View source for Delensing sensitivity - preliminary results

This posting compares forecasts for different configurations of the delensing LAT. The configurations are taken from this [https://docs.google.com/spreadsheets/d/1KZ8TjDfHP2YocfIFfHf6dJJCmYaduHDq74WtTyFmpEY/edit?usp=sharing spreadsheet], and the efficiencies are taken from this [https://docs.google.com/document/d/1MuGRNom-Z2MfZaw8l8c06Pooioi1texwGNW2xQyvc14/edit analysis.] The shape of the noise in multipole space (specifically the values of l_knee and power-law exponent) come from achieved SPT performance as documented on the wiki page [[Delensing Lat Noise Shape Prediction]].


= Summary =


{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz)  !! A_L (quadratic) !! A_L (iterative) !! sigma(r) no decorr. RF !! sigma(r) no decorr. VB !! sigma(r) decorr. VB
|-
| V3R0 || 0.20 || 0.073 || 3.7e-4 ||  3.7e-4  || 4.9e-4
|-
| V3R0 LF+ || 0.20 ||0.076 || 3.8e-4 || 3.8e-4 || 5.0e-4
|-
| V3R0 MF+ || 0.19 || 0.068 || 3.6e-4 || 3.5e-4 || 4.8e-4
|-
| V3R0 HF+ || 0.20 || 0.078 || 3.9e-4 || 3.8e-4 || 5.0e-4
|-
| V3R0 25 || 0.19 || 0.065 || 3.5e-4 || 3.4e-4 ||4.7e-4
|-
| V3R0 MF+ 25 || 0.19 || 0.061 || 3.4e-4 || 3.3e-4 || 4.6e-4
|-
|}

This table summarizes the expected level of lensing residual and sigma(r) for the different delensing LAT configurations combined with the DSR configuration for the SATs. Victor Buza provided Fisher forecasts without decorrelation for comparison, as well as results with decorrelation, which was used as the DSR baseline.

= Preliminary results for joint LAT and SAT analysis =


{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz)  !! A_L (iterative) !! sigma(r) no decorr. RF 
|-
| V3R0 ||0.073 || 3.4e-4 
|-
| V3R0 LF+ ||0.076 || 3.5e-4  
|-
| V3R0 MF+ || 0.068 || 3.3e-4 
|-
| V3R0 HF+ || 0.078 || 3.6e-4 
|-
| V3R0 25 || 0.065 || 3.1e-4 
|-
| V3R0 MF+ 25 ||  0.061 || 3.1e-4 
|-
|}

This table summarizes the expected level of lensing residual and sigma(r) for a preliminary joint analysis of delensing LAT and SATs. The underlying assumption is that EE LAT data and BB LAT data above l=300 are used to delens the LAT and SAT data below l=300. The delensed LAT and SAT data below l=300 is then used to place constraints on r.  

At present, it assumes the same hit maps and weights for both surveys, which is likely suboptimal for the LAT survey. Furthermore, it currently uses a rough approximation for the LAT transfer functions, which should be improved.

= Survey specifications =

The survey duration is assumed to be 7 years, and the hits map is taken to be pole deep v1 described [https://cmb-s4.org/wiki/index.php/Deep_SAT_from_the_Pole here]  

{| class="wikitable" style="text-align: right; margin-left: 51px;"
| Duration (yrs)|| 7
|-
| fsky_signal (%) || 1.93
|-
| fsky_noise (%) || 2.88
|-
| fsky_cross (%) || 2.45
|-
|}

= SAT specifications =

The forecasts of sigma(r) assume the DSR SAT configuration. The expected noise levels for this survey are

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz)  !! 30 !! 40 !! 85 !! 95 !! 145 !! 155 !! 220 !! 270
|-
| Beam FWHM (arcmin) || 72.8 || 72.8 || 25.5 || 22.7 || 25.5 || 22.7 || 13.0 || 13.0
|-
|noise T (uK-arcmin) || 5.64 || 7.14 || 1.41 || 1.24 || 2.71 || 2.90 || 7.50 || 12.85
|-
|l_knee T  || 150 || 150 || 150 || 150 || 230 || 230 || 230 || 230
|-
|exponent T  || -4.4 || -4.4 || -4.4 || -4.4 || -3.8 || -3.8 || -3.8 || -3.8
|-
|noise E (uK-arcmin)  || 3.74 || 4.73 || 0.93 || 0.82 || 1.25 || 1.34 || 3.48 || 8.08
|-
|l_knee E  || 60 || 60 || 60 || 60 || 65 || 65 || 65 || 65
|-
|exponent E  || -2.2 || -2.2 || -2.2 || -2.2 || -3.1 || -3.1 || -3.1 || -3.1
|-
|noise B (uK-arcmin) || 3.53 || 4.46 || 0.88 || 0.78 || 1.23 || 1.34 || 3.48 || 5.97
|-
|l_knee B  || 60 || 60 || 60 || 60 || 60 || 60 || 60 || 60
|-
|exponent B  || -1.7 || -1.7 || -1.7 || -1.7 || -3.0 || -3.0 || -3.0 || -3.0
|-
|}

=V3R0=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 2 || 2 || 12 || 12 || 4 || 4 
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4 
|-
| Wafer NET (uK-rts) || 77.43 || 63.74 || 41.01 || 15.55 || 14.37 || 20.88 || 49.46
|-
| Band NET (uK-rts) || 38.72 || 22.54 || 14.50 || 2.24 || 2.07 || 5.22 || 12.37
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}

This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 8.67 || 5.05 || 3.25 || 0.50 || 0.46 || 1.17 || 2.77
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.71 || 0.66 || 1.65 || 3.92
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.71 || 0.66 || 1.65 || 3.92
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}

=V3R0 LF+=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 4 || 4 || 11 || 11 || 3 || 3
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4
|-
| Wafer NET (uK-rts) || 77.43 || 63.74 || 41.01 || 15.55 || 14.37 || 20.88 || 49.46
|-
| Band NET (uK-rts) || 38.72 || 15.94 || 10.25 || 2.34 || 2.17 || 6.03 || 14.28
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}

This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 8.67 || 3.57 || 2.30 || 0.52 || 0.49 || 1.35 || 3.20
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 12.26 || 5.05 || 3.25 || 0.74 || 0.69 || 1.91 || 4.52
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 12.26 || 5.05 || 3.25 || 0.74 || 0.69 || 1.91 || 4.52
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}

=V3R0 MF+=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 2 || 2 || 14 || 14 || 2 || 2
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4
|-
| Wafer NET (uK-rts) || 77.43 || 63.74 || 41.01 || 15.55 || 14.37 || 20.88 || 49.46
|-
| Band NET (uK-rts) || 38.72 || 22.54 || 14.50 || 2.08 || 1.92 || 7.38 || 17.49
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}

This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 8.67 || 5.05 || 3.25 || 0.47 || 0.43 || 1.65 || 3.92
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.66 || 0.61 || 2.34 || 5.54
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.66 || 0.61 || 2.34 || 5.54
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}

=V3R0 HF+=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 2 || 2 || 10 || 10 || 6 || 6
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4
|-
| Wafer NET (uK-rts) || 77.43 || 63.74 || 41.01 || 15.55 || 14.37 || 20.88 || 49.46
|-
| Band NET (uK-rts) || 38.72 || 22.54 || 14.50 || 2.46 || 2.27 || 4.26 || 10.10
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}


This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 8.67 || 5.05 || 3.25 || 0.55 || 0.51 || 0.95 || 2.26
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.78 || 0.72 || 1.35 || 3.20
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 12.26 || 7.14 || 4.59 || 0.78 || 0.72 || 1.35 || 3.20
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}

=V3R0 25=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 2 || 2 || 12 || 12 || 4 || 4
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4
|-
| Wafer NET (uK-rts) || 69.25 || 57.01 || 36.68 || 13.91 || 12.85 || 18.68 || 44.24
|-
| Band NET (uK-rts) || 34.62 || 20.16 || 12.97 || 2.01 || 1.85 || 4.67 || 11.06
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}


This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 7.75 || 4.51 || 2.90 || 0.45 || 0.42 || 1.05 || 2.48
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 10.97 || 6.38 || 4.11 || 0.64 || 0.59 || 1.48 || 3.50
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 10.97 || 6.38 || 4.11 || 0.64 || 0.59 || 1.48 || 3.50
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}

=V3R0 MF+ 25=

The instrument is characterized by

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Tubes || 1 || 2 || 2 || 14 || 14 || 2 || 2
|-
| Wafers/tube || 4 || 4 || 4 || 4 || 4 || 4 || 4
|-
| Wafer NET (uK-rts) || 69.25 || 57.01 || 36.68 || 13.91 || 12.85 || 18.68 || 44.24
|-
| Band NET (uK-rts) || 34.62 || 20.16 || 12.97 || 1.86 || 1.72 || 6.60 || 15.64
|-
|f_year || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70 || 0.70
|-
|f_scan || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80 || 0.80
|-
|f_pass || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69 || 0.69
|-
| efficiency || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39 || 0.39
|-
|}



This leads to the following expected performance

{| class="wikitable" style="text-align: right; margin-left: 51px;"
! Frequency (GHz) !! 20 !! 27 !! 39 !! 93 !! 145 !! 225 !! 278
|-
| Beam FWHM (arcmin) || 10.0 || 7.4 || 5.1 || 2.2 || 1.4 || 1.0 || 0.9
|-
|noise T (uK-arcmin) || 7.75 || 4.51 || 2.90 || 0.42 || 0.38 || 1.48 || 3.50
|-
|l_knee T || 700 || 700 || 700 || 700 || 700 || 700 || 700
|-
|exponent T || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise E (uK-arcmin) || 10.97 || 6.38 || 4.11 || 0.59 || 0.54 || 2.09 || 4.95
|-
|l_knee E || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent E || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|noise B (uK-arcmin) || 10.97 || 6.38 || 4.11 || 0.59 || 0.54 || 2.09 || 4.95
|-
|l_knee B || 150 || 150 || 150 || 150 || 200 || 200 || 200
|-
|exponent B || -2.7 || -2.7 || -2.7 || -2.6 || -2.2 || -2.2 || -2.2
|-
|}