### Why does the Fourier transform of this CMB image have a hole in it?

• The BBC's Desert telescope takes aim at ageing our Universe contains the image below of the Cosmic Microwave Background from the Atacama Cosmology Telescope or ACT. It looks like this is plotted with a diverging colormap which makes sense since they've likely subtracted off the average temperature and probably at least its dipole component if not more (CMBR dipole anisotropy (ℓ = 1)

But looking at it closely, I thought I noticed a strange regularity to the spatial scale, so I downloaded it and imported into Python and took the Fourier transform to see what I'd find.

Despite this being an ugly and very unscientific analysis, I'm still seeing both a sharp cutoff below a spatial frequency of 1.0 inverse degrees, and "ringing" or $$J_1$$ Bessel-like ripples at higher frequencies.

Are either or both of these profound and important to the analysis, or an instrumental artifact, or something else?

Image in the BBC news item is a JPEG and you can see the subfield discontinuities (part of the way the JPEG wavelets are implemented) once the the thee RGB color channels are separated, but this is a square grid and not related to the clearly circular patterns in the Fourier transform.

Try and see what you get with an image of white noise?

• For that specific E-mode map we have applied a Wiener filter to highlight the high SN modes (those "rings").

I also further apply the following filter: $$((1 + (kx/5)^{-4})^{-1}) * ((1 + (k/150)^{-4})^{-1})$$. This second filter gives the "hole" and a "thin" vertical line in your 2D PS. The image above is just for PR purposes.

In Aiola et al. (2020) the maps shown are made by applying the kx and k filter, but we do not apply any Wiener filter (again the filtering is done for visualization purposes).

The original raw maps used for the analysis are available here: https://lambda.gsfc.nasa.gov/product/act/actpol_prod_table.cfm

As amaurea points out, that is a E-mode map and not a temperature map.

I see! 1, 2 :-) Thanks you very much and *Welcome to Stack Exchange!*