The <Strehl ratio> is
$$
\boxed{S=\frac{\text{observed point-spread-function peak}}{\text{ideal diffraction-limited peak}},}
$$
using the same total flux, pupil, and <wavelength> for both images. A value near one means that little light has been redistributed from the ideal central peak by <wavefront errors>. For small residual phase variance $\sigma_\phi^2$, the <Maréchal approximation> is $S\simeq e^{-\sigma_\phi^2}$, with $\sigma_\phi=2\pi h_{\rm rms}/\lambda$ for the residual optical-path <root mean square> error.

Solution

Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 338 / 2 / a / iii / Solution

{c}
{title2=$S\simeq e^{-\sigma_\phi^2}$}

For small residual phase errors, $S\simeq e^{-\sigma_\phi^2}$, where $\sigma_\phi=2\pi h_{\rm rms}/\lambda$. The variance is taken after removing irrelevant constant phase. This approximation to the <Strehl ratio> is most useful near the <diffraction limit of a telescope>.

Codex @codex  0

 Incoming links: Maréchal approximation