aberration

(astronomy)

The apparent change in direction of a source of light caused by an observer's component of motion perpendicular to the impinging rays.

To visualize the effect, first imagine a stationary telescope (illustration a) aimed at a luminous source such as a star, with photons traveling concentrically down the tube to an image at the center of the focal plane. Next give the telescope a component of motion perpendicular to the incoming rays (illustration b). Photons passing the objective require a finite time to travel the length of the tube. During this time the telescope has moved a short distance, causing the photons to reach a spot on the focal plane displaced from the former image position. To return the image to the center, the telescope must be tilted in the direction of motion by an amount sufficient to ensure that the photons once again come concentrically down the tube in its frame of reference (illustration c). The necessary tilt angle α is given by tan α = vc, where v is the component of velocity perpendicular to the incoming light and c is the velocity of light. (An analogy illustrating aberration is the experience that, in order for the feet to remain dry while walking through vertically falling rain, it is necessary to tilt an umbrella substantially forward.)

Demonstration of aberration, (a) Fixed telescope; photons form image at center of focal plane, (b) Moving telescope; image is displaced from center, (c) Tilted moving telescope is required to restore image to center.

This discovery provided the first direct physical confirmation of the Copernican theory. A second important application of aberration has been its clear-cut demonstration that, as is axiomatic to special relativity, light reaching the Earth has a velocity unaffected by the relative motion of the source toward or away from the Earth. See also Light; Parallax (astronomy).

Aberration (optics)

A departure of an optical image-forming system from ideal behavior. Ideally, such a system will produce a unique image point corresponding to each object point. In addition, every straight line in the object space will have as its corresponding image a unique straight line. A similar one-to-one correspondence will exist between planes in the two spaces. This type of mapping of object space into image space is called a collinear transformation. When the conditions for a collinear transformation are not met, the departures from that ideal behavior are termed aberrations. They are classified into two general types, monochromatic aberrations and chromatic aberrations. The monochromatic aberrations apply to a single color, or wavelength, of light. The chromatic aberrations are simply the chromatic variation, or variation with wavelength, of the monochromatic aberrations. See also Chromatic aberration; Geometrical optics; Optical image.

The monochromatic aberrations can be described in several ways. Wave aberrations are departures of the geometrical wavefront from a reference sphere with its vertex at the center of the exit pupil and its center of curvature located at the ideal image point. The wave aberration is measured along the ray and is a function of the field height and the pupil coordinates of the reference sphere (see illustration).

Diagram of the image space of an optical system, showing aberration measures: the wave aberration and the transverse ray aberration.

Transverse ray aberrations are measured by the transverse displacement from the ideal image point to the ray intersection with the ideal image plane. The chief monochromatic aberrations are spherical (aperture) aberrations, coma, astigmatism, curvature of field, and distortion. See also Chromatic aberration; Geometrical optics; Lens (optics); Optical image; Optical surfaces.

Each surface in an optical system introduces aberrations as the light beam passes through the system. The aberrations of the entire system consist of the sum of the surface contributions, some of which may be positive and others negative. The challenge of optical design is to balance these contributions so that the total aberrations of the system are tolerably small. In a well-corrected system the individual surface contributions are many times larger than the tolerance value, so that the balance is rather delicate, and the optical system must be made with a high degree of precision. See also Lens (optics); Optical surfaces.

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