I have a question relating to the Etherington Theorem.
The luminosity distance is defined by the equation for flux, i.e.
where flux is in units energy per unit time (luminosity) per unit area.
The angular diameter distance is defined by
$D_A=\theta/R$, where $\theta$ is the observed angular size measured by a telescope, and $R$ denotes the proper size of an object.
These two quantities are related by $D_L=(1+z)^2D_A$
I have never read a clear explanation for this relationship, nor have I come across a derivation. Could anyone explain to me where the redshift dependence $(1+z)^2$ comes from?