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Chapter 7:
Chromatic Aberrations
So far, we have discussed the imaging relations without explicitly stating the wavelength of the object radiation. Because the refractive index of a transparent substance decreases with increasing wavelength, a thin lens, for example, made of such a substance will have a shorter focal length for a shorter wavelength. Consequently, an axial point object emanating white light will be imaged at different distances along the axis depending on the wavelength, i.e., the image will not be a “white” point. Similarly, the height of the image of an off-axis point object will vary with the wavelength, resulting in different sizes of the image of a multiwavelength object. The axial and transverse extents of the image of a multiwavelength point object are called longitudinal and transverse chromatic aberrations, respectively. They describe a chromatic change in the position and magnification of the image, which are discussed in this chapter. The longitudinal chromatic aberration is also called the axial color. There is ambiguity about the definition of the chromatic change in magnification. As a differential of the image height, it represents the difference in image heights of the chief rays of two colors in their respective Gaussian image planes. From a practical standpoint, the quantity of interest is the difference of image heights in a given image plane. The latter is referred to as the lateral color. We define a system as being achromatic if both the axial and lateral colors are zero. We start this chapter with a discussion of the chromatic aberrations of a single refracting surface and apply the results to obtain the chromatic aberrations of a thin lens, a doublet, and finally, a general system consisting of a series of refracting surfaces. The chromatic aberrations of a plane-parallel plate are considered as an example of the general theory. A doublet consisting of two thin lenses that are separated, or in contact so that its focal length is achromatic, is discussed. Numerical examples are given to illustrate the concepts.
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