Why do CMB Images Look 2-D
Most recent answer: 04/21/2015
The basic answer is that the images are indeed 2-D. There's no direct information in the photon to say how far away it originated. Furthermore, our well-supported model is that all the CMB photons originated at nearly the same (local) time, the point at which the universe became nearly transparent when electrons and protons cooled down enough to combine to form hydrogen atoms. Since the locations of the sources are determined by how long the photons have had to travel to reach us now, having the same start time means starting at places that form a spherical shell around us. So it's all really 2-D to a good approximation.
To analyze the effects that give rise to the slight unevenness requires some theoretical modeling. What would happen if region A were slightly hotter than region B? Region A would become transparent a little later than region B. So the temperature and time effects get mixed together in producing the net Doppler shift.
(published on 04/21/2015)