Show that for quasimonochromatic, stationary thermal light, the fourth-order coherence function [ boldsymbol{Gamma}_{1234}left(t_{1}, t_{2}, t_{3}, t_{4} ight)=Eleft[mathbf{u}left(P_{1},

Show that for quasimonochromatic, stationary thermal light, the fourth-order coherence function

\[ \boldsymbol{\Gamma}_{1234}\left(t_{1}, t_{2}, t_{3}, t_{4}\right)=E\left[\mathbf{u}\left(P_{1}, t_{1}\right) \mathbf{u}\left(P_{2}, t_{2}\right) \mathbf{u}^{*}\left(P_{3}, t_{3}\right) \mathbf{u}^{*}\left(P_{4}, t_{4}\right)\right] \]

can be expressed as \[ \boldsymbol{\Gamma}_{1234}\left(t_{1}, t_{2}, t_{3}, t_{4}\right)=\sqrt{I_{1} I_{2} I_{3} I_{4}}\left[\boldsymbol{\mu}_{13} \boldsymbol{\mu}_{24}+\boldsymbol{\mu}_{14} \boldsymbol{\mu}_{23}\right] e^{-j 2 \pi v_{0}\left(t_{1}+t_{2}-t_{3}-t_{4}\right)} \]
where \[ \boldsymbol{\mu}_{m n}=\frac{E\left[\mathbf{u}\left(P_{m}, t\right) \mathbf{u}^{*}\left(P_{n}, t\right)\right]}{\sqrt{E\left[\left|\mathbf{u}\left(P_{m}, t\right)\right|^{2}\right] E\left[\left|\mathbf{u}\left(P_{n}, t\right)\right|^{2}\right]}} \]