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5.5: Temporal Coherence and the Michelson Interferometer
https://phys.libretexts.org/Bookshelves/Optics/BSc_Optics_(Konijnenberg_Adam_and_Urbach)/05%3A_Interference_and_coherence/5.05%3A_Temporal_Coherence_and_the_Michelson_Interferometer
Then: \[\begin{aligned} \Gamma(\tau) &=\frac{1}{4}\left\langle\left(e^{-i(\bar{\omega}+\Delta \omega / 2) t}+e^{-i(\bar{\omega}-\Delta \omega / 2) t}\right)\left(e^{i(\bar{\omega}+\Delta \omega / 2)(t...Then: $\begin{aligned} \Gamma(\tau) &=\frac{1}{4}\left\langle\left(e^{-i(\bar{\omega}+\Delta \omega / 2) t}+e^{-i(\bar{\omega}-\Delta \omega / 2) t}\right)\left(e^{i(\bar{\omega}+\Delta \omega / 2)(t-\tau)}+e^{i(\bar{\omega}-\Delta \omega / 2)(t-\tau)}\right)\right\rangle \\ & \approx \frac{e^{-i(\bar{\omega}+\Delta \omega / 2) \tau}+e^{-i(\bar{\omega}-\Delta \omega / 2) \tau}}{4} \\ &=\cos (\Delta \omega \tau / 2) \frac{e^{-i-\bar{\omega} \tau}}{2} \end{aligned} \nonumber$ where in the seco…

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