Point spread function ($\mathrm{PSF}$)

The point spread function is the image of an unresolved point source. It describes blurring from diffraction, optical aberrations, and astronomical seeing.

A diffraction-limited system has imaging performance set primarily by diffraction rather than by optical aberrations.

For a circular illuminated aperture of diameter $D$, the characteristic angular diffraction scale is $\lambda /D$. The first zero of the ideal intensity pattern lies at approximately $1.22\lambda /D$.

The Strehl ratio compares the peak of an observed point spread function with the ideal diffraction-limited system peak for the same pupil and total flux. It measures how strongly wavefront errors redistribute light away from the central peak.

For small residual phase errors, $S\simeq e^{-{\sigma }_{\varphi }^2}$, where ${\sigma }_{\varphi }=2\pi h_{\mathrm{rms}}/\lambda$. 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.