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In Chapters 1 through 18, we have attempted to discuss some of the various aspects of image formation and the background that is needed for a quantitative treatment of this subject. Indeed, it is a fairly obvious statement to say that the problem of image formation and evaluation appears to be a perennial one in optics. Historically, the very early developments in the theory of image formation were in geometrical descriptions of the process, and the techniques of ray tracing were devised. The Gaussian lens formula is indeed simple and useful, and we showed how this result can be obtained from the general treatment of image formation in terms of wave optics. More accurate descriptions of image formation depend on the discussion of the problem in terms of the wave nature of light - a purely monochromatic approximation leading to the coherent imaging result, and the statistical nature of light leading to the more familiar incoherent image formation. The subject took on an entirely new character in the early 1950s with the application of communication theory to optics. This resulted in a new vocabulary being introduced into the optical literature; image formation was now described in terms of the impulse response of the imaging system or in terms of the system transfer function. Frequency domain analysis has thus become a powerful tool in the description and evaluation of optical systems; so much so that lens manufacturers provide modulation transfer function curves with their lenses, and film handbooks now contain modulation transfer functions for films.
The communication theory approach, however, also led to a more detailed study of coherent image formation and to the field of study now known as optical data processing of information, both analog and digital. While this latter is a reasonably new development, it has its roots in the early work of Abbe in his discussions of image formation in a microscope. Basically, Abbe's theory was that an optical image is formed by the superposition of interference fringes. It is worthwhile to discuss here the implications of Abbe's theory in a little more detail.
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