Telescope aperture and resolved surface brightness ($A_{\mathrm{tel}}{\Omega }_{\mathrm{res}}\sim {\lambda }^2$)

For a diffraction-limited telescope, collecting area scales as $D^2$ while a native angular resolution element scales as $(\lambda /D{)}^2$. Counts from a smooth resolved source per native resolution element therefore do not increase with aperture, at fixed radiance, exposure and throughput. Counts in a fixed angular bin instead grow as $D^2$, and the photon-noise-limited signal-to-noise ratio grows as $D\sqrt{t}$. Conservation of etendue and cosmological surface-brightness dimming do not forbid this latter gain.