View source for Sep 09, 2021 - Smoothed kappa maps

Dick suggested that our problems with sensitivity to places where kappa is close to one and magnification diverges can be solved by smoothing the kappa maps. A natural first guess for the smoothing scale is an effective radius of the pixel. It is given by

<math>
\pi \theta^2 = \frac{4\pi}{N_{pix}}
</math>

and evaluates to

<math>
\theta = (\sqrt{3}N_{side})^{-1} .
</math>

Using the healpy smoothing routine with <math>\sigma = \theta</math>, we pre-process the maps before lensing.

As visible from histograms, it helps to cure the tails:

[[File:smooth_kappa_1.png|300px]]
[[File:smooth_kappa_9.png|300px]]
[[File:smooth_kappa_17.png|300px]]

Just for illustration we show what the smoothing does to the kappa map (shell 17):

[[File:kappa_example_17.png|600px]]
[[File:smooth_kappa_example_17.png|600px]]