We have looked at noise integrating down with time in posts like 20180618_mapnoise. As far as I know we have not looked much at noise integrating down with number of detectors. In 2013 Keck ran with five 150GHz receivers. We store the coadded maps on a per receiver basis (jack01) offering the opportunity to accumulate to 1-receiver, 2-receiver, 3-receiver etc. maps with minimal effort.
Below are the polarization weight maps \(1/Q_{\mathrm{var}} + 1/U_{\mathrm{var}}\) for each of the five cases. We see that rx4 is the most valuable player.
Fig1:
Since these are noise realizations they contain roughly equal E and B so no special techniques are need to take angular power spectra. The left plot shows the first 100 realizations and the right plot shows the means. We see a rise to low \(\ell\) as expected followed by a falloff in the lowest (junk) bin due to the timestream filtering. Note that the \(\ell(\ell+1)/2\pi\) factor has been divided out to plot "raw \(N_\ell\)".
Fig2:
Taking the mean of bandpowers 2&3 and the region \(200<\ell<400\) and plotting log-log style we get the below. The dashed lines just scale the first point by the ratio of the total weights. We see that for the higher \(\ell\) things follow the prediction closely but for lower \(\ell\) there is some excess. The final point is about 30% higher than the extrapolation. This is presumably due to the effect of correlated noise amongst the pairs - see 20180205_cov_noise_penalty for a related posting.
Fig3:
An interesting next step would be to do the same thing with BICEP3. A special per tile coadd could be built and then the tiles added up in an order that builds to full sky coverage quickly and then maintains roughly uniform sky coverage.
% look at N_ell as a function of N_det
% Keck 2012/13 was 5x150GHz rx
%load('maps/1351/0016_a_filtp3_weight3_gs_dp1100_jack01.mat'); uk=get_ukpervolt('201208','keck');
load('maps/1351/0016_b_filtp3_weight3_gs_dp1100_jack01.mat'); uk=get_ukpervolt('201308','keck');
%load('maps/1351/0016_f_filtp3_weight3_gs_dp1100_jack01.mat'); uk=get_ukpervolt('201608','keck');
% look at ind rx maps
ac=cal_coadd_ac(ac,uk);
map=make_map(ac,m);
plot_map(m,map(2).Pwitime); colorbar
% build cumulative maps and record total weight
for i=1:5
acc=coadd_ac_overrx(ac(1:i));
map(i)=make_map(acc,m);
% Pitime field has problems due to use of dwmax field - a few crazy high weights messes it up -
% now there shouldn't be any crazy high weights but...
it(i)=nansum(map(i).Pwitime(:));
% the Pw field is generated in add_masks as 1/(Qvar+Uvar)
% for total weight it might make more sense to use 1/Qvar+1/Uvar
tw(i)=nansum(1./map(i).Qvar(:)+1./map(i).Uvar(:));
end
setwinsize(gcf,800,500); clf
subplot(3,2,1); plot_map(m,1./map(1).Qvar+1./map(1).Uvar); colorbar; title('1rx');
subplot(3,2,2); plot_map(m,1./map(2).Qvar+1./map(2).Uvar); colorbar; title('2rx');
subplot(3,2,3); plot_map(m,1./map(3).Qvar+1./map(3).Uvar); colorbar; title('3rx');
subplot(3,2,4); plot_map(m,1./map(4).Qvar+1./map(4).Uvar); colorbar; title('4rx');
subplot(3,2,5); plot_map(m,1./map(5).Qvar+1./map(5).Uvar); colorbar; title('5rx');
mkgif('fig1.gif',1);
return
% build 1,2,3,4,5 rx N_ell
uk=get_ukpervolt('201308','keck');
apsopt.coaddrx=1;
for i=1:5
apsopt.ukpervolt=NaN*ones(1,5);
apsopt.ukpervolt(1:i)=uk;
apsopt.daughter=sprintf('%1drx',i);
reduc_makeaps('maps/1351/0??6_b_filtp3_weight3_gs_dp1100_jack01.mat',apsopt);
end
reduc_makesimset('1351/0??6_b_filtp3_weight3_gs_dp1100_jack01_overrx_1rx.mat');
reduc_makesimset('1351/0??6_b_filtp3_weight3_gs_dp1100_jack01_overrx_2rx.mat');
reduc_makesimset('1351/0??6_b_filtp3_weight3_gs_dp1100_jack01_overrx_3rx.mat');
reduc_makesimset('1351/0??6_b_filtp3_weight3_gs_dp1100_jack01_overrx_4rx.mat');
reduc_makesimset('1351/0??6_b_filtp3_weight3_gs_dp1100_jack01_overrx_5rx.mat');
return
load('aps/1351/xxx6_b_filtp3_weight3_gs_dp1100_jack01_overrx_1rx.mat'); aps1=aps;
load('aps/1351/xxx6_b_filtp3_weight3_gs_dp1100_jack01_overrx_2rx.mat'); aps2=aps;
load('aps/1351/xxx6_b_filtp3_weight3_gs_dp1100_jack01_overrx_3rx.mat'); aps3=aps;
load('aps/1351/xxx6_b_filtp3_weight3_gs_dp1100_jack01_overrx_4rx.mat'); aps4=aps;
load('aps/1351/xxx6_b_filtp3_weight3_gs_dp1100_jack01_overrx_5rx.mat'); aps5=aps;
sf=2*pi./(aps.l.^2);
setwinsize(gcf,500,500); clf
s=4;
h1=plot(aps.l,squeeze(repmat(sf,[1,1,size(aps1.Cs_l,3)]).*aps1.Cs_l(:,s,:)),'b');
hold on
h2=plot(aps.l,squeeze(repmat(sf,[1,1,size(aps1.Cs_l,3)]).*aps2.Cs_l(:,s,:)),'r');
h3=plot(aps.l,squeeze(repmat(sf,[1,1,size(aps1.Cs_l,3)]).*aps3.Cs_l(:,s,:)),'g');
h4=plot(aps.l,squeeze(repmat(sf,[1,1,size(aps1.Cs_l,3)]).*aps4.Cs_l(:,s,:)),'c');
h5=plot(aps.l,squeeze(repmat(sf,[1,1,size(aps1.Cs_l,3)]).*aps5.Cs_l(:,s,:)),'m');
hold off
xlabel('multipole'); ylabel('BB N_l (\muK^2)');
legend([h1(1),h2(1),h3(1),h4(1),h5(1)],{'1rx','2rx','3rx','4rx','5rx'});
title('First 100 noise realizations');
mkgif('fig2a.gif',1);
aps1.Cs_l=mean(aps1.Cs_l,3);
aps2.Cs_l=mean(aps2.Cs_l,3);
aps3.Cs_l=mean(aps3.Cs_l,3);
aps4.Cs_l=mean(aps4.Cs_l,3);
aps5.Cs_l=mean(aps5.Cs_l,3);
setwinsize(gcf,500,500); clf
h1=plot(aps.l,sf.*aps1.Cs_l(:,s),'b.-');
hold on
h2=plot(aps.l,sf.*aps2.Cs_l(:,s),'r.-');
h3=plot(aps.l,sf.*aps3.Cs_l(:,s),'g.-');
h4=plot(aps.l,sf.*aps4.Cs_l(:,s),'c.-');
h5=plot(aps.l,sf.*aps5.Cs_l(:,s),'m.-');
hold off
ylim([0,1e-4]);
xlabel('multipole'); ylabel('BB N_l (\muK^2)');
legend([h1(1),h2(1),h3(1),h4(1),h5(1)],{'1rx','2rx','3rx','4rx','5rx'});
title('Mean of first 100 noise realizations');
mkgif('fig2b.gif',1);
i1=aps.l>10&aps.l<100;
i2=aps.l>200&aps.l<400;
of(1)=mean(sf(i1).*aps1.Cs_l(i1,s));
of(2)=mean(sf(i1).*aps2.Cs_l(i1,s));
of(3)=mean(sf(i1).*aps3.Cs_l(i1,s));
of(4)=mean(sf(i1).*aps4.Cs_l(i1,s));
of(5)=mean(sf(i1).*aps5.Cs_l(i1,s));
wn(1)=mean(sf(i2).*aps1.Cs_l(i2,s));
wn(2)=mean(sf(i2).*aps2.Cs_l(i2,s));
wn(3)=mean(sf(i2).*aps3.Cs_l(i2,s));
wn(4)=mean(sf(i2).*aps4.Cs_l(i2,s));
wn(5)=mean(sf(i2).*aps5.Cs_l(i2,s));
setwinsize(gcf,500,500); clf
loglog(tw,of,'b.-');
hold on
loglog(tw,wn,'r.-');
% extrapolate forward from the first point based on relative map weight
ofp(1)=of(1); ofp(2:5)=of(1)*tw(1)./tw(2:5);
wnp(1)=wn(1); wnp(2:5)=wn(1)*tw(1)./tw(2:5);
plot(tw,ofp,'b--')
plot(tw,wnp,'r--')
hold off
grid
xlabel('total polarized map weight (1rx, 2rx, 3rx, 4rx, 5rx)'); ylabel('mean BB N_l (\muK^2)');
legend({'mean bandpowers 2&3','mean 200