Biomedical Imaging

If, in addition to being stationary, the field is also monochromatic, Γ is constant in time (up to a trivial harmonic term). This is directly evident for the case that the two probing points coincide spatially, which gives γ(τ) = exp(−iωτ), a function of constant magnitude in time.

Wiener–Khinchin theorem and longitudinal coherence

Next, we consider the more realistic case of quasi monochromatic fields, i.e., radiation with a small bandwidth Δω centered around a mean angular frequency ω = 2πν, or correspondingly, a wavelength band Δλ around an average λ. For the mutual intensity function, taken at identical points but at a time difference τ, we equally have unit magnitude

$\gamma \left(\tau \right)=\frac{\langle u\left(t\right)u^{*}\left(t+\tau \right)\rangle }{\sqrt{\langle I^2\rangle }}\stackrel{\tau \Delta v\ll \lambda /\left(2\Delta \lambda \right)}{\simeq }{\text{e}}^{i\omega \tau },$