Spherical aberration it is to use a single aspheric lens. "Positive" spherical aberration means peripheral rays are bent too much. "Negative" spherical aberration means peripheral rays are not bent enough. The effect is proportional to the fourth power of the diameter and inversely proportional to the third power of the focal length, so it is much more pronounced at short focal ratios, i.e., "fast" lenses. In lens systems, the effect can be minimized using special combinations of convex and concave lenses, as well as using aspheric lenses or aplanatic lenses. For simple designs one can sometimes calculate parameters that minimize spherical aberration.
Compound refractive lens Compound refractive lens A Compound refractive lens (CRL) is a series of individual lenses arranged in a linear array in order to achieve focusing of X-rays in the energy range of 5-40 keV. They are an alternative to the KB mirror. For all materials the refractive index for X-rays is close to 1, hence a single conventional lens for X-rays has an extremely long focal length (for practical lens sizes). In addition, X-rays attenuate as they pass through a material so that conventional lenses for X-rays have long been considered impractical. The CRL gets its reasonably short focal length, on