# Delensing LAT relative Nhits v0p0

This posting documents initial stabs at answering the question: how should the Nhits map of the Delensing LAT be optimized in order to minimize <math>\sigma(r)</math>?

## Contents

## Background

So far (e.g. in low-ell BB Data Challenge 06), the relative Nhits maps of the Delensing LAT is taken to be identical to those of the Pole Deep SATs. Given that the lensing template is generated from CMB x phi(CMB, CMB) as opposed to direct imaging of map fluctuations in other components, one would expect the S/N of the lensing modes vs those of the other components to scale differently for the same input noise.

In this post, I use a very simple case to build intuition. Specifically, I answer this question: given a single-frequency SAT Nhits map, what should the Delensing LAT distribution of noise levels be such that S/N = 1 for the residual lensing modes.

In the regime where delensing is the limiting factor for sigma(r), this would give a close approximation of the actual distribution of noise levels (and hence Nhits) for the Delensing LAT. I list the next steps in order to make this more realistic and applicable to the survey design of the Delensing LAT.

## Method

- Generate 100 realizations of 1/ell noise given the DSR configuration of the SAT 95GHz Pole deep survey on flatsky (1 arcmin pixels) using this table ;
- Apply scale factor specified below table 1 of this posting ;
- Divide the noise map by the square-root of the SAT 95GHz relative hits map;
- Calculate the noise levels in uK-arcmin per pixel by measuring the standard deviation of each pixel across the 100 realizations of noise; this gives the white noise level.
- Scale the noise levels by ~1.17 in order to estimate the noise levels at ell~100 (factor is eyeballed from input 1/ell noise spectrum);
- Estimate (by interpolation of inputs to fig.68 of the DSR and extended to higher pol noise levels) the input Delensing LAT noise levels (at 95GHz, i.e. 2.6' FWHM) required in order for the residual lensing power to match the SAT noise power.

## Results

**Fig.1 DC05 95GHz Pole Deep SAT noise levels [uK-arcmin]**

**Fig.2 required LAT noise levels for residual lensing S/N=1 [uK-arcmin]**

**Fig.3 SAT vs LAT noise level slices**