Moving-mirror photon interception rate ($R_{\mathrm{hit}}=R(1-\beta )$)

For a photon emitted from the origin and arriving at receding mirror position $x(t)$, its emission time is $t_e=t-x(t)/c$. Thus $d{t}_e/dt=1-\beta$ and a steady source rate $R$ gives impact rate $R(1-\beta )$ in source-frame coordinate time. This is distinct from the emission rate and from a rate per mirror proper time.