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More on Apodization Effects on MSE Analysis

More on Apodization Effects on MSE Analysis. S. D. Scott, H. Yuh, R. Grantez 19 May 2003 Thanks to Donald Nelson for PowerPoint XP!. Note : This presentation is best viewed with PowerPoint 2002 or later. Magnitudes of Apodization Errors.

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More on Apodization Effects on MSE Analysis

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  1. More on Apodization Effects on MSE Analysis S. D. Scott, H. Yuh, R. Grantez 19 May 2003 Thanks to Donald Nelson for PowerPoint XP! Note: This presentation is best viewed with PowerPoint 2002 or later

  2. Magnitudes of Apodization Errors • Term #2 results from the beat of PEM#1 and #2. It can be eliminated by choosing • a time window with a duration equal to an integral number of periods of the beat • waveform. • Term #4 results from multiplying a “constant” noise source N by a rectifying sine • wave at w1. It can be eliminated by ‘zero-centering’ the data, i.e. subtracting • a constant value from each datum within a given integration window so the average • value is zero. • All of the terms should decrease if we apply a Hanning weighting function that • reduces the contribution of the ‘edges’ to the integration window. • Effect on measured angle: Dq = 14.3oD(A2/A1). So a 1% error in each of A1 and A2 • would generate an error = 0.20o.

  3. ‘Zero-centering’ the data does reduce the FFTamplitude at the PEM drive frequency(arising from unpolarized background light) no zero-centering factor ~25 reduction FFT amplitude zero-centering • Shot 1021016025 (nebar = 1.6-2.0 e10) • MSE channel 3 (3rd or 4th from outer edge) • I don’t know why the reduction isn’t bigger – maybe due to width of the FFT feature ??

  4. Fourier components of MSE signal * sin(40, 44 kHz) * sin(40 kHz) * sin(44 kHz) FFT amplitude of MSE signal * sin (40 or 44 kHz) • Zero-centered data. • Note the extra lobes at 2, 4, 6, and 8 kHz offset

  5. Fourier components of MSE signal * sin(40, 44 kHz) * sin(40 kHz) * sin(44 kHz) FFT amplitude of MSE signal * sin (40 or 44 kHz) Note the extra lobes at 2, 4, 6, and 8 kHz offset

  6. Fourier components of MSE signal * sin(40, 44 kHz) * sin(44 kHz) FFT amplitude of MSE signal * sin (40 or 44 kHz) * sin(40 kHz) ? ? w1 – w2 • Zero-centered data and Dt = 4.5 ms (no special selection of time window).

  7. MSE degrees Shots: 1030502 [020, 022, 023, 024] 4.5 ms time bins (data), 10 ms for noise Std Deviation of Angle over Time Bins • Time bins not a multiple of PEM beat. • Hanning weighting is OFF zero centering = OFF zero-centering = ON This is the expected behavior … zero-centering improves the scatter in time.

  8. Statistical Uncertainty in MSE Angle is 0.02-0.06 degreesfor gas-only calibration shots 0.06 degrees 0.02 degrees • Zero-center the data but no apodization or Hanning weighting. • 4 ms time bins during DNB, 10-20 ms for pre/post-beam noise measurement • Measure standard deviation, s, of angles over N time periods • Reported uncertainty in mean angle = s / sqrt(N). • Reported uncertainty is in frame of polarimeter. Uncertainty in field-line pitch • is larger by geometric factor 4-5 at the plasma edge.

  9. Statistical Uncertainty in MSE Angle is 0.03-0.10 degreesat nebar = 1.0 1020 m-3 1030502020 1030502022 1030502023 1030502024 0.10 degrees 0.03 degrees • Zero-center the data but no apodization or Hanning weighting. • 4 ms time bins during DNB, 10-20 ms for pre/post-beam noise measurement • Measure standard deviation, s, of angles over N time periods • Reported uncertainty in mean angle = s / sqrt(N). • Reported uncertainty is in frame of polarimeter. Uncertainty in field-line pitch • is larger by geometric factor 4-5 at the plasma edge.

  10. Statistical Uncertainty in MSE Angle is 0.05-0.15 degreesfor r/a > 0.5 at nebar = 1.6-2.0 1020 m-3 Uncertainty in Mean 1021016025 1021016028 1021016029 Shot-shot scatter 0.15 degrees 0.05 degrees • Worse at edge. Terrible at center (presumably due to beam attenuation). • Zero-center the data but no apodization or Hanning weighting. • 4 ms time bins during DNB, 10-20 ms for pre/post-beam noise measurement • Measure standard deviation, s, of angles over N time periods • Reported uncertainty in mean angle = s / sqrt(N). • Reported uncertainty is in frame of polarimeter. Uncertainty in field-line pitch • is larger by geometric factor 4-5 at the plasma edge.

  11. Statistical Uncertainty Scales As Expected with Length of Time Bin Scatter decreases as time bins get longer But uncetainty in mean Angle remains constant • Vary the time binning from 1 ms to 20 ms (overlapping windows) • Zero-center the data. • Compute standard deviation of measured angle over all time bins, s (top graph). • Compute uncertainty in average angle = s/sqrt(N) (bottom graph)

  12. Shot-Shot Scatter is Somewhat Larger than EstimatedUncertainty in Mean Angle D(angle), Shot 1021004016-017 Uncertainty in mean, 017 Uncertainty in mean, 016 Fibers removed • The uncertainty-of-the-mean angle ascertained from the variation of several • time points within a single shot should equal the shot-shot variation.

  13. Same result on other calibration shots in the October 2002 Calibration Run: Shot-Shot Scatter is Somewhat Larger than Estimated Uncertainty in Mean Angle D(angle) shot 1021004003 - 004 Uncertainty in mean shot 004 Uncertainty in mean shot 003

  14. Shots: 1030502 [020, 022, 023, 024] 4.5 ms time bins (data), 10 ms for noise Std Deviation of Angle over Time Bins No zero-centering No hanning weighting Time window = integral multiple of PEM beat waveform Time window not a multiple of PEM beat waveform Why does the scatter increase when we “properly” choose the time bin?

  15. Shots: 1030502 [020, 022, 023, 024] 4.5 ms time bins (data), 10 ms for noise Std Deviation of Angle over Time Bins No zero-centering No special selection of time bins Hanning weighting is OFF Hanning weighting is ON This is the expected behavior … imposing the hanning window reduces the scatter.

  16. Shots: 1030502 [020, 022, 023, 024] 4.5 ms time bins (data), 10 ms for noise Std Deviation of Angle over Time Bins Hanning weighting = off Time window = multiple of PEM beat waveform, but no zero-centering Time window not a multiple of PEM beat waveform. Zero centering turned ON.

  17. Shots: 1030502 [020, 022, 023, 024] 4.5 ms time bins (data), 10 ms for noise Std Deviation of Angle over Time Bins “The works”: Zero centering = ON time bin = multiple of PEM beat hanning weighting = ON “center only”: zero centering = ON time bin = not a multiple of PEM beat hanning weighting = OFF This is a problem … in general, the scatter Is larger when we turn on all “improvments”

  18. Std Deviation of Angle over Time Bins Nothing: no centering, no hanning, no special time binning Window: no centering, no hanning, but time bins = integral multiple of PEM beat Center: centering=ON, no hanning, no special time binning Hanning: no centering, hanning=ON, no special time binning Standard: centering=ON, no hanning, time bins = multiple of PEM beat All: centering=ON, hanning=ON, time bins = multiple of PEM beat

  19. Shot-to-Shot scatter 0.6 Nothing: no centering, no hanning, no special time binning Window: no centering, no hanning, but time bins = integral multiple of PEM beat Center: centering=ON, no hanning, no special time binning Hanning: no centering, hanning=ON, no special time binning Standard: centering=ON, no hanning, time bins = multiple of PEM beat All: centering=ON, hanning=ON, time bins = multiple of PEM beat 0.02

  20. Selecting integration window to remove effect ofPEM beat waveform does not eliminate the observed scatter of measured angle in time. • 4 ms time windows, overlapping. • Analysis did not apply zero-centering. • Analysis did choose integration time = integral multiple of beat period. • Shot 1030502020 • Channels 3-7

  21. Slides from last week Summary Removing apodization effects in the MSE analysis substantilly improves the shot-to-shot statistical measurement of the raw MSE angle The analysis technique also removes the spurious oscillation in apparent angle versus time.

  22. Comments on Apodization correction • Howard has developed a different approach to dealing with the apodization problem – qualitatively looks the same. • In first set of shots examined, scatter is about 0.1 degrees. • The error in field-line pitch angle will be larger by a geometrical factor approaching 5 at the edge. • It may be possible to recover shots from last run period – apodization rather than mirror movement may have been responsible for shot-shot scatter. • We haven’t necessarily optimized the treatment of the apodization effect – might gain something by applying Hanning function prior to FFT.

  23. Selecting an integration interval that matches the beat period of the 40 and 44 kHz PEM drive substantially reduces the time scatter in Measured pitch-angle direction Old analysis New analysis

  24. Set of Nearly Identical Shots on May 2: same Ip within 1 kA

  25. Actual scatter on these shots is 0.1-0.2 degrees over most of the profle Each curve represents the Measured profile for a single shot (obtained by averaging the profile Over about 10 4.5 ms time bins).

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