Random Phasor Sums

Abstract

In this chapter we examine the first-order statistical properties of the amplitude and phase of various kinds of random phasor sums. By “first-order” we mean the statistical properties at a point in space or, for time-varying speckle, in space–time. While in optics it is generally the intensity of the wave that is ultimately of interest, in both ultrasound and microwave imaging, the amplitude and phase of the field can be detected directly. For this reason, we focus attention in this chapter on the properties of the amplitude and phase of the resultant of a random phasor sum. In the chapter that follows, we examine the corresponding properties of the intensity, as appropriate for speckle in the optical region of the spectrum.