Aberrations

Aberrations are errors in an optical system. There are six optical aberrations that may affect the image produced by a telescope. Some affect the quality of the image, others affect its position. They are:

• Chromatic aberration: error of quality

• Spherical aberration: error of quality

• Astigmatism: error of quality

• Field curvature: error of position

• Distortion: error of position

Chromatic aberration is an error of refractive systems and is therefore of consideration for all binoculars. Because any light that does not impinge normally on a refractive surface will be dispersed, single converging lenses will bring different wavelengths (colors) of light to different foci, with the red end of the optical spectrum being most distant from the lens. This is longitudinal (or axial) chromatic aberration. Lateral chromatic aberration manifests as different wavelengths of light forming different size images. It is sometimes referred to as color fringing, which is descriptive of the visual effect of its presence.

Visible chromatic aberration can exist in objective lenses and eyepieces. Chromatic aberration can be reduced, but not eliminated, by using multiple lens elements of different refractive indices and dispersive powers. An achromatic lens has two elements and brings two colors to the same focus (Figure 2.20).

The choice of glass and lens design will determine not only which colors are brought to the same focus, but also the distance over which the secondary spectrum is focused. An apochromatic lens uses three elements and will bring three colors to the same focus.

Spherical aberration is an error of spherical refractive and reflective surfaces that results in peripheral rays of light being brought to different foci to those near the axis (Figure 2.21). If the peripheral rays are brought to a closer focus than the near-axial rays, the system is undercorrected. If they are brought to a more distant focus, the system is overcorrected. Spherical mirrors and converging lenses are undercorrected and diverging lenses are overcorrected.

In compound lenses, spherical aberration can be suppressed in the design of the lens by using several lenses of minimal curvature as a substitute for one of considerable curvature, by choosing appropriate curvatures for the converging and diverging elements, or as a combination of both. In Newtonian mirrors, such as those used in most reflecting binocular telescopes, the spherical aberration is corrected by progressively deepening the central part of the mirror so that all regions focus paraxial rays to the same point. The shape of the surface is then paraboloid, that is the surface that results from a parabola being rotated about is axis.

There are other manifestations of spherical aberration, the most common of which is zonal aberration, in which different zones of the objective lens or primary mirror have different focal lengths. Spherical aberration increases as a direct cubic function of an increase in aperture and is independent of field angle.

Figure 2.20. Chromatic aberration.

*

n As aperture increases, the rays are focused at shorter lengths

// Paraxial focus

/

—>-

—>-

Figure 2.21. Spherical aberration in a converging lens.

Figure 2.21. Spherical aberration in a converging lens.

Coma is a lop-sided spherical aberration. If an objective lens is corrected for paraxial rays, then any abaxial ray cannot be an axis of revolution for the lens surface and different parts of the incident beam of which that ray is a part will focus at different distances from the lens. The further off-axis the object, the greater the effect will be. The resulting image of a star tends to flare away from the optical axis of the telescope, having the appearance of a comet, from which the aberration gets its name. In objective lenses, coma can be reduced or eliminated by having the coma of one element counteracted by the coma of another. It is

Tear-shaped image 'points' towards the \ J optical axis of the lens.

r

Figure 2.22. Coma in a converging lens.

Figure 2.22. Coma in a converging lens.

usually particularly noticeable in ultrawide angle binoculars (Figure 2.22). Coma increases as direct square (quadratic) function of aperture increase and increases as a linear function of increase in field angle.

Astigmatism results from a different focal length for rays in one plane as compared to the focal length of rays in a different plane. A cylindrical lens, for example, will exhibit astigmatism because the curvature of the refracting surface differs for the rays in each plane and the image of a point source will be a line (Figure 2.23). Astigmatism will, therefore, result from any optical element with a surface that is not a figure of revolution. It can also occur in surfaces that are figures of revolution. Consider two mutually perpendicular diameters across a beam of light impinging obliquely upon a lens surface. The curvature of the lens under one diameter differs from that under the other, and thus astigmatism will result. Such astigmatism can be corrected by an additional optical element that introduces equal and opposite astigmatism. Astigmatism is not normally a problem in binoculars, which are primarily used for visual work, unless they have very wide fields. Astigmatism increases linearly with an increase in aperture and as a direct square (quadratic) function of an increase in field angle.

Field Curvature No single optical surface will produce a flat image—the image is focused on a surface that is a sphere tangential to the focal plane at its intersection with the optical axis (Figure 2.24). Field curvature, which manifests as the inability to focus the periphery of the image at the same time as the center is focused, is particularly noticeable when it is present in widefield binoculars. It can be corrected in the design of the lenses. In particular, if a negative lens can be placed close to the image plane, it will flatten the field. Field curvature increases

Figure 2.23. Astigmatism.
Figure 2.24. Field curvature.

Positive or

'Pincushion'

distortion

Undistorted image

Figure 2.25. Distortion.

Positive or

'Pincushion'

distortion

Undistorted image

Figure 2.25. Distortion.

linearly with an increase in aperture and as a direct square (quadratic) function of an increase in field angle.

Distortion is an aberration by which a square object gives an image with either convex lines (negative or barrel distortion) or concave lines (positive or pincushion distortion). It is the only aberration that does not produce blurring of the image (Figure 2.25). It results from differential magnification at different distances from the optical axis. It almost always originates in the eyepiece, so any correction should be inherent in eyepiece design. A small amount of pincushion distortion can be desirable because it attenuates the "rolling ball" effect that results in an undistorted field of view (see Chapter 3). Distortion is unaffected by aperture and increases as a direct function of the cube of field angle.

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