# Optical aberration

An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration.

Although defocus is technically the lowest-order of the optical aberrations, it is usually not considered as a lens aberration, since it can be corrected by moving the lens (or the image plane) to bring the image plane to the optical focus of the lens.

Comparison of an ideal image of a ring (1) and ones with only axial (2) and only transverse (3) chromatic aberration

Chromatic aberration occurs when different wavelengths are not focussed to the same point. Types of chromatic aberration are:

Aberration of axial points (spherical aberration in the restricted sense)Aberration of elements, i.e. smallest objects at right angles to the axis

Since the aberration increases with the distance of the ray from the center of the lens, the aberration increases as the lens diameter increases (or, correspondingly, with the diameter of the aperture), and hence can be minimized by reducing the aperture, at the cost of also reducing the amount of light reaching the image plane.

Aberration of lateral object points (points beyond the axis) with narrow pencils — astigmatism
Image plane of a flat-top beam under the effect of the first 21 Zernike polynomials. The beam goes through an aperture of the same size, which is imaged onto this plane by an ideal lens.

There are even and odd Zernike polynomials. The even Zernike polynomials are defined as

corrected for the angle of aperture u* (the height of incidence h*) or the angle of field of view w*.
(1) Largest aperture; necessary corrections are — for the axis point, and sine condition; errors of the field of view are almost disregarded; example — high-power microscope objectives.
(2) Wide angle lens; necessary corrections are — for astigmatism, curvature of field and distortion; errors of the aperture only slightly regarded; examples — photographic widest angle objectives and oculars.
Between these extreme examples stands the normal lens: this is corrected more with regard to aperture; objectives for groups more with regard to the field of view.
(3) Long focus lenses have small fields of view and aberrations on axis are very important. Therefore zones will be kept as small as possible and design should emphasize simplicity. Because of this these lenses are the best for analytical computation.