All real lenses made from spherical

All real lenses made from sphericalsurfaces may display spherical berration. Additionally, ifthe object point is distant from the axis of the lens, or off-axis, theimage may display otheraberations such as astigmatism, coma, dstortion, and field curvature. Furthemore, the indek ofrfiation of the lens is a function of wavelength, so its focal lngh varies lighaly wih wvelnghthe resulting aberration is called chromatic aberration.Spherical aberaion appears both on the axis and off the axis, and does not depend on thedistance off-axis. Astigmatism occursbecause an off-axis bundle of rays strikes the lensasymmetrially. This asymmetry causes a pair of line images to appear: one behind the plane of bestfocus and the other in front of it. Coma gives rise to a cometike image; the head of the comet is theparaxial image point, and the aberration manifests itself as the tail. The tail points away from theaxis of the lens and is 3 times longer than its wide. The length of the comatic image, from theparaxial image point to the end of the tail, increases in proportion to the square of the lens diameterand to the distance of the image point from the axis of the lens. The image projected by a lens doesnot truly lie on a plane but rather on a curved surface, even if other aberrations are zero. Thisaberration is called field curvature. If the magnification is function of the distance of an image pointfrom the axis, then the image will not be rectilinear. The resulting aberration is called distortion.Aberrations may be reduced by adjust the radii of the curvature of lens elements so that, forexample, angles of incidence are minimized; this process is sometimes called bending the lens.Astigmatism, however, is only weakly influenced by bending the elements. Similarly, oneaerration can sometimes be balanced against another. For example, spherical abrration can beparial compensated by moving the image plane from the paraxial image plane to the waist, that is,by compensting spherical abeationo by defocusing. Similarly, coma, dsrtin, and asgmataismcan be reduced by adjusting the axis position of the aperture stop.