Optical Signal Processing

2

Geometrical Optics

2.1.   INTRODUCTION

The main emphasis in this book is on physical optics, which describes how light interacts to produce diffraction effects useful in optical signal processing. Although most of the results in this chapter can be obtained from physical optics, we first provide a working knowledge of geometrical optics because it often provides the same results through more straightforward calculations. Geometrical optics is the characterization of optical systems based on an assumption that the wavelength of light is zero and that light travels only along ray paths.

As it turns out, we cannot isolate a single ray. If we attempt to do so, we find that the harder we try, the more difficult it becomes. In both Figure 2.1(a) and Figure 2.1(b) we successfully introduce apertures that reduce the spatial extent of the incident light beam. Figure 2.1(c), however, shows that a further reduction in the size of the aperture does not isolate a ray; in fact, light actually diverges after the aperture. The finite wavelength of light causes this spreading action or diffraction, as discussed extensively in Chapter 3, and is the foundation on which much of optical signal processing is built. In this chapter we proceed as though we can actually isolate a ray.

2.2.   REFRACTIVE INDEX AND OPTICAL PATH

The velocity c of light in vacuum is approximately 3(10⁸) m/sec. The velocity v of light in any other medium, however, is lower than c. The inverse relative velocity n = c/v is ...