Why do CMB Images Look 2-D

I have often seen the images produced by the cosmic microwave background (CMB) detectors like COBE, WMAP, Planck etc.All of their images seem to lack "depth." and seem like 2D images (but not 3D images). I assume the detectors can measure the direction each CMB photon is coming from, its frequency, and the number of photons from that direction etc. but can they measure the distances to the points where the CMB photons were emitted? The CMB radiation images look as if the CMB photons are coming from the surface of a distant sphere but I assume they were all produced in a 3D volume a long time ago. Is this not the case? If so (if not so, why?), How can we produce 3D images (or 3D distribution) of the CMB radiation? Could you list a few methods? Or could you show URLs to the CMB 3D images (where they perhaps show the CMB 3D sphere (or a layer of the CMB sphere with thickness) cut open in half or in parts showing the internal structure/distribution?)?The only method I can think of now is the Doppler (red / blue) shift (=frequency difference) in the CMB photons and I assume this is shown as temperature variation (with colors) in the CMB map (surface). but 1) does the variation mean the slightly hotter areas (=higher frequency area) are closer to us and the slightly colder areas (red shifted) are further away from us (from Hubble's law)? or 2) the temperature variation is due to the local temperature difference when the CMB was emitted years ago? How can we tell which (1 or 2) caused this temperature variation? To recapitulate, does (can) the CMB carry any depth / distance information in principle and is it detectable in experiments? If so or not so, how and why? and any other methods to determine the CMB distance besides the Doppler shit?
- Anonymous

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. 

Mike W.

(published on 04/21/2015)