Correlation of reconstructed lensing template to ideal
February 1 2019, Clem Pryke
In Sim map sets to demonstrate "real delensing" (02.00 and 02.09) I introduced some high res sims to run lensing reconstruction on. In Ready for delensing use lensing maps 02.00 Julien Carron provided reconstructed Q/U lensing templates from these. In  I took these through to power spectra. Finally in  Caterina showed that these templates deliver effective A_L around 0.5 In the last posting it is also shown with that a perfect lensing template delivers A_L close to zero. (Where by a perfect template I mean the difference of the lensed and unlensed sims.)
I think Julienne ran his reconstruction on the 145GHz high res maps from 02.00 - it says so in Lensing reconstructions 02.00. The high res sims for 02 where made for 95/145/220 GHz bands just copying the uK-arcmin levels from the corresponding low res bands of the 02 set. These appear to be 1.40/2.19/5.61 uK-arcmin. So 145GHz may not have been the best choice - 95GHz would be better.
To gauge the fidelity of lensing templates it presumably isn't necessary to go all the way through to sigma(r). Instead we can just take the B-mode cross correlation between the reconstructed and perfect templates. The plot below shows this for the first realization. We get about 0.7 correlation at ell 30 to 150 - so if it goes as the square that matches the A_L=0.5 equivalent. Julien also provided templates reconstructed from the signal only maps, but I think he then used the same noise based filtering that was applied when reconstructing from the signal+noise maps - so that may be why the correlation is only a little higher.
Next steps include asking Julien to provide templates from the 95GHz signal+noise maps and probably also from the signal only maps using all modes so that we can probe the algorithmic limitations coming from non-iterative reconstruction.