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In optics, aberration is a property of optical systems such as lenses that causes light to be spread out over some region of space rather than focused to a point.[1] Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics.[2] In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.[3]

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.

Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.

## Overview

Reflection from a spherical mirror. Incident rays (red) away from the center of the mirror produce reflected rays (green) that miss the focal point, F. This is due to spherical aberration.

With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane (or, more generally, the image surface). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called aberrations of the lens.

Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.

Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.

### Monochromatic aberrations

The most common monochromatic aberrations are:

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.

In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.

### Chromatic aberrations

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:

• Axial (or "longitudinal") chromatic aberration
• Lateral (or "transverse") chromatic aberration

## Theory of monochromatic aberration

In a prefect optical system in the classical theory of optics,[4] rays of light proceeding from any object point unite in an image point; and therefore the object space is reproduced in an image space. The introduction of simple auxiliary terms, due to Gauss,[5][6] named the optics, aberration is a property of optical systems such as lenses that causes light to be spread out over some region of space rather than focused to a point.[1] Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics.[2] In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.[3]

An image-forming optical

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.

Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.

With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane (or, more generally, the image surface). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called aberrations of the lens.

Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.

Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.

### Monochromatic aberrations

The most common monochromatic aberrations are:

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.

In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.

### Chromatic aberrations

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:

• Axial (or "longitudinal") chromatic aberration
• Lateral (or "transverse") chromatic aberration

## Theory of monochromatic aberration

In a prefect optical system in the classical theory of optics,[4] rays of light proceeding from any object po

Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.

Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.

The most common monochromatic aberrations are: