asferische

Asferische is a term used to describe surfaces that are not perfect spheres. In geometry and optics, an aspheric (or aspherical) surface deviates from a constant radius of curvature, which characterizes a sphere. This allows more flexible shaping of the surface to meet imaging or functional goals. In optical design, aspheric surfaces are commonly used to reduce aberrations such as spherical aberration, coma, and astigmatism, enabling sharper images with fewer elements or thinner lenses.

Mathematical models and representations: An aspheric surface can be described by a base conic section combined with higher-order terms or by a general polynomial representation. A widely used form for rotationally symmetric aspheres is the sag equation z(r) = (c r^2) / (1 + sqrt(1 - (1 + k) c^2 r^2)), where r is the radial distance, c is the curvature (the reciprocal of the radius), and k is the conic constant. More flexible models add polynomial coefficients or use non-rotational aspheres for complex fields of view. In practice, modern optical design relies on computer-aided optimization to tailor the aspheric surface to specific performance goals.

Applications and manufacturing: Aspheric elements are common in eyeglasses, camera lenses, and telescope objectives, as well as in laser optics and lithography. They can reduce the number of elements required, improve image quality across the field, and enable thinner, lighter lenses. Manufacturing methods include precision grinding and polishing, diamond turning, and injection molding or replication for plastic substrates; coatings are often applied to boost transmission and minimize reflections.

Origin and terminology: The concept emerged with advances in optical theory and fabrication in the 19th and 20th centuries. The term “aspheric” is used in English, while equivalent terms in other languages reflect the same idea of non-spherical surfaces. The topic spans geometry, optical engineering, and manufacturing.