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Chapter 2:
Coherent-Mode Representation of Optical Systems
Linear system theory has been successfully employed for describing optical systems. Within the framework of the linear system approach, the output of an optical system g(x ′ ) and its input f(x) are related by a linear transformation of the general form g(x ′ )=∫ ∞ −∞ f(x)h(x ′ ,x)dx, where h(x,x ′ ) is the so-called impulse response of the system, i.e., the output at x ′ resulting from the impulse input at point x. Such a linear transformation describes an optical system with both completely coherent and completely incoherent illumination. In the first case, f(x) and g(x ′ ) have the meaning of light intensities; while in the second case, they should be considered as the complex amplitudes of an optical field. At the same time, as it has been shown first by Gamo and then by Thompson, when partially coherent illumination is used, an optical system exhibits an essential nonlinear nature. In this case, to describe an optical system, one must apply the basic ideas from nonlinear system theory.
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