Validating Transfer Line Fit University of Wisconsin-Madison James N. Bellinger University of Wisconsin-Madison 7-Oct-2011 James N Bellinger UW Madison

Validation Exercise Stage 1 Fix Transfer Lines using positions at MAB3 Predict DCOPS centers all along the lines Compare my prediction with Barrel MAB1 DCOPS centers Two possible sources for MAB3 positions Barrel fit (more likely to be self-consistent w/ MAB1?) Link fit (use z-bar fit) Fit fixing Barrel MAB1 and MAB3 positions Look at residuals 2 January 2019 James N Bellinger UW Madison

Validation Exercise Stage 2 From estimated errors in Link or Barrel predict estimated errors at ME stations Project anchored lines to ME stations Using Rphi only, fit for best agreement with Photogrammetry, letting disk X,Y,and RotZ vary Find the residuals and compare with estimated errors Look for strangeness 1/2/2019 James N Bellinger UW Madison

Description of Stage 1 Study “radial” direction for DCOPS: insensitive to MAB rotations, and “tangential=RPhi” directions which are Given PG MAB calibration, find DCOPS center wrt MAB center Use the Barrel fit for MAB center and orientation to calculate the DCOPS center position for all MABs Anchor my laser line fits using the Barrel MAB3 DCOPS Centers from 3 Calculate “radial” positions for all other DCOPS Compare MAB1 Barrel fit position w/ my prediction My fit does not include MAB1 Barrel information: independent 2 January 2019 James N Bellinger UW Madison

Schematic of my fit using MAB3 Calculate relative offsets for each DCOPS and add to the anchor line Compare w/ Barrel fit for MAB1 Fit fixes relative offset=0 Barrel or Link fit position used to define an anchor line Calculation uses average profile position at center of DCOPS—no tilt of laser fan MAB+3 MAB-3 Given profile centers for both lasers, fit for laser lines and DCOPS offsets 2 January 2019 James N Bellinger UW Madison

Schematic of my fit using all MAB Line fit holding MAB radial offsets to Barrel-fit values, creates anchor line Look at residuals 1) Residuals within MAB 2) Residuals for fit to disk position (stage 2) Calculation uses average profile position at center of DCOPS—no tilt of laser fan MAB+3 MAB+1 MAB-1 MAB-3 Given profile centers for both lasers, fit for laser lines and DCOPS offsets 2 January 2019 James N Bellinger UW Madison

Fit for Disk Position, global Stage 2 1/2/2019 James N Bellinger UW Madison

Fit for Disk Position, local Stage 2 Y PG shift from nominal Fit shift from nominal X Fit Shift Difference in shifts from nominal. Combination of disk shift, disk rotation, and measurement error Use all 6 stations to fit for disk shift and rotation. Only RPhi used -PG Shift 1/2/2019 James N Bellinger UW Madison

Barrel MAB3, look at MAB1 Predicted radius - Barrel radius 0.56mm systematic shift RMS=0.27mm! Very tight distribution Why the offset? 2 January 2019 James N Bellinger UW Madison

Barrel MAB3, look at MAB1 Predicted RPhi – Barrel RPhi Again an offset; 1.2mm= 2x the radial RMS is better than earlier analyses, but not as good as radial Rotation about CMS-Z? 2 January 2019 James N Bellinger UW Madison

Barrel MAB3, look at MAB1 RPhi Predicted – Barrel; Fit details Difference of differences is almost the same at each line, (modulo sign change)! Strongly suggests calculation artifact somewhere Precision better than accuracy 2 January 2019 James N Bellinger UW Madison

Barrel MAB3; look at MAB1 Predicted radius - Barrel radius MAB+1 and MAB-1 have consistent mean and RMS (MAB+1/Line5 MAB did not read out) MAB-1 2 January 2019 James N Bellinger UW Madison

Repeat Using Link for MAB3 Still use barrel for MAB1 Some MAB rotations are default values The fit is exactly the same—the only thing that changes are the points I use to anchor the DCOPS line. This uses the Link fit to MAB3 instead of the Barrel fit. 2 January 2019 James N Bellinger UW Madison

Link MAB3: look at MAB1 Radial Differences Line 4 looks bad. If I omit it, the mean =0.47 RMS =0.71 Compare w/slide 9 mean =0.56 RMS =0.27 Consistent Nota bene: I use defaults for some Link MAB params 1/2/2019 James N Bellinger UW Madison

Link MAB3, looking at MAB1 Predicted RPhi – Barrel RPhi Looks worse: See Slide 10 Here: mean=-1.80 RMS=1.27 Before: mean=-1.22 RMS=0.71 Consistent 2 January 2019 James N Bellinger UW Madison

Link MAB3, lookng at Barrel MAB1 Looking for Artifacts in Rphi Line 6 is out of line with the rest. Most show about 1mm between residuals, as before—but with a new sign pattern. See slide 7 2 January 2019 James N Bellinger UW Madison

Link MAB3, looking at MAB1 Predicted – Barrel RPhi w/o Line 6 Without 6, distribution tighter, offset smaller. Compare w/ Slide 15, 10 Here (Link cut): -1.26±0.58 Link uncut (15) -1.8±1.27 Slide 6 (barrel): -1.22±0.71 2 January 2019 James N Bellinger UW Madison

Repeat MAB1 and MAB3 Use Barrel MAB1 and MAB3 to anchor the fit. Look at residuals for smoking guns Compare with Link MAB3 2 January 2019 James N Bellinger UW Madison

Comparing MAB3 Barrel and Link RPhi R Either I’ve made some blunder or there’s a lot of variation between what the Barrel fit finds and what Link finds for the MAB3 DCOPS centers. I’m not sure I can usefully compare a Barrel-anchored fit to the Link MAB3 values. Plus Minus 1/2/2019 James N Bellinger UW Madison

Stage 1 Conclusions Using MAB3 as fixed points validates the precision of the Transfer Line fit at the MAB1 positions at the .7mm RMS level in RPhi and .27mm in radius. The accuracy of the fit there I estimate from the offsets: 1.2mm in RPhi and .6 in R. Link-based MAB3 gives precisions about as good as Barrel-based MAB3, but bad measurements can throw the accuracy off 2 January 2019 James N Bellinger UW Madison

Barrel Error estimates Quoted numbers are 1mm and 1μrad I find an offset of 1.2mm in RPhi, but with an rms of 0.7mm—Barrel precision is potentially better than quoted, especially in radial (rms=0.27mm) We see systematic offsets from the Transfer Line prediction to the Barrel measurements, whether we fix the MAB using the Barrel or Link THIS SHOULD BE FED INTO THE BARREL FIT, IF AT ALL POSSIBLE 1/2/2019 James N Bellinger UW Madison

Stage 2 Fit to Barrel MAB1 and MAB3 Project to ME stations using default Z ASSUME Transfer Plates are precise Transform PG values to Transfer Plate coordinate frame position of Transfer Line DCOPS Take difference of projection and PG estimate Fit for disk shift in X/Y and rotation by Z Examine residuals 1/2/2019 James N Bellinger UW Madison

Estimated Error in Projection 4-MAB fit Given the precision seen in the MAB1 study, dominated by uncertainties in MAB DCOPS position If uncertainties are the same in a given direction (σ quoted as 1mm) Station Approx error ME1 0.7σ ME2 0.8σ ME3 1.0σ ME4 1.1σ 1/2/2019 James N Bellinger UW Madison

Estimated Error in RPhi Projection: Link anchored There are “good” and “fair” uncertainties RPhi has contributions from position and Phi_Z Position: good=0.22μ , fair=210μ Rotation: good=0.014μrad , fair=230μrad Station RPhi err from angle Overall err ME+4 0.3mm 0.33mm ME+3 0.2mm 0.25mm ME+2 0.1mm 0.18mm ME+1 0.01mm 0.15mm ME-1 1.0mm ME-2 1.1mm ME-3 1.2mm ME-4 1.3mm 1/2/2019 James N Bellinger UW Madison

Fits to disk position and rotation All MAB Anchor Stations ME+2 and ME+3 are on the same disk, likewise ME-2 and ME-3 I’d hope the fits would give the same results for the disk positions Station dX (mm) dY (mm) dZ (mrad) ME+4 .37 2.20 0.16 ME+3 1.97 8.23 0.24 ME+2 1.13 6.65 ME+1 0.48 2.62 0.77 ME-1 4.60 1.38 0.79 ME-2 4.45 4.61 -0.004 ME-3 7.09 3.94 0.65 ME-4 4.57 3.51 0.67 1.9mm Poor agreement: >5mm 1/2/2019 James N Bellinger UW Madison

Raw Residuals All MAB Anchor RMS=1.8mm not as good as hoped 1/2/2019 James N Bellinger UW Madison

Residuals vs Station All MAB Anchor Curiosities: Line 1 (black) and 4 (blue) drive most of the RMS. ME+4 and -4 have much tighter distributions! I expect a butterfly shape! 1/2/2019 James N Bellinger UW Madison

Station by Station All MAB Anchor RMS (mm) ME+4 0.84 ME+3 2.56 ME+2 1.91 ME+1 1.95 ME-1 2.23 ME-2 1.23 ME-3 1.74 ME-4 0.67 I expect the distribution to be tighter near the anchored region and grow as you get farther away. We don’t see that. The photogrammetry cannot be that bad, because it was used to reconstruct chamber positions with better precision than this. Even potato-chipping bending of the disk won’t give RPhi shifts of this magnitude 1/2/2019 James N Bellinger UW Madison

Why are the farthest away best? Spread is less than half the average RMS Means are 0 because of fit 1/2/2019 James N Bellinger UW Madison

Repeat Anchoring w/ Link MAB3 1/2/2019 James N Bellinger UW Madison

Fit to Disk Position and Rotation Anchor to the Link Station dX(mm) dY(mm) dRotZ(mrad) ME+4 0.37 2.20 0.16 ME+3 3.39 10.01 0.36 ME+2 2.54 8.43 0.28 ME+1 1.10 4.24 0.78 ME-1 0.72 2.11 0.21 ME-2 -0.94 5.74 -0.69 ME-3 2.77 4.60 0.02 ME-4 -0.25 4.05 -0.02 1.9mm Poor agreement: >6mm Like Slide 25. 1/2/2019 James N Bellinger UW Madison

Difference Between Disk Fit using MAB Anchor and Link Anchor ME+4 is the same?! Plus side much better agreement Minus side systematic shifts Some bias at work Station dX(mm) dY(mm) dRotZ(mrad) ME+4 0. ME+3 1.42 1.87 0.12 ME+2 1.41 1.78 ME+1 0.62 1.62 0.01 ME-1 -3.88 0.73 -0.58 ME-2 -5.39 1.13 -0.69 ME-3 -4.32 0.66 -0.63 ME-4 -4.82 0.54 1/2/2019 James N Bellinger UW Madison

Raw Residuals Link MAB3 Anchor RMS=2.3mm worse than Barrel fit in Slide 26 1/2/2019 James N Bellinger UW Madison

Residuals vs Station Link MAB3 Anchor Compare Slide 27 All but ME+4 have large rms No smoking gun Does not look like predictions in Slide 24 1/2/2019 James N Bellinger UW Madison

Something odd The ME+4 looks the same again Line fit fixes MAB3! Station RMS (mm) 4-MAB Link ME+4 0.84 ME+3 2.56 3.39 ME+2 1.91 2.87 ME+1 1.95 2.73 ME-1 2.23 1.41 ME-2 1.23 1.99 ME-3 1.74 1.62 ME-4 0.67 2.70 The ME+4 looks the same again Line fit fixes MAB3! Repeat dropping bad line? 1/2/2019 James N Bellinger UW Madison

Status Either there has been a substantial blunder in my fit for the disk position, or the projections are not as accurate as they could be. The Link MAB anchor is potentially very accurate, but something, possibly the Minus side measurements, prevents it. The Transfer Line is precise at the .5-.7mm level. Even ME+4, as far as you can get, has RMS of .84mm I cannot demonstrate the accuracy of the predictions to better than a sigma of 1.8mm overall Varies by station Driven by problems in anchoring the lines 1/2/2019 James N Bellinger UW Madison

BACKUP 2 January 2019 James N Bellinger UW Madison

ME+4 – ME-4 Coords VS Phi ME+4 – ME-4 Vertical (radius) and Horizontal (tangent) Clear pattern: YE+3 is shifted wrt YE-3 by O(5.5mm) (Transfer Plate mounting corrections NOT included) 2 January 2019 James N Bellinger UW Madison

YE+3 vs YE+2 ME+4 vs ME+2 Very clearly YE+3 is shifted wrt YE+2 by O(5.1mm) 2 January 2019 James N Bellinger UW Madison

Consistency at/between YE+2 YE-2 Fair agreement YE2 bending: Expect ME3-ME2 radius O(-4): OK variation in horiz O(.2): not dR=-5.7±1.3 dRPhi=-1.2±.9 dR=-3.9±.6 dRPhi=-1.5±.4 PG variation in mounting O(1.5) 2 January 2019 James N Bellinger UW Madison

Calculation I use a Pari/gp script, interpreted by the gp program. Not COCOA I know what it is doing Chi-squared calculation rather than fit Arbitrary precision in matrix inversions Generates relative offsets Fast. I used this for producing the position vs time plots to determine if a MAB fall had caused blockage or whether the floor was sagging. Processing a thousand events took hours—Cocoa would have spent days at it. 2 January 2019 James N Bellinger UW Madison

Data Event from 10-June Barrel event 3981 Almost all Transfer Line stations reproducible! Barrel event 3981 MAB+1/9 does not read out; no position fit Calculations done using tools shown in http://www.hep.wisc.edu/~jnb/cms/25Jul2011/index.html 2 January 2019 James N Bellinger UW Madison

Notes Difference between DCOPS center radius and the local “Vertical” coordinate is at most 12 microns, so I don’t worry about it The local DCOPS coordinate center is taken at the ideal position Positive “Horizontal” coordinate is in the direction of positive phi 2 January 2019 James N Bellinger UW Madison