Optical aberration

In optics, an aberration is a characteristic of systems like lenses and mirrors where the image they produce does not accurately match the object being viewed. Depending on the type, aberrations can make an image blurry, misshapen, or show color fringes and other effects absent from the original object. Essentially, an aberration is a deviation from what paraxial optics would predict for the system’s performance. In an imaging setup, this happens when light from a single point on the object fails to converge to (or diverge from) a single point after passing through the system. These issues arise because the simple paraxial model is not a fully accurate description of how optics affect light—they are not due to defects in the lenses or mirrors themselves. A system with aberration produces an image that lacks sharpness, so instrument makers must correct for these effects. Aberrations can be studied using geometrical optics; the articles on reflection, refraction, and caustics cover general ray behavior.

With a perfect lens, light from any object point would pass through and meet at a single point on the image plane (or surface). But real lenses, even when flawlessly made, do not focus light to a single point. These deviations from ideal performance are called lens aberrations. They fall into two categories: monochromatic and chromatic. Monochromatic aberrations stem from the lens or mirror’s geometry and occur with both reflected and refracted light; they appear even when using light of a single color. Chromatic aberrations, on the other hand, come from dispersion—the change in a lens’s refractive index with wavelength. Because of this, different wavelengths focus at different points. Chromatic aberration does not occur with monochromatic light.

The most common monochromatic aberrations are defocus, spherical aberration, coma, astigmatism, field curvature, and image distortion. Although defocus is technically the lowest-order aberration, it is usually not treated as a lens aberration because moving the lens or image plane can correct it by bringing the image plane to the focus. Additionally, piston and tilt shift the focal point’s position, but they are not true optical aberrations: an otherwise perfect wavefront altered by piston and tilt still forms a perfect, aberration-free image, just shifted elsewhere.

Chromatic aberration happens when different wavelengths fail to focus at the same point. Its types are axial (or longitudinal) chromatic aberration and lateral (or transverse) chromatic aberration.

In classical optics, a perfect system would have rays from any object point meet at an image point, reproducing the object space in an image space. Gauss introduced auxiliary terms—focal lengths and focal planes—that allow determining the image of any object for any system. But Gaussian theory holds only when all rays make infinitely small angles with the optical axis, meaning infinitesimal objects, images, and lenses. In practice, these conditions are not met, and uncorrected systems produce ill-defined, often blurred images if the aperture or field of view exceeds certain limits. Work by James Clerk Maxwell and Ernst Abbe showed that the properties of such reproductions—like relative position and image size—are not special to optical systems but necessary consequences of assuming every point in a space is reproduced as an image point, regardless of how the reproduction occurs. However, they also showed that no optical system can meet these assumptions because they contradict the fundamental laws of reflection and refraction. Thus, Gaussian theory is only a convenient approximation of reality; real systems fall short of this unattainable ideal. Currently, the best that can be done is to project a single plane onto another plane, but even then aberrations always occur, and it may be unlikely they will ever be fully corrected.

For axial points, consider any optical system S. Rays from an axial point O at an angle u₁ meet at O′₁, while those at angle u₂ meet at O′₂. With refraction at a collective spherical surface or through a thin positive lens, O′₂ lies in front of O′₁ when u₂ is larger than u₁ (under-correction); the opposite occurs with a dispersive surface or lens (over-correction). The caustic in the first case looks like a greater-than sign (>), and in the second like a less-than sign (<). If u₁ is very small, O′₁ is the Gaussian image. The distance O′₁O′₂ is called the longitudinal aberration, and O′₁R the lateral aberration of the pencils with aperture u₂. If the pencil at angle u₂ has the maximum aberration among all transmitted pencils, then in a plane perpendicular to the axis at O′₁ there is a circular disk of confusion with radius O′₁R, and in a parallel plane at O′₂ another disk with radius O′₂R₂; between these two lies the region of best focus.