= Cosmological surface-brightness dimming
{title2=$I_{\rm bol,obs}=I_{\rm bol,em}/(1+z)^4$}
For freely propagating radiation with the usual <distance duality relation>, a fixed emitted bolometric <surface brightness> is observed smaller by $(1+z)^4$. One factor each comes from <photon energy> and arrival rate, and two from the relation of projected angular area to <luminosity distance>. In a fixed observed <photometric passband>, spectral shifts add a band-dependent correction; the bolometric power is not automatically the monochromatic one. A distortion created by scattering the local <cosmic microwave background> has a different redshift comparison, as in the <thermal Sunyaev-Zeldovich effect>.
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