Overview: In this chapter we study the effects of a spatially partially coherent beam. Several investigations of the properties of such beams have led to the conclusion that the use of a diffuser at the exit aperture of a coherent laser can produce reduced scintillations at the receiver under the proper conditions. The same model, however, may also serve as a useful model for certain studies concerning the reflection of an optical wave from a partially rough surface.
We begin by reviewing the Gaussian Schell-model for the autocorrelation function of the surface roughness of the diffuser that is used in most studies of partially coherent beams. We then illustrate an equivalent formulation using the power spectral density for the diffuser roughness that we model as associated with a thin phase screen. The mutual coherence function for such a beam in free space is used to infer the spot size increase caused by the diffuser and the speckle size in both the receiver and detector plane. In developing models for the scintillation index, we take into account the coherence time of the detector versus that of the diffuser. In particular, we investigate the effect of a partially coherent beam in the presence of both slow and fast detectors. Also treated is the bit error rate (BER) for pulsed modulation using on-off keying (OOK) in a digital communication link operating in an open atmospheric channel.
The free-space analysis of an optical wave reflected from a partially rough surface such as that associated with certain lidar systems is explored through use of the same partially coherent beam model. By adjusting the surface roughness correlation length, such a target can take on characteristics associated with a smooth reflector (specular target) and also that of a fully diffuse or Lambertian target. Once again we consider separately slow and fast detectors with regard to the temporal fluctuations associated with the surface roughness.