A monochromatic, unit-amplitude plane wave falls normally on a "sandwich" of two diffusers. The diffusers are moving in opposite directions with equal speeds, as shown in Fig. 5-5-10pp. The amplitude transmittance of the diffuser pair is expressible as

\[ \mathbf{t}_{A}(\xi, \eta)=\mathbf{t}_{1}(\xi, \eta-v t) \mathbf{t}_{2}(\xi, \eta+v t) \]

where \(\mathbf{t}_{1}\) and \(\mathbf{t}_{2}\) may be assumed to be drawn from statistically independent ensembles (since knowledge of one tells nothing about the other). Show that if the diffusers have identical Gaussian-shaped autocorrelation functions, \[ \gamma_{t}(\Delta \xi, \Delta \eta)=\exp \left\{-a\left[(\Delta \xi)^{2}+(\Delta \eta)^{2}\right]\right\} \]
the mutual coherence function of the transmitted light is separable.

Transcribed Image Text:

Speed P Opaque screen 00 Laser Moving diffusers Speed Observing screen Figure 5-10p