First-Rytov coherent mean (source code)

= First-Rytov coherent mean
{title2=$\mathbb E[\psi_R]=\psi_i\exp(\mu^2\mathbb E[\chi_1^2]/2)$}

If the first logarithmic perturbation $\chi_1$ is a centered linear functional of a <Gaussian random field>, the <complex Gaussian exponential moment> gives the displayed mean of the first <Rytov approximation> $\psi_R=\psi_i e^{\mu\chi_1}$. This is the mean of the truncated logarithmic model. A nonzero mean of the omitted second logarithmic perturbation can change the true field mean at order $\mu^2$.