Optical Aberrations

If an imaging system is not focused to the actual distance of the imaged objects, the image becomes blurred. That problem is not necessarily considered as an imperfection of the optical system, which needs to be addressed via design optimization, since one could simply correct the focus adjustment accordingly. However, that works only as long as all imaged objects are within a certain distance range for which reasonably sharp images can be obtained: Imaging systems usually have a limited depth of field. Also, perfect focusing over the full image area may not be possible due to field curvature (see below).

Due to chromatic dispersion (caused by wavelength-dependent refraction), a lens will usually have a focal length which slightly depends on the optical wavelength. Obviously, that phenomenon can cause substantial degradations of image quality, called chromatic aberrations, since the visible wavelength range spans nearly one octave (roughly 400 nm to 700 nm). However, there are certain ways to obtain achromatic optics, essentially by properly combining different lenses made from different optical materials. Another possibility is to work with reflective optics, which are generally free of chromatic aberrations.

See the article on chromatic aberrations for more details.

The further sections explain types of aberrations which occur even for monochromatic light. They are the five types of primary aberrations as identified by Phillip Ludwig Seidel in the 19^th century.

Most optical lenses have spherical surfaces, because those are most easily fabricated. That surface shape, however, is not ideal for imaging; the outer parts of the lens are then too strongly curved. This results in so-called spherical aberrations which can seriously degrade the image quality.

This problem can be solved either by using aspheric lenses or by using a combination of lenses designed such that spherical aberrations are well compensated. The development of improved optical fabrication methods for aspheric optics has led to their increased use, allowing manufacturers to make high-performance objectives with fewer lenses – which can also result in improved light throughput.

Note that spherical aberrations are also often considered in a more general sense of non-ideal phase changes for larger radial positions. Such errors can also be caused by simple optical plates and by thermal lensing in laser crystals, for example.

See the article on spherical aberrations for more details.

The problem of astigmatism is frequently observed when light propagates with a substantial angle against the optical axis. For example, when light rays hit a lens or a curved mirror under substantial angle, the distance from the lens to the focal point somewhat differs between the vertical and horizontal direction, or more precisely in the meridional and sagittal plane. In the focal plane corresponding to each of those directions, a point is thus imaged to an elliptical region.

Astigmatism of a lens depends on the lens design, but cannot be fully corrected for a single lens. Also, it does not disappear simply by using a narrow aperture stop, preventing light from going through the outer region of a lens. Nevertheless, anastigmatic optical systems (i.e., systems not exhibiting astigmatism) can be designed with a suitable combination of lenses.

See the article on astigmatism for more details.

The phenomenon of coma occurs when light has a substantial angle to the optical axis and in addition propagates throughout outer regions of a lens. An object point is then imaged to a region with a more or less complicated shape, often somewhat reminiscent of that of a comet.

Coma can be reduced with an aperture stop (at the cost of losing image brightness) or with more sophisticated design methods.

As an example, astigmatism and coma may be observed by watching a small dot on a piece of paper through a magnifying glass which is substantially tilted against the viewing direction. It is more pronounced for glasses with high magnification.

Field curvature denotes the problem that the focal points of a lens as obtained with different incidence angles do not lie on a plane, but on a curved surface – particularly for wide open apertures. When using a plane image sensor, for example, that can make it impossible to adjust the optics for sharp imaging over the full image plane. One will therefore either try to minimize field curvature or in some cases to use an appropriately curved image sensor.

The problem of field curvature has been analyzed particularly by Joseph Petzval, and is therefore often called Petzval field curvature. It is particularly relevant for measurement microscopes, for example.

There are geometric image distortions, letting straight lines of an object appear as non-straight curves in an image. Frequently encountered problems are barrel distortions and pincushion distortions. Such problems are particularly observed in wide-angle objectives.

A common method for characterizing any kind of monochromatic aberrations (i.e., everything except for chromatic aberrations) is based on a set of mutually orthogonal functions developed by Frits Zernike. These functions depend on the polar coordinates ρ and φ. The radial part as described by Zernike polynomials, while the azimuthal factor is cos mφ or sin mφ. One decomposes the wavefront distortions versus position in two dimensions, and the obtained coefficients of those functions quantify the corresponding types of aberrations.

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

Please do not enter personal data here; we would otherwise delete it soon. (See also our privacy declaration.) If you wish to receive personal feedback or consultancy from the author, please contact him e.g. via e-mail.