26.14

Lens Aberrations

Rather than forming a sharp image, a single lens typically forms an image that is slightly out of focus. This lack of sharpness arises because the rays originating from a single point on the object are not focused to a single point on the image. As a result, each point on the image becomes a small blur. The lack of point-to-point correspondence between object and image is called an aberration.
One common type of aberration is spherical aberration, and it occurs with converging and diverging lenses made with spherical surfaces. Figure 26-44a shows how spherical aberration arises with a converging lens. Ideally, all rays traveling parallel to the principal axis are refracted so they cross the axis at the same point after passing through the lens. However, rays far from the principal axis are refracted more by the lens than those closer in. Consequently, the outer rays cross the axis closer to the lens than do the inner rays, so a lens with spherical aberration does not have a unique focal point. Instead, as the drawing suggests, there is a location along the principal axis where the light converges to the smallest cross-sectional area. This area is circular and is known as the circle of least confusion. The circle of least confusion is where the most satisfactory image can be formed by the lens.

Figure 26-44 (a) In a converging lens, spherical aberration prevents light rays parallel to the principal axis from converging to a common point. (b) Spherical aberration can be reduced by allowing only rays near the principal axis to pass through the lens. The refracted rays now converge more nearly to a single focal point F.

Spherical aberration can be reduced substantially by using a variable-aperture diaphragm to allow only those rays close to the principal axis to pass through the lens. Figure 26-44b indicates that a reasonably sharp focal point can be achieved by this method, although less light now passes through the lens. Lenses with parabolic surfaces are also used to reduce this type of aberration, but they are difficult and expensive to make.
Chromatic aberration also causes blurred images. It arises because the index of refraction of the material from which the lens is made varies with wavelength. Section 26.5 discusses how this variation leads to the phenomenon of dispersion, in which different colors refract by different amounts. Figure 26-45a shows sunlight incident on a converging lens, in which the light spreads into its color spectrum because of dispersion. For clarity, however, the picture shows only the colors at the opposite ends of the visible spectrum—red and violet. Violet is refracted more than red, so the violet ray crosses the principal axis closer to the lens than does the red ray. Thus, the focal length of the lens is shorter for violet than for red, with intermediate values of the focal length corresponding to the colors in between. As a result of chromatic aberration, an undesirable color fringe surrounds the image.

Figure 26-45 (a) Chromatic aberration arises when different colors are focused at different points along the principal axis: FV = focal point for violet light, FR = focal point for red light. (b) A converging and a diverging lens in tandem can be designed to bring different colors more nearly to the same focal point F.

Chromatic aberration can be greatly reduced by using a compound lens, such as the combination of a converging lens and a diverging lens shown in Figure 26-45b. Each lens is made from a different type of glass. With this lens combination the red and violet rays almost come to a common focus and, thus, chromatic aberration is reduced. A lens combination designed to reduce chromatic aberration is called an achromatic lens (from the Greek “achromatos,” meaning “without color”). All high-quality cameras use achromatic lenses.

Test your understanding of the material in Sections 26.6, 26.7, 26.8, 26.9, 26.10, 26.11, 26.12, 26.13 and 26.14 :

· | Lenses
· | The Formation of Images by Lenses
· | The Thin-Lens Equation and the Magnification Equation
· | Lenses in Combination
· | The Human Eye
· | Angular Magnification and the Magnifying Glass
· | The Compound Microscope
· | The Telescope
· | Lens Aberrations

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.