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Chapter 3:
Linear Systems Theory
The previous chapter reviewed the basic principles underlying light propagation phenomena that are of interest for this book. We have seen that the propagation of light in space and matter satisfies the wave equation which is derived from Maxwell's equations. In free space Maxwell's equations are linear in their variables (the electric and the magnetic fields). When the electromagnetic field interacts with matter, the structure of the material introduces nonlinear effects, namely, the optical characteristics of the material are themselves dependent on the electromagnetic field. However, except for some special materials, the nonlinearities are rather small unless the light has extremely high intensities. Accordingly, for most applications discussed in this book, nonlinear effects can be ignored. If we disregard nonlinear effects, light propagation may be considered a linear process which can be treated using the advanced procedures of linear systems theory. Traditional linear systems theory was developed for the treatment of temporal signals that are modified by some electronic instrument. In optics we shall be mainly interested in two-dimensional spatial signals. This chapter contains a review of linear systems theory adapted to two-dimensional signals. Assuming that the reader is familiar with the basic concepts of linear systems and Fourier analysis, we shall not dwell on mathematical rigor and many of the results will be stated without proof. All the details can be found in the relevant literature.
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