are produced by grinding and polishing or with diamond turning; modern processes include computer-controlled grinding, precision polishing, magnetorheological finishing, and specialized coating techniques. Tolerances and alignment affect performance; test methods include interferometry and null testing to verify surface accuracy.

Applications: Aspheres are widely used in camera lenses, projection optics, telescope mirrors, and lithography. The use of aspheric surfaces can reduce the number of elements, decrease system size, and improve image quality across the field, but they introduce higher manufacturing and testing complexity and cost.