= Photon reception by a uniformly accelerated observer
{title2=$\nu/\nu_0=e^{-a\tau},\quad t_e=L-a^{-1}e^{-a\tau}$}
For the standard right-wedge <hyperbola> and a stationary source at $x=L$ emitting rightmoving <photons>, the retarded <null coordinate> is $p=t-x=-e^{-a\tau}/a$. Equating it to the emission value $t_e-L$ gives the displayed reception relation. Differentiating yields the Doppler <frequency> ratio $\nu/\nu_0=dt_e/d\tau=e^{-a\tau}$. The limiting emission time $L$ is a supremum: emission exactly at that time is never received at finite <proper time>. These expressions use $c=1$ and <acceleration> continued indefinitely.
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