Page 100 - Modern Optical Engineering The Design of Optical Systems

The Primary Aberrations 83

object and image are interchanged. Thus a camera lens with barrel
distortion will have pincushion distortion if used as a projection lens
(i.e., when the film is replaced by a slide). Obviously if the same lens
is used both to photograph and to project the slide, the projected image
will be rectilinear (free of distortion) since the distortion in the slide
will be canceled out upon projection.

5.3 Chromatic Aberrations

Because of the fact that the index of refraction varies as a function of the
wavelength of light, the properties of optical elements also vary with
wavelength. Axial chromatic aberration is the longitudinal variation of
focus (or image position) with wavelength. In general, the index of
refraction of optical materials is higher for short wavelengths than for
long wavelengths; this causes the short wavelengths to be more strongly
refracted at each surface of a lens so that in a simple positive lens, for
example, the blue light rays are brought to a focus closer to the lens than
the red rays. The distance along the axis between the two focus points
is the longitudinal axial chromatic aberration. Figure 5.10 shows the
chromatic aberration of a simple positive element. When the short-
wavelength rays are brought to a focus to the left of the long-wavelength
rays, the chromatic is termed undercorrected, or negative.
The image of an axial point in the presence of chromatic aberration
is a central bright dot surrounded by a halo. The rays of light which
are in focus, and those which are nearly in focus, form the bright dot.
The out-of-focus rays form the halo. Thus, in an undercorrected visual
instrument, the image would have a yellowish dot (formed by the
orange, yellow, and green rays) and a purplish halo (due to the red and
blue rays). If the screen on which the image is formed is moved toward
the lens, the central dot will become blue; if it is moved away, the central
dot will become red.

Figure 5.10 The undercorrected longitudinal chromatic aberration of a simple
lens is due to the blue rays undergoing a greater refraction than the red rays.