(Solved): 7. (a) (20\%)For partial coherent wave shown in figure (a) and (b), explained their difference in ...

7. (a) (20\%)For partial coherent wave shown in figure (a) and (b), explained their difference in terms of (i) complex degree of temporal coherence \( g(\tau)=\frac{G(\tau)}{G(0)}=\frac{\left\langle U^{*}(t) U(t+\tau)\right\rangle}{\left\langle U^{*}(t) U(t)\right\rangle}, G(\tau)=\left\langle U^{*}(t) U(t+\tau)\right\rangle \) (ii) coherent time \[ \tau_{c}=\int_{-\infty}^{\infty}|g(\tau)|^{2} d \tau \] (iii) intensity spectral density \( I=\int_{0}^{\infty} S(\nu) d \nu \) (b) for a partial coherent plane wave as Fig. (c), it has a complex wave function \[ U_{p}(t)=\left\{\begin{array}{ll} A_{p} \exp \left(-\frac{t}{\tau_{e}}\right) \exp \left(j 2 \pi \nu_{0} t\right), & t \geq 0 \\ 0, & t<0 . \end{array}\right. \] Derive (i) (ii) and (iii) above (a) (b) (c) (c) What will be the cross correlation coefficient look like for case (c) (a) (b) CS Scanned with CamScanner