R-dependence
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Nov 2, 2007
It occurred to me that it might be worth looking at the radial-dependence....
chisq = new TH3F("chisq","Chisquare Dist (log10)",100,-5,3,7,59,192,250,1.495,3.995);
...
chisq->GetXaxis()->SetRange(1,88)
for (int rbin=1;rbin<8;rbin++) {
chisq->GetYaxis()->SetRange(rbin,rbin);
(mm = chisq->Project3D("xz"))->SetName(Form("rr%d",rbin));
nn =((TH2D*) mm)->ProfileX();
nn->SetLineColor(2);
}
c1->Clear()
c1->Divide(3,2)
c1->cd(1)
rr1.Draw()
rr1_pfx.Draw("same")
c1->cd(2)
rr2.Draw()
rr2_pfx.Draw("same")
c1->cd(3)
rr3.Draw()
rr3_pfx.Draw("same")
c1->cd(4)
rr5.Draw()
rr5_pfx.Draw("same")
c1->cd(5)
rr6.Draw()
rr6_pfx.Draw("same")
c1->cd(6)
rr7.Draw()
rr7_pfx.Draw("same")
Here are the GG = -65V and the external resistor runs:
GG= -65V above ^^^^ and external resistor below vvvv
A few things we learn:
1) That the external resistor doesn't distort the data at large radius means there's little sensitivity there. So there's a lot more spread in the distributions there (and lower chi values), while at low radius the omegatau is rather well-constrained to be in the ~2.6-3.2 region.
2) Likewise, the GG run shows almost no sensitivity for the middle radii and lower chi values there.
3) The GG run shows a preference towards large omegatau (~2.8) at small radii, and smaller omegatau (~2.0) at large radii. Note that the small radii omegatau agree between the two datasets. This is not ambiguous: very few hits prefer omegetau above 2.5 for the largest radii, and very few prefer omegatau below 2.5 for small radii.
4) I thought maybe I see an inner/outer padrows difference in the chi values (implying different errors), but I think this is due to the sensitivity to distortions as mentioned in point 1.
I also took a look at the GG=-165V run, and it looks pretty similar to the -65V run so I won't post it here. It gives omegatu of ~2.8 at small radii and ~2.1 at large radii. Larger omegatau means smaller Const_1 and smaller distortions, so the data wants smaller distortions at small radii than it does at large radii.
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Could it be the (r-phi vs r) vs. (y vs x) issue? The distortion map is in r-phi. We're talking about distortions that are at most ~2 mm in the GG runs, and 7mm in the external resistor run. For 7mm at radius=60cm, the r-phi vs. y difference is:
0.7-60*sin(atan2(0.7,60.0)) = ~0.00005
So we're talking about a mere half micron for even the largest of my distortions. I don't think this can be the issue. The difference between omegatau of 2.35 and 2.77 is on the order of 100 microns (more at larger drifts) in the GG runs, and as much as ~1mm in the external resistor run. Anyhow, turns out I do plot r-phi vs. r:
"sqrt(fy*fy+fx*fx)*(atan2(fy,fx)-(%f)):sqrt(fy*fy+fx*fx)"
where I subtract off the angle of the outer starting point of the laser in r-phi.
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Here's another idea: the r-distortion caused by the field. I've ignored this for the calibration of omegatau-rphi. For the external resistor, again, we're talking about moving the points by something like 10% of their distortion (something like 700 microns out of the 7 mm distortion)
In that vein, here's the distortion curves (external resistor) vs. r for z=30cm for omegatau=2.38 (red) and 2.77 (blue) zoomed in at small radii:
So in order to get the 2.77 curve when it should really be the 2.38 curve, the data needs to be reconstructed about 3-4cm inwards (at smaller radii) than they really were (e.g. the hit we measure at radius 60cm truly originated at radius 63cm).
Here's the distortion curves for the GG=-65V run (same as above):
This one's a little closer, needing perhaps a 2-3 cm shift.
According to Howard's web page (http://www-rnc.lbl.gov/~wieman/gs/DistortionFC3GG.htm), the radial distortion should be under 1cm. Actually, he predicts about 0.6cm radial distortion using omegatau = 2.8. But if omegatau is 2.38, then that radial distortion increases by the factor that const_0 increases = const_0(2.38)/const_0(2.8) = 1.50/1.13 = 1.33 => 0.8cm. Still under 1cm at omegatau = 2.1. Even at omegatau = 1.5, it's still only 1.6cm shift. And is it even in the correct direction? And I think the radial distortion goes in opposite directions at the small and large radii for the GG distortion, so both small and large radii would want to push omegatau in the same direction (increasing or decreasing), with the implication that the true omegatau is either well above 2.8 or below 2.3, not between them.
I'm not sure this is the answer to my problems, but it may in fact be a consideration: the radial distortion does affect the omegatau I calibrate even if it's just a 0.8cm shift in the GG run. An outward radial push on the data is similar to a diminishing of the observed distortion, thereby wanting a larger omegatau. I would estimate this as an affect on the level of 0.1 in omegatau!!! Perhaps this plays a role in why the GG runs have a spread of ~0.1 in their omegatau going for 65V to 165V: it gets pushed lower for the distortion in one direction, and higher for the distortion in the opposite direction. This seems consistent and points to an omegatau between them.
It occurs to me that I might be able to handle this in my macro by reading it the r distortion as well as the r-phi distortion, and applying the r-shift before calculating the point to use in the r-phi map.
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Quick things I've learned:
1) For the external resistor run, all r get shifted to larger r by the distortion. In other words, as an example, the distortion we measure at r=60cm was really produced at r=59.6cm. In this case, it means we are seeing a large distortion than is really there, and we're obtaining a smaller omegatau than it should really be in my old method....I think.
2) I did not alter the omegatau used in Const_0, which is used for the radial distortion. So the radial distortion at present is constant vs. my changes in omegatau. It might be a bit much to vary this simultaneously! But maybe this is what I eventually want to do: vary them both simultaneously. But that's a lot of distortion maps! I would need to reduce the granularity of my distortion maps. Maybe to the 0.1 level. Then I could do a 25x25 grid. And I could then possibly do a finer scale grid as a second pass only in the region of interest. Or maybe I can interpolate between omegatau maps to find the omegatau with even finer precision: this may work well because of how monotonicly things change with omegatau. I like this idea.
I was right: it now wants omegatau=2.79 for the external resistor run. And it brings better match between the GG runs as a set. But it doesn't bring the GG values any closer to the external resistor run value :-(
For the GG, the values are now:
-65V: 2.34
-90V: 2.35
-140V: 2.40
-165V: 2.39
Now what? Should I begin doing the radial omegatau from tangential laser tracks and see how the two dimensional map goes? Since I'm looking at values between 2 and 3, maybe I only need to do the range of omegatau from 1.5 to 3.5.
Hmmm.....it just occurred to me that I should change omegatau ONLY for the UndoShortedRing distortion, since the other distortions are calibrated to the old omegatau values. But no.....the shorted ring is the ONLY correction I'm doing, so that's irrelavant. Sorry.