TABLE OF CONTENTS In addition to the basic properties of diffraction that were just reviewed, there are a number of important features of optical systems that can be explained in terms of a formal mathematical analysis of wavefront propagation through apertures. We will review here the important properties of lens systems, where we will derive from first principles not only diffraction through apertures, but phase modulation caused by actual lens structures.
A second treatment directed at explaining imaging systems is then provided to explain lenses from a linear systems perspective. Lastly, a summary of Fourier optics and imaging systems in a simplified signal processing form is provided to draw important analogies between optics and time-domain signal processing, which may be more familiar to the practicing electrical engineer.
The most fundamental approach to the analysis of optical (lens) systems is to consider the effect of a lens on a wavefront. Consider what happens when a plane wave is incident on a lens from the left as shown in Fig. 6.1(a). A lens causes an incident wave to focus at a distance s i with wave curvature expressed as a phasor exp ( ? jkr), where r 2 = s 2 i + x 2 + y 2 t. If x and y are ? s i, then
There is an overall average phase shift of ks i radians and another phase shift versus x
