1.  lmax boosted :

2.  Bias repair solution

We try to reproduce Fig 4 of arXiv:1305.7441 :

• with
  • fsky = 0.7, planck-like mask
  • 2.2 muK.arcmin
  • r=0.05
  • mask cpg optimization over bin range [2,20,51]
  • nside=512
  • ~ 200 simulations

and obtain :

• we observe :
  • almost the same BB spectrum error
  • a spectrum bias

2.1  Lowering number of nodes solution

• Too many nodes given to the x2pure function can cause a bias !

2.2  boost lmax

After discussion with J.Grain : no additionnal optimized spin smoothing should be require. however, the problem might come from lmax parameter.

• boosting lmax from 50 -> 500
• masks bins are [2, 20, 50, 500]
• err on PCG relaxed from 1e-10 -> 1e-4

• observations :
  • No more bias at masks steps. Small downward bias on all spectrum, especially visible at low ells => due to random spectrum generator x2pure (J.Grain)

3.  1rst tests

Optimization is realized using nside=512, lmax= 50, and varying 3 parameters :

• Binning
  • either 3 bins [2,10,20,51] : labeled nb3
  • either 2 bins [2,20,51] : labeled nb3
• input 'r' for spectrum model
  • r0 means r=0
  • r3 = mean r=1e-3
• noise :
  • 1 muK.arcmin
  • 5 muK.arcmin

Simulation is realized with

• uniform binning with delta ell = 1
• 0.0 muK-arcmin (no noise)
• input r=1e-3

y labels are inverted : First panel correspond to BB spectrum error, and second panel corresponds to mean BB spectrum estimation. The black curve is the classic Namaster std using combinning the min std of all apodization lenght.

• observation :
  • optimization with 1 muK does not converge (typically err=1e-3 for the first bin)
  • optimization with 5 muK does converge (typically err=1e-6, 1e-10, for the first bin)
  • changing the binning has little impact
  • changing the input r has little impact
  • There is a small gain compared to the classic method (namaster). But the low ell's error 'explosion' remains.