1. Performance Evaluation of Shintake Monitor (IPBSM) Americas Workshop on Linear Colliders 2014 May 12-16, 2014 Fermilab, IL, USA 12013/07/20 Jacqueline Yan, S. Komamiya, K. Kamiya （ The University of Tokyo ） T.Okugi, T.Terunuma, T.Tauchi, K.Kubo (KEK) AWLC14

2. IPBSM error study is essential for achieving ATF2 Goal 1 ! At the same time, reducing signal jitters/ drifts is important for both stable measurement of σ y < 40 nm and error studies Outline of this talk Recent Beam Time Status IPBSM Performance Evaluation Summary & Goals Introduction Signal Jitters Systematic errors Systematic errors Phase jitter study Phase jitter study real data analysis & simulation AWLC14

3. Beam Time Status AWLC14

4. Spring 2013 10 consecutive scans @174° M 〜 0.3 (S.D. 〜 7 %)  σ y 〜 65 nm smaller after correct for phase jitter (?) Best measurement stability 〜 5% Stable contribution to e- beam focusing and studies (e.g. wakefield effects) ICT : 0.5E9 Apr, 2014 various hardware improvement to improve signal jitters/ drift Tune laser (profile & position/ timing stability) detector collimation Dec 2013 – Mar 2014 Observed improvement in signal fluctuation  enabled effective linear / nonlinear knob tuning at 174 deg mode observed effect from e- beam stabilization (improvement of orbit feedback and tuning knobs) 4/17 ／ 2014, Nav=10 ICT : 0.5E9 early Apr : Consistent measurement of M > 0.3 mid-Apr: Consistent measurement of M > 0.35 (  σy < 61 nm) ( see next page) High M measured at 2-8 deg, 30 deg mode dedicated data taking for IPBSM systematic error studies AWLC14

5. Consistency scans @174 deg mode Again !! higher M and better stability 1 st time: ： 4/9 before knob tuning M = 0.29 +/- 0.04 （ S.D. ） : 15 % measurement stability （ σy = 66 +/- 4 nm (S.D) 2 nd time: 4/10 ( ～ 14 hrs later ） ： after all linear/nonlinear knobs M =0.34 +/-0.02 (S/D. ) 7.2 % stability (σy = 62 +/- 2 nm (S.D) ) 3 rd time: 4/17 (following week ）： after linear/nonlinear knob tuning Improved orbit feedback and tuning knobs M =0.40 +/-0.03 (S/D. ) 7.3 % stability (σy = 57 +/- 2 nm (S.D) ) higher M and better stability Preliminary before error correction M > 0.4 reproduced at peaks of linear / nonlinear knob ex) M : 0.3  0.45 after Y26 knob

6. (1) reinforcement of shielding (Pb and parafine) around detectors (2)Stabilization of electron beam improved tuning multiknobs, orbit feedback showed effect in Apr run (3) speed up DAQ software: 1 Hz  3 Hz : reduced effect from drifts (?) (4) Improved laser profile  Reduce pointing jitter at IP  use iris on laser table to clip fluctuating outer parts of profile (round profile preserved)  Adjust reducer lens setup to reduce multi-component in profile & relax laser focusing 4/18, (30 deg ) 4/11 (174 deg ) focal lens scan  -----  Broad Rayleigh length 〜 4 mm by IPBSM group@ATF2 Relaxed laser focusing What contributed to stabilized measurements in Apr, 2014? Changed lens setup on laser hut table  reduced intensity bias in profile (Mar, 2014) Before After: Rounder profile  laser tuning, filter exchange by Spectra Physics  changed laser Q-SW trigger system  improved buildup and timing stability AWLC14

7. comments Laser pointing jitters (H relative position jitter) observed jitter (CCD) 5-10% of laser profile radius derived “Δx” using laserwire scans : 5 〜 15% of laser radius Phase jitter Δφ (V relative position jitter ) for Δφ = 0.5 rad, M = 0.5 : < 〜 10 %@ peak, < 〜 20%@mid Laser power jitter< 10% from PIN-PD signal Timing jitter 1 – 3 ns peak to peak, add < few % to signal jitters statistical fluctuationsnot certain : could exceed 10% if detector not catching enough photons Other minor factors BG fluctuation< 5 %, (?) recently, not important for recent high S/N e- beam intensity (ICT) monitor resolution Few % Change with beam condition affected by collimator, detector, beam intensity Potential Sources of Signal Jitters observe overall sig jitter in fringe scan 〜 20-40% depend on phase drifts are hard to separate from jitters sometimes Also a M reduction factor Sum up  ΔE/Eavg = 20 – 30 % AWLC14

8. Previous Issues with signal jitter/ drifts & laser profile ( 〜 Mar 2014)  Oscillating Compton signal jitters (period 〜 few min)  pointing jitters seem related to complex internal structure of laser profile at IP non-Gaussian multi- components from Okugi-san ‘s weekly meeting slides fringe scan AWLC14 Apr, 2014: signal jitters reduced (?) but still an issue sometimes 30 deg 174 deg Compare θ dependence : jitters seem slightly more for 174 deg mode (?) Efforts to improvement laser profile & reduce jitters

9. Laser pointing stability : 4/9 from Nav = 50 laserwire scan @174 deg Δx / (laser spot radius) = 12 +/- 7 % AWLC14 Contribution from σx subtracted Assuming Gaussian laserwire profile (but not always so) ICT: 2E9 condition seems relatively stable (improved) in April 2014 However signal jitters/drifts still remains an issue stability varies for different periods 174 deg, Apr vs Mar 2014 Drift of Fitted Initial Phase in 174 deg continuous scans ( 〜 30 min) this drift is convolution may be from laser and/or beam Relative RMS jitter ΔE/E(φ)

10. power jitter < ～ 10% Note: due to sensor size < laser spot size, part of “vertical jitter” may be pointing jitter Timing jitter : 2-3 ns peak to peak Timing and Power Stability PIN-PD @hut Power and Profile Measurements (4/25-30)  Measured spot size and profile  Parallel propagation until final lenses  balanced profiles between U and L paths  Before transport: 2 X original by expander  After transport : 0.75 X original after reducer  Measured laser power at various locations power balance (U/L path) 〜 95% (174 deg mode) loss in transport (laser hut  IP) < 7% laser table round profile hot intensity spots evened out transport to vertical table become only a little oval, but much improved from 2013 AWLC14

11. Study Effect of Vertical Jitters by Simulation [1] assume Gaussian vertical jitters modeled by “C factors” [2] nonlinear instabilities sudden jumps, drifts, oscillating jitters, etc… AWLC14

12. Fitted M Fitting error Range of recent Clinear Effect of Vertical Jitters on fitted M a few % systematic M reduction in typical ranges Effect of Vertical jitters on relative M fitting error (ΔMfit / Mfit) ΔMstat /M < 2 % in typical ranges c.f. real data is affected by all jitter sources together  ΔMstat/M 〜 few % Input : Nav=50, 174 deg, M0 = 0.636, Δφ=0, change 1 C factor at a time, keep others 0 AWLC14 Range of recent Clinear Simulation: Avg of 100 random seeds

13. 相対誤差 は低い M 0 ほど大きい 2: M reduction due to Cstat (statistical fluctuation) small M0 : 4- 6 % error large M0 : < 1 % error 1: sudden intensity decrease(drift) Vertical jitters In this case, M over-evaluation ex) 50% reduction Input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad Depending on the condition, nonlinear fluctuations can cause both under & over evaluation of M Examples of SIMULATION :observe rel. M error = (M fit – M exp ) / M exp 3: periodically oscillating jitters few % M over-evaluation 100%  75%  50%  75%  100% Weak dependence on Nav X axis: Cstat simulation AWLC14

14. Focusing on IPBSM Phase Jitter (Δφ) Simulation Input conditions: σ 0y = 40 nm, M 0 = 0.64, 174 deg mode study of systematic errors (M reduction factors)

15. Error sourceM reduction factor phase jitter (V relative position jitter ) study using simulation and analyze actual data Fringe tilt (z, t) Optimization by “tilt scan” Laser polarization polarization measured  optimize by “λ / 2 plate scan ” Misalignment Laser profile shot-by-shot non-Gaussian fluctuation of laser profile  sometimes observe 10-20% M reduction Phase drift Negligible during typical beam tuning if drift is linear and < 100 mrad/min maybe coupled with laser position drift / jitters, e- beam drift AWLC14 Details coming up Systematic errors ： M reduction Factor σ y over evalution M under-evaluation Priority is to resolve signal jitters / drifts (  enable precise evaluation of M reduction factors) dominant

16. Before: fitted M 16 After correction Phase jitter Δφ (relative position jitter Δy) (relative position jitter Δy) Hard to separate phase jitter from e- beam jitter and vertical jitters conditions change over time (example) (example) if Δφ = 400 mrad, CΔφ 〜 90.5 % if Δφ = 400 mrad, CΔφ 〜 90.5 % σ y0 = 40 nm  σ y,meas = 44 nm σ y0 = 40 nm  σ y,meas = 44 nm Δφ  M reduction M reduction from Δφ Δφ [rad] Horizontal jitters Small σy* especially sensitive !! we have developed a method for extracting Δφ AWLC14 M is corrected almost back to nominal using extracted Δφ simulation Δφ [rad] simulation M 0 = 0.636 σ y0 = 40 nm M corr = M meas / C Δφ simulation

17. Study of Systematic errors of measured Modulation for now, take into account : phase jitter Δφ DOMINANT (?) extracted from fringe scan (details coming up) alignment issues (position, profile) from laserwire scan / zscan / pointing jitter analysis Important to demonstrate reliability of Δφ extraction method demonstrated acceptable precision under certain “realistic” (?) conditions (see past slides for LCWS & ATF2 project Meeting) tested limit of “unknown factors” using simulation limitations from model which assumes Gaussian distr. of Δφ and vertical jitters effect from nonlinear instabilities, drifts & jumps coupling from other instability sources tested method by inputted real measured phase jitters into simulation Dedicated beam time data for study of Δφ was analyzed Results from recent 174 deg continuous scans (preliminary, need confirmation)  Apr 9-10 : about 10 nm systematic error on σy  Apr 17 : < 〜 10 nm systematic error on σy errors reduced due to improved beam stability (?) Potential Causes for phase jitter  Pointing stability: angular/ pos jitter when injecting into half-mirror, mirror vibrations  electron beam jitter (ΔΦ is convolution of laser and e beam) c.f. Fringe scan piezo jitter is checked : not an issue at present AWLC14

18. Study of IPBSM Phase Jitter Tested Method using Simulation Input conditions: σ 0y = 40 nm, M 0 = 0.64, 174 deg mode

19. test Δφ extraction precision using simulation fix {M,φ 0, E avg, C const, C sta t} to jitter plot signal jitter vs phase STEP1: generate fringe scan try to assume “realistic” ATF2 conditions fringe scan vertical jitter Jitter from Δφ Model AWLC14 Signal energy vs phase Input vertical jitters input: σ y0 = 40 nm, 174°mode Δφ = 0.7 mrad, 24.5 % vertical jitter simulation Δφ input Δφ, Clinear (2 free parameters) fixed parameters:  M, φ 0, E avg : from STEP 1  Cconst, Cstat: estimated (slight uncertainties are negligible) STEP2: extract Δφ from fitting

20. Rms spread is larger for a smaller Nav Nav = 20 vs Nav = 50 Simulation Avg and rms of 100 random seeds In typical Δφ region (0.4-0.7 rad) Δφ error < 〜 3%  1% error for M [2] Distribution of extracted phase jitter X: seed number Y: extracted Δφ error < 〜 7% for single scan better if average over multiple scans large Nav scans are preferred for Δφ study Assume a “relaistic” ATF2 condition Input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=50, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 590 rad Simulation [1] Precision of extracted phase jitter X: input ΔΦ Y: extracted Δφ AWLC14

21. Mean : 1.77 +/- 0.035 Δφ_real RMS = 0.448 rad data read out in 3 Hz (0.33 sec) intervals Reproduced Δφ measured using phase monitor by T. Yamanaka in 2009 (beam off, old IPBSM laser) Δφreal RMS = 0.448 rad Consistent with Yamanaka-M thesis Δφrms (real) = 0.448 rad 1. Input “Δφ_real” into fringe scan simulation 2. used my method to extract Δφ_out Extracted results: Δφ_out = 0.45 +/- 0.06 (rms) close to Δφ_real RMS OK even if move large jitters to beginning of scan next, inputted “slow linear drift “ OK if drift < 150 mrad/ min (similar to real drift) precision worsen if bigger drift (> 240 mrad/min) avg and rms of 100 random seeds OK even if Cstat gets large M_meas is affected by nonlinear drifts, may be reduced more than expected from a Gaussian Δφ Effect depends on location / length of drift : too complicated to model Extracted results for ΔΦ Input: M0 = 0.64, σy0 = 40 nm, 174 deg Clinear = 0.25, Cconst = 0.05,

22. AWLC14 Analysis of Δφ from real data

23. Phase Jitter @ 174 deg Using Nav=50 scans example: 4/10 4/10 : Δφ=0.85 +/- 0.06 rad Clinear = 0.15 +/- 0.03 4/17 : Δφ=0.67 +/- 0.04 rad Clinear = 0.11 +/- 0.03 M plot RMS jitter plot Decrease in Δφ reflect improvement of orbit stability (feedback) ?? AWLC14

24. History of Phase Jitter in 2014 Mar 2014 Jan – Feb, 2014 AWLC14 Apr, 2014, 30 deg Apri, 2014 2-8, 30 ° mode ： generally Δφ = 200 - 600 mrad regardless of vertical jitters 174 ° mode: generally Δφ = 600 – 850 mrad 174 ° ： σy, meas < 65 nm  -- 2-8°, 30 ° : larger σy --  RECENT Δφ very different for 30 deg and 174 deg Δy / σymeas similar for 30 and 174 deg (50-60%)  Indicate e beam jitter is dominant ?? phase jitter Δφ  relative position jitter Δy Convolution of laser and e beam : difficult to separate at present We won’t know unless we have independent measurement of e- beam jitter !! anticipate results from IPBPM

25. 174 degMmeas(174) 0.29 +/-0.01  σmeas = 66+/- 1 nm Ctot(174)> 0.66 Mcorr0.44 +/-0.02 30 degMmeas(30)0.77+/-0.01  σmeas = 81+/- 2 nm Mexp0.82+/-0.01 Ctot,exp0.93+/-0.01 ---------------- Ctot(30)>0.94 using data immediately before / after mode switching (174  30°) Difference in ΔΦ maybe due to : Effect of laser pointing jitter : path length after 50% beamsplitter is longer for 174 °than 30 ° Effect of electron beam jitter Characteristics of data taken in Apr 2014: stability and jitters improved in Apr, 2014 that’s why this study is possible !! total M reduction for 30 °, (esp Δφ) is less than before etc…… total M reduction compared to 174 °results Ctot, exp and Ctot(30) consistent, almost no residual M reduction ??!! from Δφ (dominant) and alignment M reduction derived independently using 30 deg data only from Δφ and alignment Dedicated study of “fringe Contrast” = total M reduction factor “ Ctot” AWLC14  σcorr = 54+/- 1 nm

26. stable measurement and offline error study of IPBSM must go hand in hand in order to achieve ATF’s Goal 1 Summary  multiple sets of continuous scans ＠ 174° in Apr, 2013  M 〜 0.3 before multiknob tuning @174°  effective implementation of linear/non-linear knobs  reproducibility of M > 0.4 e.g. 4/17 : 11 scans M = 0.40 +/- 0.03 (S.D.) 〜 7 % measurement stability  more stable performance after reduction of signal jitters / drifts by Terunuma-san and Okugi-san σy measurement status also reflects improvement of e- beam stabilization and tuning methods Dedicated beam time for IPBSM systematic error studies preliminary analysis conducted (reliability of method need confirmation ) Phase jitter ΔΦ may be dominant M reduction factor, 〜 10 nm systematic error(?) to σy@174° Δφ show some θ dependence  maybe explained by laser pointing jitters and e beam jitter simulation study on effect of vertical jitters, jumps, oscillating jitters AWLC14

27. Plans Continue to identify and suppress sources for jitters / drifts essential for ATF2 Goal 1 Personal tasks: analyze data to evaluate effect of hardware upgrades Use simulation to study the effect on M meas and error analysis precision from various instabilities Improve precision of error analysis Final Goal: evaluate precise systematic error for measured σy will be summarized in J.Y’s D thesis ( 〜 Jan 2015) based on σy measurement @ 174° in Apr 9-17 study of jitters/ drifts and M reduction factors (simulation & real data analysis) TIPP2014 (Jun 2-6) : talk on IPBSM performance peer-reviewed proceedings will be published by Proceedings of Science ( 〜 6/20) will quote beam size results from Kubo-san’s IPAC proceedings This priority should be achieved for precise M reduction evaluation

28. BACKUP SLIDES AWLC14

29. N + N - [rad] N: no. of Compton photons Convolution between e- beam profile and fringe intensity Focused Beam ： large M Dilluted Beam ： small M Small σ y Large σ y 29 Detector measures signal Modulation Depth “M” measurable range determined by fringe pitch depend on crossing angle θ (and λ ) AWLC14

30. Crossing angle θ 174°30°8°2° Fringe pitch 266 nm1.03 μm3.81 μm15.2 μm Lower limit20 nm70 nm170 nm700 nm Upper limit90 nm340 nm1.3 μm5.2 μm AWLC14 σ y and M σ y and M for each θ mode select appropriate mode according to beam focusing Measures σ y * = 20 nm 〜 few μm with < 10% resolution Expected Performance

31. almost no M reduction due to polarization Polarization Measurement P contamination : P p /P s < 1.5 % Set-up IPBSM optics designed for linear S polarization Also measured “half mirror” reflective properties Rs = 50.3 %, Rp = 20.1 %  match catalogue value half mirror power ratio confirmed “S peaks” maximize M Beamtime ： “λ/2 plate scan S peaks” also yields best power balance between 2 paths !! AWLC14 #2 Rotate λ/2 plate angle [deg]

32. AWLC14 Other IPBSM Data “tilt scan” confirm (almost) no M reduction from relative tilt between fringe and beam tilt scan takes very long time (few hrs) effected by rifts not sure if this represent condition at time of actual beam size measurement should not have been much M reduction due to fringe tilt 0 deg: S peak 45 deg: P peak 90 deg: S peak pitch roll Ex) if ΔΦ = 3 mrad, 〜 7 nm to σy (for σy0=60 nm)

33. Change in Status of IPBSM Signal Jitters /Drifts X: fringe scan phase Y: relative signal jitter = (rms jitter) / (energy) at each phase 174 deg mode data, Apr vs Mar 2014 30 deg mode data, Apr vs Mar 2014 However signal jitters/drifts still remains an issue stability varies for different periods Drift of Fitted Initial Phase During 174 deg mode continuous scans ( 〜 30 min) this drift is convolution may be from laser and/or beam condition seems relatively stable (improved) in April 2014 AWLC14

34. Fitted M Fitting error Range of recent Clinear Effect of Vertical Jitters on fitted M a few % systematic M reduction in typical ranges Effect of Vertical jitters on relative M fitting error (ΔMfit / Mfit) ΔMstat /M < 2.5 % in typical ranges c.f. real data is affected by all jitter sources together  ΔMstat/M 〜 few % AWLC14 Range of recent Clinear Simulation: Avg of 100 random seeds Input : Nav=50, 174 deg, M0 = 0.636, Δφ=0, change 1 C factor at a time, keep others to default : Cconst = 0.05, Cstat = 0.15,Clinear= 0.25

35. M reduction due to phase jitter x: axis: input Δφ (0 – 0.9 rad ) y axis: fitted M Nav = 10 has bias small Nav shows larger bias Should take Nav > 50 data for “final” measurements if evaluate syst error using extracted Δφ Simulation: Mean & RMS (S.D.) of 100 random seeds M reduction due to Δφ Avg and rms of 100 random seeds Systematic from vertical jitters worse systematics for very small Δφ because dominated by vertical jitters Input : M0 = 0.636, Nav=10, 174 deg mode, Cconst = 0.05, Cstat=0.15, Clinear=0.25 AWLC14

36. compare relative signal jitter of Apr 9, 2014 with Mar 2014 (blue) Recent condition at least as stable as last year Mar 2013 (??) many setups have changed within this year Apr 9, 2014 Mar 11, 2014

37. Looking at fringe scans (Nav=10,20,50) 2/5 – 2/6, 2014 AWLC14 2/6/ 2014 30 deg 2/20 / 2014 6.9, 30 deg, Nav-50 2/27/2014 5.3 deg 2/25/ 2014 5.3 deg overall signal jitter in 2-8 deg, 30 deg deg mode for Cherenkov

38. AWLC14 Systematics on Mmeas, Cstat Nav=20, 50 Δφ = 0 effect is slightly stronger for smaller Nav 〜 5 % systematics from vertical jitters (under-evaluation) Change Cstat (Cconst = 0.05, Clinear = 0.25) Nav=50 Nav=20 Fitted M Range of recent Clinear Effect of Clinear on fitted M < 5 % systematic M reduction expected from Clinear Input : 100 random seeds, Nav=10, 174 deg mode, M0 = 0.636, Cconst = 0.05, Cstat = 0.1, Δφ = 470 mrad

39. Mistaken evaluation of Δφ Input Δφ = 0 If Cstat < 20%, : < 100 mrad pushed to Δφ Change Cstat (Cconst = 0.05, Clinear = 0.25) AWLC14

40. average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad Fitted Modulation Jitter period 〜 few min  close to length of fringe scan type 1: light case: normal  85%  65%  85%  normal type 2: heavy case: normal  75%  50%  75%  normal Try to imitate oscillating jitters M plot RMS jitter plot to get Δφ 25% decrease 50% decrease Few % systematics weak dependence on Nav M expected AWLC14

41. Assume Comp. signal intensity suddenly decrease @ 7 – 17 rad (drift ?) Include 2 valleys, jump range < 〜 4π Input : M0 = 0.636, Nav=10, 174 deg mode, Δφ = 470 mrad, Clinear = 0.3, Cstat = 0.1, Cconst = 0.05 Simulation :100 random seeds Over evaluation of M in this particular case Actually we can tell from the large chi^2 / ndf ?? Fitted M, Nav=10 Fitted M, Nav=50 M expected from Δφ Sudden decrease E’ / E = 0.5 AWLC14

42. input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad If fix Cstat as real (input) Cstat average and rms/sqrt(100) of 100 random seeds Δφ is under-evaluated if fix too large Cstat ex) if real Cstat is 0.15, but Cstat fixed to 0.07, about 10% over- evaluation of Δφ real (input) Cstat is 0.07 Δφ is over-evaluated if fixed Cstat is too small 0.07 even if real (input) Cstat is larger Δφ extraction precision looks good

43. average and rms/sqrt(100) of 100 random seeds input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25,Cstat = 0.10, Cconst = 0.05, Δφ = 0. 588 rad Jitter period 〜 few min  close to length of fringe scan type 1: light case: normal  85%  65%  85%  normal type 2: heavy case: normal  75%  50%  75%  normal Try to imitate oscillating jitters AWLC14 Extracted Δφ Extracted Clinear Δφ extraction not much affected in this particular case (?) Clinear is over-evaluated

44. Beam intensity about 0.5E9 Signal trend: Cherenkov (top) vs CsI (bottom), during Zscan At low beam intensity, smaller jitter for CsI than Cherenkov Cherenkov mainly dominated by statistic errors i.e. Amount of Compton signal - better fitting and smaller ΔMsyst for CsI, esp for smaller M at 174 deg mode AWLC14

45. actual data (blue) Nav = 20 fringe scan(Mar 11 2014) @ 174 deg mode RMS signal jitter (green) vs Energy at each phase Sig jitter due to phase jitter (red) is larger at fringe mid point and smaller at fringe peak (compare with bottom plot)

46. AWLC14 Include slow linear drift over long time scale Input : M0 = 0.64, σy0 = 40 nm, 174 deg Clinear = 0.25, Cstat = 0.15, Cconst = 0.05 Reproduced CH1 data Read out in 3 Hz (0.33 sec) intervals Δφmeasured by T. Yamanaka in 2009 Using phase monitor (beam off, old laser)

47. AWLC14 input: M0 = 0.64, σy0 = 40 nm, 174 deg mode, Nav=20, Clinear = 0.25, Cconst = 0.05, Δφ = 0. 588 rad If fix Cstat as real (input) Cstat average and rms/sqrt(100) of 100 random seeds Clinear is under-evaluated if fix too large Cstat Clinear is over-evaluated if Cstat is fixed to a too small 0.07 even if real (input) Cstat is larger

48. AWLC14 Very large & consistent M,meas before switching to 30 deg  M reduction studies Nav=5 Nav=10 Nav=50 summary of consistency scan140220_221459 dataMΔφClinearNav 2214590.925 5 2217360.8420.350.2310 2221190.9250.270.2310 2224590.8420.420.2650 Avg0.880.350.24 ERR=STD/ sqrt(N-1)0.030.050.01 summary of consistency scan140220_221459 dataMΔφClinearNav 351000.7610.5490.1750 408320.8480.340.2250 418490.7760.510.1750 Avg0.800.470.19 ERR=STD/ sqrt(N-1)0.030.080.02 2/20, 6.9 deg, M = 0.88 /- 0.03 2/27 5.3 deg, M = 0.80 /- 0.03 All are Nav=50

49. Δφ Nav = 10 Clinear Nav = 100 Clinear Nav = 10 Δφ Nav = 100 Simulation test : Mean & RMS (S.D.) of 100 random seeds Little systematics on fitted center value RMS increase for large Δφ and small Nav Input Clinear = 0.23 AWLC14

50. Proposal by Kubo-san on more accurate fitting function for signal jitters before, I used just E = Eavg*(1+ M*cos(φ+φ0)) Vertical jitters Signal jitter due to phase jitter Convolution of phase jitter and vertical jitters AWLC14