Signal Processing in DUNE - PowerPoint Presentation

1. Signal Processing in DUNEXin QianBNL1

2. OutlineGeneral Introduction of TPC Signal ProcessingExpected Electronic NoisesExpected Field Response Signal to Noise Ratio vs. Signal LengthSummary2

3. Overview of TPC Signal FormationInduction wire is essential due to lack of amplification and limitations in power consumptionInduction signal strongly depends on the local charge distribution3Number of ionized electronsSignal on Wire PlaneField ResponseSignal to be digitized by ADCElectronics ResponseHigh-level tracking …(Signal Processing)v: velocityEw: weighting fieldqI: charge

4. Example I: ideal track (uniform charge density) Black lines are used to illustrate the wire boundary (+- half wire pitch)4TimeQTimeQeffTaking into account change in response functionTaking into account dynamic induced chargeTimeQeffThis charge is from next wire

5. Now look at the raw signal after convolute with bi-polar signal5TimeQTimeQIn the middle, the raw signal will be close to zero due to cancellation of bipolar response functionTimeQeffTimeQeffIf the signal is rising slowly, the net contribution on the raw digit will be small, however the signal will be longThe induction plane signal can be very small in height  importance of signal processing

6. Example from MicroBooNE Event Displayhttp://www-microboone.fnal.gov/first-neutrinos/run3493_subrun821_event41075_ind0_small.png6Look at this trackA track traveling close to perpendicular to wire planesRaw digits is very smallWe developed a procedure to recover this signal!

7. Trouble with 1-D Deconvolution7Fourier transformationTime domainFrequency domainBack to time domainAnti-Fourier transformation There is NO universal “average” response functionA deconvolution assuming universal response function would lead to gaps in the images which CANNOT be explained by the dead channels Vertex activityEM showerTrack with various angles

8. The Rescue: 2-D Deconvolution8With induced signals, the signal is still linear sum of direct signal and induced signalR1 represents the induced signal from i+1th wire signal to ith wireSi and Si+1 are not directly relatedThe inversion of matrix R can again be done with deconvolution through 2-D FFT

9. Just 2D deconvolution will not be enough  ROI + Adaptive Baseline9The bi-polar nature of induction signal amplify the low-frequency noise during deconvolutionOne can improve the situation through ROI (Bruce Baller, Robert Sulej) and adaptive baseline technique (M. Mooney)Given N time bins with 2 MHz digitization frequency, The highest freq is 1 MHzThe lowest freq (above 0) is 2/N MHz 200 bins  10 kHzObviously not sensitive to noise < 2/N MHzAdaptive baseline  linear baseline correction instead of flat baseline correction

10. DiscussionIt is very difficult to get all the response functions from the dataNeed the dedicated calibration program! (Yichen)The signal processing is to recover the number of ionized electrons from the digitized TPC waveform  in analogy to recover the number of photoelectrons from the digitized PMT waveformIn the following, we use Garfield simulated response function for simulation study10

11. Metrics for Signal ProcessingIn my opinion, there are only two solid metrics can be used to evaluate the noise and signal processing ENC (equivalent noise charge)  basically proportional to the pedestal RMS in terms of ADC Noise level after TPS signal processing (i.e. deconvolution), can be compared with the number of ionized electrons from real signal, it depends on ENC (noise level) Response function used for deconvolution (field response for the real signal)Time window (band width)11

12. Expected NoiseThe ENC’s expectation:At 14 mV/fC and 2 us shaping time, the RMS noise vs. wire length is expected to be RMS (ADC) = (1.019 + 0.00173 * L cm)/1.1The induction wire of DUNE is about 7.3 m, so the RMS level is 2.1 ADC Collection is omitted, since the signal to noise ratio is not a problem12

13. Expected Field ResponseBased on Garfield simulation performed by Yichen0th wireis theclosestwire13

14. Some DetailsNoise calculation (RMS) is based on 2 us (4 ticks) sum of the deconvoluted signalAdaptive baseline is based on average of 8 ticks on each side of the windowWe are going to study the RMS vs. Time window for DUNE14 mV/fC gain and 2 us shaping time14

15. Monte Carlo nu_e signal events for DUNE

16. Simulated Noise Waveform16Time domainADC RMS ~ 2.1Freq (MHz)Noise model in frequency domain2 us shaping time assumed

17. Use the Following “Wiener-like” Deconvolution Filter FunctionsWhen we perform the fit, we have all three parametersTo implement in, set [0] = 1, so that the filter will normalize to 1 For this study, [1] = 0.1589 (MHz), [2] = 5.66617Gaussian filter for the wire, 1-sigma = half wire pitch

18. Simulation ResultSimulate 2000 wiresDo 2D deconvolution18

19. Deconvolution Result19

20. About Adaptive Baseline TechniqueIdentify the signal region (ROI)get the baseline before and after the signal region do a linear correctionSimilar to “local baseline” calculation 20Adaptive baseline technique works better for short signal (i.e. parallel tracks) Need to be careful in how to select the signal region, can lose signal if the algorithm is not robust Also filter out the low frequency noise M. Mooney

21. Preliminary RMS Results21Assuming that we cut at half of the MIP (red line) for the RMS, the time limit is about 350 us If cut at 350 us, 0.999999 vs. 0.999682Need to double check response functions, and software filters … Does it matter? Look at Vertex, gap etc…MIP traveling 3.2 mm

22. Summary2D deconvolution + ROI + adaptive baseline is necessary to deal with the induction plane signalTwo useful metrics: ENC on the raw digitNoise level (or signal to noise ratio) after signal processing (ENC, time window, response functions, filters)22